Measurement of Charm and Beauty Cross Sections in Photoproduction using Events with Muons and Dijets at HERA

Transcription

1 Measuremen of Charm and Beauy Cross Secions in Phooproducion using Evens wih Muons and Dijes a HERA Disseraion zur Erlangung des Dokorgrades des Deparmen Physik der Universiä Hamburg Vorgeleg von Mira Krämer aus Engelskirchen Hamburg 29

2 ii Guacher der Disseraion: Guacher der Dispuaion: Prof. Dr. Rober Klanner PD Dr. Andreas Meyer Prof. Dr. Rober Klanner PD Dr. Olaf Behnke Daum der Dispuaion: 23. Juli 29 Vorsizender des Prüfungsausschusses: Vorsizender des Promoionsausschusses: Dekan der MIN Fakulä: Leier des Deparmen Physik: Prof. Dr. Dieer Horns Prof. Dr. Rober Klanner Prof. Dr. Heinrich Graener Prof. Dr. Joachim Barels

3 Absrac A measuremen of open charm and beauy cross secions in phooproducion using dije evens conaining a muon a he ep collider HERA is presened. The analysed daa are colleced wih he H deecor in he years 26 and 27, corresponding o an inegraed luminosiy of 79 pb. Evens are seleced, which conain a leas wo jes wih ransverse momena of p je(2) > 7(6) GeV in he pseudorapidiy region 2.5 <η je(2) < 2.5. Amuonwiha minimal ransverse momenum of p µ > 2.5 GeV in he pseudorapidiy range.3 <ηµ <.5 is required. The muon is associaed o one of he wo seleced jes. The mehod used o deermine he fracion of evens conaining charm or beauy is based on he ransverse momenum of he muon relaive o is associaed je and he impac parameer of he muon rack wih respec o he primary verex. Differenial cross secions for charm and beauy are measured as a funcion of he ransverse momenum of he muon, he pseudorapidiy of he muon, he ransverse momenum of he highes p je, he azimuhal angular separaion of he wo seleced jes and he observable x obs γ. Double differenial cross secions for charm and beauy are measured in he region of direc and resolved processes. Kurzfassung Ziel dieser Analyse is die Messung von Charm und Beauy Wirkungsquerschnien in ep Kollisionen bei HERA. Die Messung erfolg im kinemaischen Bereich der Phooprodukion mi Hilfe von Zweije-Ereignissen, die ein Myon beinhalen. Die analysieren Daen wurden mi dem H Deekor in den Jahren 26 und 27 aufgezeichne. Die zur Verfügung sehende inegriere Luminosiä beräg 79 pb. Es werden Ereignisse selekier, die mindesens zwei Jes mi einem minimalen Transversalimpuls von p je(2) > 7(6) GeV im Rapidiäsbereich 2.5 <η je(2) < 2.5 aufweisen. Ein Myon mi einem Transversalimpuls von mindesens p µ > 2.5 GeV im Rapidiäsbereich.3 <ηµ <.5 wirdzusäzlich geforder. Dieses Myon wird einem der beiden Jes mi den höchsen Transversalimpulsen zugeordne. Die hier verwendee Mehode zur Besimmung des Aneils von Ereignissen mi Charm und Beauy Kandidaen beruh zum einen auf dem relaiven Transversalimpuls des Myons zu dem ihm zugeordneen Je und zum anderen auf dem Soßparameer der Myonspur in Bezug auf den Primärverex. Differenielle Wirkungsquerschnie von Charm und Beauy werden als Funkion des Transversalimpulses des Myons, seiner Pseudorapidiä, dem Transversalimpuls des führenden Jes, dem azimualen Winkel zwischen den beiden selekieren Jes, sowie der Observablen x obs γ besimm. Zusäzlich werden doppel differenielle Wirkungsquerschnie für Charm und Beauy in direken und aufgelösen Prozessen gemessen.

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5 Conens Inroducion 2 Heavy Quark Phooproducion 5 2. Quanum Chromodynamics Descripion of ep Scaering Proon Srucure Quark Paron Model Facorizaion Theorem and Srucure Funcions Paron Evoluion Models Heavy Quark Producion QCD Calculaion Schemes Fragmenaion Mone Carlo Even Generaors QCD Predicions Properies of Charm and Beauy Hadrons Recen Resuls of Heavy Quark Producion The Experimen 3 3. The HERA Acceleraor The H Deecor Tracking Deecors Calorimery Muon Sysem Triggering a H Even Reconsrucion Muon Idenificaion and Reconsrucion Impac Parameer Track Reconsrucion CST improved Tracks Primary Verex Reconsrucion Tuning of he CST Simulaion Resoluions v

6 vi CONTENTS 4.5 Reconsrucion of he Hadronic Final Sae Je Reconsrucion Calibraion of he Hadronic Final Sae Trigger Elemens and heir Efficiencies Even Selecion Daa Sample Heavy Quark Selecion in Phooproducion Kinemaic Selecion Muon Selecion Je Selecion Background Sudies Dije Even Observables Reconsruced and Generaed Variables Resoluions and Correlaions Puriy and Sabiliy Reconsrucion Efficiency Quark Flavour Separaion Separaion Mehods The Mass Mehod The Lifeime Mehod Fiing Procedure Sabiliy and Consisency of he Fi Combined Fi Resuls Cross Secion Measuremen 3 7. Sysemaic Uncerainies Cross Secion Definiion Charm and Beauy Dije Muon Cross Secions Differenial Cross Secions Differenial Cross Secions in wo x obs γ regions Discussion Conclusions 25 A Daa Tables 27 B Fi Resuls 4

7 Chaper Inroducion The idea ha all maer is composed of fundamenal building blocks was firs conceived of by Greek philosophers such as Democrius and Leucippus, more han wo housand years ago. This idea remained unesed unil he 2h cenury. In he beginning of he 9s, experimens o invesigae subaomic srucures were performed and led o he developmen of physical models such as he Ruherford model. In he 95s, he invenion of bubble chambers and spark chambers revoluionised elemenary paricle physics. A large number of hadrons and heir resonances were discovered. Since physiciss prefer he idea of fundamenal paricles, hey began immediaely o classify he discovered paricle zoo. In 963, he quark model was inroduced independenly by Murray Gell-Mann and George Zweig. Here, he hadrons can be classified as combinaions of quark-aniquark pairs, which are called mesons, or as combinaions of hree quarks, he baryons. A his ime, only hree quarks were known, namely he up, down and srange quarks. In he years o follow, hree furher quark flavours - beauy, charm and op - were inroduced o solve inconsisencies of he developing heory. The experimenal evidences of he new quarks were found several years laer. The charm quark was discovered in 974 by wo groups independenly: by he group around Samuel C. C. Ting in Brookhaven and Buron Richer in Sanford. Three years laer, in 977, he experimen E288 a Fermilab discovered he beauy quark. Finally, he op quark was discovered in 995 by he experimens CDF and D a Fermilab. The force beween he quarks can be described by srong ineracions. The mos acceped heory of srong ineracions, namely Quanum Chromodynamics (QCD), is an imporan par of he Sandard Model of paricle physics. The srong ineracion is one of he four fundamenal forces and describes he ineracion beween he quarks via he exchange of gluons, he gauge bosons of he srong ineracion. The quark and gluons carry colour and inerac wih each oher. The gluons can also inerac wih oher gluons, which can be explained heoreically by he non-abelian colour symmery group, which is he basis of QCD. This leads o a running srong coupling consan α s, which decreases wih he energy scale and increases wih he disance, causing he principle of colour confinemen. Due o confinemen, quarks canno be observed direcly, bu only hrough hadronisaion. Their experimenal observaion is herefore based on he invesigaion of jes, which consis of colour-neural hadrons. The elecron proon collisions a HERA provide an opporuniy o sudy he srucure of he

8 2 CHAPTER. INTRODUCTION proon as well as he properies of srong ineracions. Due o he running of α s, he energy scale a which α s is evaluaed plays a crucial role in QCD calculaions. A HERA, several hard scales are relevan, for example he virualiy of he phoon Q 2, ransverse momenum p and he mass m q of he quarks. This muli-scale problem complicaes he siuaion, since he perurbaive expansion canno be opimized for all scales a once. The simulaneous occurrence of scales in he same heavy quark producion process allows imporan insighs ino he naure of QCD and especially furher invesigaions of he calculaion schemes. The resuls obained a HERA are crucial for he developmen of QCD heories as well as for he upcoming LHC projec, where proon proon collisions are sudied. A LHC, he main background o he signals from expeced new physics will be heavy flavour physics including jes. To obain clear signals, he background needs o be undersood very well. Recen analyses a HERA and oher colliders show ha charm and beauy producion is in general reasonably well undersood. QCD NLO calculaions are able o predic he measuremen in mos of he disribuions, bu in some regions, e.g. for resolved processes, furher invesigaions are needed o improve he heory as well as o reduce he experimenal uncerainies. In his analysis, a measuremen of charm and beauy dije muon cross secions in phooproducion using HERA II daa is performed. The aim of his analysis is o conribue o he presen undersanding of heavy quark producion by invesigaing he exclusive final sae. The increase in he amoun of daa colleced by a facor of 3.5 compared o he HERA I analyses, provides no only significan improvemens of he saisical precision, bu also a beer undersanding of he H deecor. The beauy cross secions are measured in an exended phase space compared o previous resuls. For he firs ime, charm dije muon cross secions are deermined simulaneously. In addiion, he charm and beauy cross secions are measured in he regions of direc and resolved processes separaely. Evens conaining a leas wo jes are seleced, wih he furher requiremen of a muon associaed o one of hese jes. The muon is seleced o analyse semi-leponic decays, while he wo jes represen a heavy quark aniquark pair. The experimenal mehod o separae he conribuions from he differen quark flavours is based on a combinaion of wo variables, which are sensiive o, which is he ransverse momenum of he seleced muon relaive o he associaed je axis, and he impac parameer δ, which reflecs he disance beween he seleced muon rack and he primary verex. This hesis is organised as follows. Chaper 2 presens he heoreical framework of heavy quark producion a HERA. General aspecs of QCD as well as special properies of he perurbaive QCD predicions used in his analysis are discussed. A he end of his chaper, recen heavy flavour measuremens performed a HERA and oher colliders are reviewed o moivae he presened analysis. In chaper 3, he experimenal apparaus is described briefly. The main focus is on he deecor componens relevan for his analysis. Chaper 4 provides a deailed overview of he even reconsrucion procedures used for he racks and jes, which are very imporan for his analysis. In his chaper, invesigaions concerning he resoluions of he rack measuremen are included. In addiion, he uning of he verex deecor simulaion is presened. This deecor componen plays an imporan role in his analysis, since i allows o measure primary and secondary verices wih a high precision. I is hus possible o measure he impac parameer disribuion of muons, which is sensiive o he quark flavours. These wo variables are p rel

9 he differen quark flavours. Chaper 5 conains he selecion deails of he analysed even sample and conrol disribuions. In chaper 6, he mehods are presened, which separae he quark flavours. The consisency and deails of he mehods are invesigaed. The cross secion measuremens and heir sysemaic uncerainies are presened in chaper 7. Finally, he obained resuls are summarized and compared o previous measuremens a HERA. 3

10 4 CHAPTER. INTRODUCTION

11 Chaper 2 Heavy Quark Phooproducion 2. Quanum Chromodynamics Quanum Chromodynamics (QCD) describes he srong ineracion beween colour charged paricles in erms of a Quanum Field Theory (QFT). The srong ineracion is similar in is concep o Quanum Elecrodynamics (QED) which describes he ineracion beween charged paricles wih phoons as gauge bosons. One of he main difference is he gauge group, since QED is based on he Abelian gauge group U() and QCD on he non-abelian SU(3) colour symmery group. This leads o addiional erms in he Lagrangian of he QCD which cause an ineracion beween he QCD gauge bosons, he gluons []. For he same reason he gluons carry colour charge. Therefore, in mos of he cases a gluon exchange leads o colour changes of he paricipaing quarks. The self-ineracion of he gluons has considerable consequences since i causes a conrary behaviour of he srong coupling consan α s in comparison o he elecromagneic fine srucure consan. The srong coupling consan is very large a low momenum ransfers and decreases owards higher energies. This behaviour leads o asympoic freedom a high energies and he so-called confinemen a low energies. In he case of asympoic freedom he parons behave like free paricles a high energies. As a consequence of confinemen, he large coupling consan causes he parons o be bound ino colour neural saes, he hadrons. The running coupling consan of he srong ineracion is depiced in figure 2.. Perurbaive QCD (pqcd) cross secions for paricle scaering are calculaed as a power series in α s. The large value of α s is causing problems in he perurbaive series, since quark and gluon loop diagrams can give large conribuions beyond Leading Order (LO). An inegraion of all paricle momena p in he loop has o be performed, o deermine hese conribuions. As always in QFT, some of he loop diagrams diverge. The logarihmically divergen inegrals have o be renormalized, which means ha hey have o be removed by a finie number of counererms. In he renormalizaion procedure an arbirary dimensionless renormalizaion scale µ R is inroduced. In pracice his scale is chosen close o he physical scales which characerise he sudied process. In heory, i is required ha every physical observable has o be independen of he arbirary choice of µ R.Ahescaleµ R > Λ QCD in one loop approximaion he srong coupling consan can be wrien as 5

12 6 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION α s.2.5. HERA QCD α s (M Z ) =.98 ±.32 (HERA combined 27) inclusive-je NC DIS je ZEUS (from dσ/de T ) (from d 2 σ/dq 2 je H de T ) 5 E T je (GeV) HERA α s working group Figure 2.: The coupling consan α s of he srong ineracion is shown as a funcion of he ransverse je energy E je T. The HERA daa (poins) are in good agreemen wih he QCD calculaion [2]. α s (µ 2 R)=, wih b = 33 2n f b ln( µ2 R ) 2π Λ 2 QCD. (2.) Here n f sands for he number of acive quark flavours wih a mass below µ R.Λ QCD denoes he scale a which α s ges very large leading o divergences of he perurbaive series in α s. In his case pqcd is no longer applicable. Experimenally Λ QCD is of he order of 2 MeV. Heavy quark producion a HERA provides an excellen esing ground for pqcd. The high masses of he heavy quarks in combinaion wih heir ransverse momena p and/or he virualiy of he exchanged boson Q 2 define a hard scale, which complicaes he siuaion. The perurbaive expansion can no be opimized for all scales a once. This so-called muliscale problem can be reaed in differen ways according o he relaive magniudes of he presen scales.

13 2.2. DESCRIPTION OF EP SCATTERING Descripion of ep Scaering The ep scaering process ep lx can be described by a single virual gauge boson exchange. If he boson is eiher a phoon γ or a Z, he scaered elecron is observed in he final sae. This is called a neural curren (NC) even wih ep ex. If he exchanged paricle is a W ± boson, his characerizes a charged curren (CC) even, ep ν e X. In figure 2.2 (a) a Feynman diagram for ep scaering is depiced, including he kinemaic variables. An incoming elecron wih 4-momenum k is scaered off a proon wih 4-momenum P. In he final sae a scaered lepon wih 4-momenum k and a hadronic sysem X wih 4- momenum P is found. The hadronic sysem is formed by he proon remnan and he scaered paron. The laer is a poinlike consiuen of he proon and can be described by he Quark Paron Model (QPM) [3], [4]. The squared cenre-of-mass energy of he reacion is s =(P + k) 2. (2.2) For unpolarised beams a a given cener-of-mass energy he kinemaics of inclusive lepon proon scaering can be described by wo Lorenz invarian quaniies. Usually wo of he hree variables Q 2, x Bj and y are chosen, which are described in he following. The negaive squared 4-momenum ransfer a he elecron verex is given by Q 2 = q 2 = (k k ) 2. (2.3) I corresponds o he virualiy of he exchanged boson. If he phoon is quasi-real (Q 2 GeV 2 ), he producion regime is called phooproducion (γp). In he case of large Q 2 he regime is called Deep Inelasic Scaering (DIS). In his hesis he analysed regime is phooproducion. The inelasiciy y is calculaed using he formula: y = Pq Pk wih y. (2.4) The observable y denoes he fracion of he incoming elecron energy in he proon res frame which is carried away by he phoon. The Bjorken scaling variable x Bj is defined as x Bj = Q2 2Pq, wih x Bj. (2.5) In he paron model x Bj sands for he momenum fracion of he proon which is carried by he sruck quark (see figure 2.2 (b)). The squared phoon-proon cenre-of-mass energy is deermined via W 2 =(P + q) 2. (2.6)

14 8 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION (a) eˉ k Q 2 eˉ (ν ) e k' γ, Z⁰ (Wˉ) (b) eˉ k Q 2 q eˉ (ν ) e k' γ, Z⁰ (Wˉ) W q X x Bj X p P' p P P Figure 2.2: Diagram for ep scaering including he kinemaic variables (a). In (b) ep scaering in he paron picure is depiced. The quaniy W 2 corresponds o s in he case of hadron-hadron scaering, if he phoon is considered as he hadronic projecile. Wih he assumpion of zero paricle masses he produc of he cenre-of-mass-energy s, inelasiciy y and he Bjorken scaling variable x Bj gives he squared 4-momenum ransfer Q 2 : Wih he same assumpion W 2 is calculaed using Q 2 = x Bj ys. (2.7) W 2 = ys Q 2. (2.8) 2.3 Proon Srucure The srucure of he proon is paramerised in erms of he srucure funcions. In he following, he quark paron model is described briefly and he facorizaion heorem is inroduced Quark Paron Model In he picure of he Quark Paron Model (QPM) [3], [4] nucleons consis of poinlike, non ineracing consiuens. These consiuens were idenified wih quarks by J. Bjorken and E. Paschos [5]. A virual phoon is exchanged beween he incoming elecron and one of hese quarks. To derive an approximaion o he cross secion calculaion for ep scaering

15 2.3. PROTON STRUCTURE 9 he so-called infinie momenum frame is used. Here he proon has an almos lighlike momenum along he collision axis and all ransverse momena can be negleced as well as he proon mass iself. This approximaion is valid a high energies as realised a HERA. The momenum fracion of he proon carried by he ineracing quark is called he longiudinal fracion x and can be deermined by din of measured elecron quaniies. In leading order QCD, gluon emission or exchanges during he collision process can be ignored. The cross secion for ep scaering can hen be deermined using he cross secion for quasi-elasic elecron-quark scaering a a given longiudinal fracion and he probabiliy f i (x)dx o find a quark a ha longiudinal fracion. The probabiliy funcions can no be calculaed using QCD perurbaion heory and have herefore o be deermined experimenally. The funcions f i (x)dx are called Paron Disribuion Funcions (PDF). The conen of he proon is paramerised by he proon srucure funcions F, F 2 and F 3 which can be exraced from NC DIS cross secion measuremens. F 3 akes he pariy violaion of he weak force ino accoun. If Z exchange is negligible, F 3 = holds. In he following, his is assumed and herefore only γ exchange is considered. Taking he spin of he paricles ino accoun, he double differenial cross secion as a funcion of x and Q 2 canbewrienas d 2 σ dq 2 dx = 4πα2 xq 4 (xy2 F (x, Q 2 )+( y)f 2 (x, Q 2 )). (2.9) Boh srucure funcions F (x, Q 2 )andf 2 (x, Q 2 ) paramerise he proon srucure and deails of he ineracion a he phoon-proon verex. In he QPM for free Dirac quarks, which is also called DIS scheme, he relaion beween hem is described by he Callan-Gross relaion [6]: F 2 (x, Q 2 )=2xF (x, Q 2 ), (2.) which is ofen used o eliminae F (x, Q 2 ). This relaion is valid if he ineracing paron coming from he proon is a fermion. In he case of bosons F (x, Q 2 ) would be equal o zero since i corresponds o he magneic form facor. The proon srucure funcion F 2 canbewrieninhedisschemeas F 2 (x, Q 2 )=x i e 2 i f i(x). (2.) Here e i denoes he charge of quark i. In he Bjorken limi, which is defined as Q 2,p q wih fixed x, he srucure funcion obeys an approximae scaling. Which means, ha i depends only on he variable x: F 2 (x, Q 2 ) F 2 (x). This independence was prediced by J. Bjorken [3]. In his picure, he increase of Q 2 does no disclose any new deail of he quasifree parons in he proon if once he parons are resolved. Experimenal resuls showed a scaling behaviour a x., which confirms he QPM in good approximaion [7]. This scaling behaviour, which is he independence of F 2 on Q 2, is inerpreed mainly as a scaering off he valence quarks. This is for example depiced in figure 2.3, where experimenal resuls

16 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION of he collider experimens H and ZEUS a HERA and fixed arge experimens of he years are shown. Bu already in he early 97s experimenal comparisons of DIS daa wih he QPM revealed, ha only 5% of he proon s momenum is carried by quarks [8], [9]. As illusraed in figure 2.3, for low x a sharp increase of F 2 wih increasing Q 2 is found. These observaions lead o he conclusion ha he QPM does no describe he full proon conen. The observable Q 2 is relaed o he Compon wavelengh, which deermines he resoluion. Wih increasing Q 2, he Compon wavelengh decreases and finer srucures of he proon can be resolved. The dependence of F 2 on Q 2 a low x, also denoed as scaling violaions, is herefore inerpreed as an increase of sea quarks produced by gluons, which can be seen due o he beer resoluion. This leads o a rising ep cross secion and a he same ime an increasing F 2 owards higher values of Q 2. To ake he gluon conribuions ino accoun and o describe he proon conen successfully, an exension of he quark paron model was necessary. In erms of pqcd he proon srucure funcion F 2 in equaion 2. can be seen as he zeroh order erm in he expansion of F 2 as a power series in α s. For aking conribuions of he order O(α s ) ino accoun, he phoon-paron subprocess diagrams shown in figure 2.4 (b) using he massless approach (cf. secion 2.6) have o be calculaed. The firs diagram in figure 2.4 (b) has a collinear divergence since he gluon can be emied parallel o he quark. To solve his problem hese singulariies are absorbed by he quark disribuion, which becomes scale dependen. In his procedure a facorizaion scale µ F is inroduced, which defines he scale where he singulariies conribue o he quark densiy Facorizaion Theorem and Srucure Funcions The facorizaion heorem [] can be considered as a field heoreical realizaion of he above described paron model. I separaes hard and sof processes, he firs ones correspond o he shor disance par while he laer ones sand for he long disance par. Hard processes are compuable in pqcd and describe he ineracion of high energy parons. Sof processes can no be deermined wih perurbaive calculaions and describe low energy ineracions. In his framework he proon srucure funcions can be described as follows. Le F a (x, Q 2 ) be he srucure funcions of all DIS processes l + p l + X. The general facorizaion formula according o [] holds for all orders in perurbaion heory. I is proven only for DIS bu urned ou o be usable for he phooproducion regime as well. I can be wrien as F a (x, Q 2 )= i=q, q,g dy ( x ) ( Λ 2 ) y f i(y,q 2 )C a,i y,α s(q 2 QCD ) + O Q 2. (2.2) The observable F a (x, Q 2 ) is facorized ino wo pars: he universal paron densiies, denoed as f i and he coefficien funcions C a,i. The firs par corresponds o he sof processes where long disance collinear singulariies are absorbed. Sof processes are considered o be processes wih lower momenum ransfers han hard processes. The paron densiies canno be calculaed in pqcd. The DGLAP evoluion equaions (cf. secion 2.4) make i possible o deermine he dependence on Q 2. The second par of equaion 2.2 sands for he hard processes. The coefficien funcions describe he shor disance subprocess and are compuable in

17 2.3. PROTON STRUCTURE HERA F 2 em F 2 -log (x) 5 x=6.32e-5 x=.2 x=.6 x=.253 x=.4 x=.5 x=.632 x=.8 x=.3 ZEUS NLO QCD fi H PDF 2 fi H 94- H (prel.) 99/ ZEUS 96/97 4 x=.2 x=.32 BCDMS E665 NMC x=.5 3 x=.8 x=.3 x=.2 2 x=.32 x=.5 x=.8 x=.3 x=.8 x=.25 x=.4 x= Q 2 (GeV 2 ) Figure 2.3: Proon srucure funcion F 2 as a funcion of Q 2 for various values of x. The daa is measured by H, ZEUS and differen fixed arge experimens using fis based on DGLAP. For a beer visibiliy an offse of log x is applied o each daa poin.

18 2 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION pqcd as a power series in α s. They are unique o he paricular srucure funcion F a.the added erm a he end of equaion 2.2 denoes non-perurbaive conribuions. I conains hadronizaion effecs, muliparon ineracions ec. These effecs are negligible for sufficienly high Q 2. Since his analysis is performed in phooproducion (Q 2 GeV 2 ), hese effecs become imporan. The srucure funcion F 2 (x, Q 2 ) is a special case of equaion 2.2. For leading order in α s and he convenien choice of µ F = Q i has he following form: F 2 (x, Q 2 )=x i=q, q e 2 q dy [ ( ( f q (y,q 2 ) δ x ) + α s x )) 2,q( y y 2π C + f g (y,q 2 ) α s x )] 2,g( y 2π C. y (2.3) The C 2,i are he coefficien funcions for he observable F 2. This prescripion is no unique, since any finie erm can be added. Therefore a scheme mus be chosen. A very common one is he modified minimal subracion scheme (MS facorizaion scheme), which ses also he renormalizaion scheme. In he MS scheme no all gluon conribuions are absorbed in he quark disribuions. Experimenally he paron densiy funcions are deermined by a fi o adjus he nonperurbaive disribuions o he experimenal F 2 (x, Q 2 ) daa from HERA and fixed arged experimens. The gluon and valence quark disribuions of he proon are depiced in figure 2.4 [2]. A low x, he gluon densiy exceeds he quark disribuion by far, which explains he scaling violaions in ha region. These paron densiies are deermined from a combined fi of he H and ZEUS daa from he HERA I period. The proon disribuions funcions obained by he CTEQ [3] group are used for his analysis. The CTEQ6L se of PDFs is deermined in leading order. This se is appropriae for Mone Carlo even generaors and achieved using a QCD coupling of α s (µ R )=.8. The srucure funcion of he phoon F γ 2 has a differen behaviour han he srucure funcion of a hadron, for example he proon. The poin-like conribuions of he resolved processes lead o a rising of F γ 2 owards large values of x. Here x is again he momenum fracion of he phoon carried by he ineracing paron. The proon srucure funcion behaves conrary and decreases owards large x, as discussed before. The firs calculaion of he phoon srucure funcion in LO QCD was performed by Wien [4]. He negleced he incalculable hadronic-like componen which leads o unreliable resuls a small values of x. Phoon quark densiy funcions have been deermined mainly in e + e scaering. The gluon conen in he phoon can be calculaed from F γ 2 measuremens wih he help of evoluion equaions. The gluon disribuion funcion increases owards small values of x. This behaviour is in conras o he quark disribuion funcion of he phoon, since i shows a decrease owards small x. The presence of gluons a low x indicaes scaling violaions which has been shown in F γ 2 measuremens summarized for example in [5]. The scaling violaion behaviour is conrary o he one of he proon, since he phoon consiss of less gluons and he resolved phoon is dominaed by quarks. There exis several paron disribuion funcions for he phoon. For his analysis he ones calculaed by Schuler and Sjösrand SaS [6] are aken. The differen phoon PDFs differ in he saring scale Q and in he inpu disribuions a his scale. There are experimenal

19 2.3. PROTON STRUCTURE 3 (a) (b) xf H and ZEUS Combined PDF Fi xg (.5) xs (.5) -3 HERAPDF. (prel.) exp. uncer. model uncer Q = GeV xu v xd v HERA Srucure Funcions Working Group April 28 - x x y k + real virual 2 Figure 2.4: Gluon and valence quark densiies of he proon in figure (a). The disribuions are deermined from fis o combined H and ZEUS daa from he HERA I period [2]. In (b) he leading order O(α s ) diagrams are shown, which conribue o he proon srucure funcion. evidences of he universaliy of he paron densiy funcions, which are for example presened in [5]. The daa used for he fiing of parameers is aken from e + e reacions. The SaS paron disribuions [6] are deermined using a hadron-like saring conribuion which is based on VMD argumens. Two ses of disribuions exis: SaS and SaS2. The firs one assumes a saring scale of Q =.6 GeV while he laer one akes Q =2GeV. In his analysis he SaS2D seinhedisschemeisused. In his hesis phooproducion processes are sudied. Based on he facorizaion heorem, he phooproducion cross secion can be decomposed as follows in he presence of a hard scale : σ γp f i/p (x p,µ 2 F ) ˆσ ij(ŝ, α s (µ 2 R ),µ R,µ F ) f j/e (x e,µ 2 F ) D(z). (2.4) Here f i/p and f j/e denoe he paron disribuion funcions of he proon and he elecron, respecively. They depend on x p and x e, which represen he momenum fracion of he paron ha paricipaes in he hard ineracion. The variable ˆσ ij sands for he cross secion of he hard subprocess. The funcion D(z) describes he fragmenaion and is explained in secion 2.7. I depends on z which represens he fracion of he original longiudinal momenum of he hadron carried by he paron.

20 4 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION (a) (b) e Q 2 P qg (z) g q z x θ q -z x n,k,n θ n P gq (z) q g z x n-,k,n- θ n- P gg (z) g q g -z z x,k θ g -z p x,k P qq (z) q q g z -z Figure 2.5: A paron evoluion diagram is shown on he lef (a). Figure (b) illusraes he spliing funcions P ab (z). 2.4 Paron Evoluion Models As discussed above, he paron densiy funcions canno be prediced by pqcd, bu heir scale dependence can be calculaed in his framework. Since he PDFs conain he sof processes up o a cerain facorizaion scale µ F, i is possible o evolve hem o any oher scale. For his evoluion he knowledge of he PDFs a a cerain scale µ is required. The deerminaion a his scale µ is done experimenally. The evoluion iself is performed by considering he paron radiaion and spliing processes. Differen paron evoluion models exis, which cover cerain regions of he phase space. The DGLAP, BFKL and CCFM evoluion equaions are presened in he following.

21 2.4. PARTON EVOLUTION MODELS 5 DGLAP Evoluion Model The DGLAP evoluion equaion [7], [8], [9], [2] is valid for large Q 2 and moderae x. A he order O(α s ) he processes γg q q and γq gq need o be included. The DGLAP evoluion equaion for he quark densiy is in his case of he following form: q(x, µ 2 ) ln µ 2 = α s 2π x dy ( ( x ) ( x )) f q (y,µ 2 )P qq + f g (y,µ 2 )P qg. (2.5) y y y The funcion P ab denoes he spliing funcion for he process b a. They are depiced in figure 2.5 (b) and describe he probabiliy for paron b o emi paron a wih momenum p a = zp b,wihx = yz. The evoluion equaion for he gluon densiy in he DGLAP approach is given as g(x, µ 2 ) ln µ 2 = α s 2π x dy ( ( x ) ( x )) f q (y,µ 2 )P gq + f g (y,µ 2 )P gg. (2.6) y y y In leading order, he DGLAP approach is based on resumming he leading (α s ln(q 2 /µ 2 )) n conribuions. In nex-o-leading order evoluion he summaion of he α s (α s ln Q 2 ) n erms is included. This so-called Leading Log Approximaion (LLA) requires a srong ordering in he ransverse momena of he emied parons, as illusraed in figure 2.5 (a): µ 2 <k 2, <k 2,2 < <k 2,n <Q 2. (2.7) The DGLAP evoluion equaion predics he scaling violaions observed a HERA down o he smalles accessible x successfully. I is used o model paron showers for Mone Carlo programs, as described in secion 2.8. In his framework all parons enering he hard subprocess are on-shell. BFKL Evoluion Model The BFKL 2 approach [2], [22], [23] leads o srongly ordered longiudinal momena z i = x i /x i. The BFKL ansaz can be used for moderae Q 2 and small x. The evoluion is performed in x and he leading α s ln(/x) erms are resummed. Here he ransverse momena k are free and herefore his approach is also called he k -facorizaion approach. In he kinemaical region of HERA he srucure funcion F 2 is no able o discriminae beween DGLAP and BFKL. The sudy of he energy dependence of jes near he proon direcion may be sensiive o reveal he BFKL mechanism. Dokshizer, Gribov, Lipaov, Alarelli, Parisi 2 Balisky, Fadin, Kuraev, Lipaov

22 6 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION CCFM Evoluion Model The CCFM 3 evoluion model [24], [25], [26], [27] combines he DGLAP and he BFKL approach. I is equivalen o he DGLAP approach for large Q 2 and moderae x and equivalen o BFKL for small x and moderae Q 2. I shows a srong angular ordering of subsequen paron emissions in a cerain region of he phase space. This is a propery of QCD since in a cascade of gluon and quark emissions he angles of he emied paricles decrease when following down a branch. The uninegraed gluon densiy A(x g,k 2,µ2 F ) sands for he probabiliy o find a paron wih longiudinal momenum fracion x g and ransverse momenum fracion k a he facorizaion scale µ F. In he CCFM model his paron densiy is more complicaed han he one in DGLAP, which depends on x and Q 2 only. The CCFM approach allows parons o be off-shell when enering he hard marix elemen. As a consequence, resolved processes are implicily included o some exend. 2.5 Heavy Quark Producion The masses of he ligh quarks u, d and s are below he Λ QCD parameer and herefore no large enough o provide a hard scale. The masses of he heavy quarks c, b, and are high enough o serve reliable perurbaive calculaions. Since he mass of op quark producion 3 Ciafaloni, Caani, Fiorani, Marchesini (a) e Direc Process: γ g b,c b,c p Resolved Processes: (b) (c) (d) (e) γ γ γ γ g b,c g b,c b,c g b,c g b,c g g g q p p p p Figure 2.6: Heavy quark producion in leading order pqcd. In (a) he direc BGF process is shown while figures (b)-(e) illusrae resolved processes.

23 2.5. HEAVY QUARK PRODUCTION 7 is ou of reach for he HERA collider, here he heavy quark physics concenraes on c (charm) and b (beauy) quarks. Heavy quark producion conribues significanly o he oal inclusive cross secion a HERA. The dominan conribuion o he heavy quark producion cross secion in leading order O(αα s ) is due o Boson-Gluon Fusion (BGF). The ep scaering process can be undersood in erms of QCD, where he phoon coming from he elecron ineracs wih parons of he proon. A low y virualiies he exchanged phoon has a relaively long lifeime and wo scaering scenarios mus be considered: Direc Phooproducion: If he phoon ineracs direcly wih a paron of he proon, he ineracion is called direc phooproducion. This process is ploed in figure 2.6 (a). In he final sae hey form a heavy quark pair γg q q. Following [28], [29] he cross secion for his process canbewrienas ˆσ BGF (ŝ, m 2 q)= πe2 qαα s ŝ [ (2 + 2ω ω 2 )ln ( +χ) ] 2χ( + χ), (2.8) χ wih ω =4m 2 q/ŝ, χ = ω. (2.9) Here ŝ =(p q + p q ) 2 represens he squared cenre-of-mass energy and e q sands for he elecric charge of he heavy quark q. The massive approach is applied which akes he masses of c and b quarks ino accoun. Due o he larger mass and he smaller charge of he b quark in comparison o he c quark, he beauy cross secion is suppressed. In he massless approach, where (m c,m b ) holds, he charm cross secion is expeced o be only a facor of four larger han he beauy cross secion in he boson-gluon fusion process. Resolved Phooproducion: If he phoon does no inerac direcly, bu flucuaes ino a q q sae before he hard ineracion, he process is called resolved phooproducion. Resolved processes represen a significan conribuion in addiion o direc processes. In figure 2.6 (b)-(e) several resolved processes in leading order are shown. In 2.6 (b) a hadron-like process is depiced. Here, a gluon or a ligh quark coming from he phoon ineracs wih a paron of he proon. In all resolved processes he phoon behaves similar o he proon - as a bunch of parons. The phoon is herefore reaed as a paricle wih a hadronic srucure which can be described by paron densiy funcions. Figures 2.6 (c)-(e) depic heavy quark exciaion processes. In his case, a heavy quark ou of he phoon paricipaes in he hard ineracion. Resolved processes may have wo differen naures: eiher he phoon flucuaes ino an unbound fermion pair or ino a q q pair forming a vecor meson. If quarks are involved, he siuaion becomes complicaed since he specrum of flucuaions is more rich and QCD correcions have o be aken ino accoun. In he fermion pair producion, he phoon is also known as a poin-like or anomalous phoon. In he second case he vecor meson ineracs wih he proon like a hadron. This process is described by he Vecor Meson Dominance Model (VDM) and also known as a hadron-like resolved process.

24 8 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION A very good agreemen beween he daa and he leading order QCD calculaion is achieved, when he resolved processes are aken ino accoun. The disincion beween resolved and direc processes is only in he LO calculaion unambiguous. 2.6 QCD Calculaion Schemes Physics simulaion programs are a fundamenal ool for every high energy physics experimen. They are required for designing deecors and help o develop experimenal analysis sraegies. For his purpose hese programs have o provide simulaions which model he collision processes as realisic as possible. The inpu of such programs are calculaions performed in pqcd a differen orders. In leading order he Mone Carlo even generaors are used. They provide an even-by-even predicion based on saisical mehods and are described in secion 2.8. For he predicion of nex o leading conribuions cross secion Mone Carlo inegraion programs are used. They are presened in secion 2.9. The physics simulaion programs are based on differen calculaion schemes. Therefore hese schemes are discussed before he descripion of he simulaion programs. The hard scale, which is se by he heavy quark mass, complicaes he siuaion since he perurbaive expansion series can no be opimized for all scales a once. Differen approaches exis o deermine nex o leading order conribuions of heavy quark producion. The heavy quark mass is reaed in differen ways according o he relaive magniudes of he scales p and Q 2,whicharealsopresen. Massive Approach In he massive approach, he heavy quarks are reaed as massive parons which are sricly independen of he phoon and proon conen. Therefore he number of acive flavours in he iniial sae is fixed and resriced o he ligh quarks. The heavy quarks appear herefore only in he final sae and are produced via he BGF mechanism. Since he number of acive quark flavours is fixed, his scheme is called he Fixed Flavour Number Scheme (FFNS). This model is valid in regions of p m q. The quark mass m q ses he scale for he perurbaive calculaions and acs as a cuoff. In he calculaion of he hard scaering cross secion all erms up o O(α 2 s) are aken ino accoun. The leading order and some NLO Feynman diagrams for heavy quark producion in he massive scheme are shown in figure 2.7. If p m q collinear gluon emissions and gluon or phoon spliings ino a heavy quark pair occur, which lead o divergences in he expansion series. To solve his problem, anoher calculaion scheme, he massless approach, is inroduced. Massless Approach In he massless approach he masses of he heavy quarks are negleced. Here he heavy quarks are par of he phoon and proon conen. For pqcd calculaions, i means, ha he heavy quarks are acive flavours in he proon and phoon srucure funcions. This ansaz holds for large scales, which means ha he p of he heavy quark mus be much larger han he quark mass iself. In consequence of his resricion, he small p regions are no calculable

25 2.7. FRAGMENTATION 9 Massive Scheme: LO virual NLO radiaive Massless Scheme: LO virual NLO radiaive Figure 2.7: Perurbaive QCD conribuions of he massive and he massless scheme. in he massless approach since he cross secions are divergen. The massless scheme is also called Zero Mass Variable Flavour Number Scheme (ZM-VFNS). The leading order and some NLO Feynman diagrams for heavy quark producion in he massless scheme are shown in figure 2.7. Mached Scheme The mached scheme combines he massive and he massless approach. I uilizes he bes appropriae scheme a a given energy scale Q 2. I is also known as he FONLL scheme [3], which sands for Fixed Order (FO) and Nex o Leading Logarihmic (NLL). I is a full massive NLO calculaion which resums addiionally he logarihms of p 2 /m 2 q. The mached scheme cerainly would provide very reliable heoreical predicions, bu i is presenly unavailable for H daa. 2.7 Fragmenaion Due o he confinemen, i is no possible o measure free b and c quarks direcly. The srongly ineracing paricles form in heir final sae colour neural saes, colourless hadrons. The process of forming hadrons is known as paron hadronisaion or fragmenaion. InMone Carlo generaors he wo parons, which are produced in he BGF process, undergo a paron shower which can be described by evoluion equaions (cf. secion 2.4). This is possible up o a cerain scale µ F, as discussed before. Aferwards i is no possible anymore o perform pqcd calculaions, since he srong coupling consan ges oo large and spoils he convergence of he pqcd calculaions. Therefore phenomenological models are used o describe he fragmenaion process for large disances (sof processes). In his analysis wo ou of several fragmenaion models are used and presened briefly in he following.

26 2 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION The sring fragmenaion model [3] is used as defaul in his analysis. In his model q q pairs and he colour field beween hem form srings. A large disances he sored poenial energy is proporional o he disance. As a consequence, he sring breaks up a larger disances, when he energy go large enough. In his case a new q q is produced ou of he vacuum. Kinks in hese srings are inerpreed as gluons in his model. In he final sae he produced sring fragmens form hadrons. According o [3], he Lund fragmenaion funcion is defined as D h q (z) z ( z)a exp( bm 2 /z), wih m = m 2 + p 2 x + p 2 y. (2.2) Here m denoes he ransverse mass of he hadron, while a and b are free parameers. z sands for he longiudinal momenum fracion. In his analysis he Lund-Bowler fragmenaion funcion is used, which is similar o equaion (2.2) [32]. In he independen fragmenaion model parons form hadrons independenly. I is implemened in he Peerson fragmenaion model [33]. The probabiliy for a quark q o form he hadron h which carries he longiudinal momenum fracion z is given by Dq h (z) ( ) 2. (2.2) z z ɛq z Thefreeparameerɛ q has o be deermined experimenally and is differen for charm and beauy quarks. This value is higher for b quarks, which corresponds o a harder fragmenaion for beauy flavoured hadrons. They ge a larger longiudinal momenum fracion on average of he iniial paron. In his analysis he Peerson fragmenaion is used o esimae sysemaic effecs arising from he choice of he fragmenaion model. 2.8 Mone Carlo Even Generaors Mone Carlo Generaors provide a predicion of he full hadronic final sae four vecors for every even. Afer generaing he even, he deecor simulaion has o be performed. The generaing process is divided ino hree pars: Firs, he hard process is generaed. In he second sep, he paron showers and evoluion equaions (cf. secion 2.4) are applied for he iniial and final sae. In he las sep, he hadronic final sae is formed by assisance of phenomenological models, such as Lund fragmenaion (secion 2.7). Addiionally hadron decays are modelled, for example semi-leponic decays of heavy hadrons. The generaed even sample can be fed ino deecor simulaion programs. The simulaed even sample can hen be compared wih daa as recorded by experimens. The deecor simulaion is usually based on he GEANT package [34]. Here, he paricle racking hrough he differen subdeecors is modelled and he deecor geomery and (dead) maerial is simulaed. The applied deecor simulaion is no par of he Mone Carlo generaor. In H i is implemened in he HSIM package. A his sage, he simulaed Mone Carlo predicion corresponds o he raw daa from ep collisions. The final sep is o reconsruc boh he daa and he simulaed Mone Carlo evens wih he H reconsrucion sofware HREC. The

27 2.8. MONTE CARLO EVENT GENERATORS 2 simulaed and reconsruced Mone Carlo even sample can be used for predicions a hadron and deecor level. The deerminaion of correcions such as reconsrucion efficiencies is now possible. To provide he self-consisency of he mehod o measure he cross secions, deecor effecs and efficiencies as well as dead maerial in he deecor have o be very well modelled by he simulaion. As long as he reconsruced and simulaed Mone Carlo describes he daa in every aspec, he Mone Carlo predicions for he quark conribuions can be used as emplaes in he fi and for he cross secion measuremen. PYTHIA In his analysis he PYTHIA 6.4 even generaor [35] is used. The PYTHIA generaor simulaes evens using he massless calculaion scheme. Here a mode is used, which maches direc, exciaion and resolved conribuions. In exciaion processes a heavy quark can originae from he phoon or proon. The proon densiy funcions are aken from CTEQ6L [3], while he phoon disribuion funcions are used from SaS2D [6]. The evoluion scheme applied in PYTHIA is DGLAP wih on-shell marix-elemens. As fragmenaion model he Lund-Bowler funcion [32] is applied. To sudy he sysemaic error arising from his choice of fragmenaion model, an addiional Mone Carlo se wih he Peerson fragmenaion is produced. The renormalizaion scale µ R is se o p 2 +(P 2 + P m2 q + m 2 q)/2, where P 2, P 2 2 represen he virualiies of he wo incoming paricles, p sands for he ransverse momenum of he scaering process and m q, m q are he masses of he wo ougoing paricles. A summary of he parameers and funcions used in he LO QCD calculaions can be found in able 2.. Three differen even samples are generaed: charm, beauy and inclusive ones. These hree samples are generaed in he inclusive mode, which is very ime consuming. For charm and beauy, he processes ep eb bµx or raher ep ec cµx are seleced ou of all inclusive processes. The luminosiy of he charm sample is 28 pb, which corresponds o roughly 6 imes he daa luminosiy. The sample conaining beauy evens has a luminosiy of 374 pb, which is a facor of 8 more han he daa. The inclusive sample consiss of evens conaining u, d, s, c, b quarks, dominaed by he ligh quarks. The luminosiy of he inclusive sample is roughly 838 pb and corresponds o approximaely five imes he daa luminosiy. The differen run ranges e + and e are aken ino accoun for he hree Mone Carlo samples. The fracions of hese hree componens are prediced by PYTHIA. The sum of he b, c, and uds conribuions is compared wih he daa o ensure ha he daa is well described by he PYTHIA Mone Carlo simulaion. The measured charm and beauy daa are compared o he charm and beauy cross secions prediced by PYTHIA. CASCADE In CASCADE [36] he process γg b b or γg c c is modelled. Here he evoluion scheme CCFM is applied which uses k uninegraed paron disribuions in he proon. As discussed in secion 2.4, he gluon densiy depends on he ransverse momenum k of he paron. The paron disribuions are aken from A [37] and are applied wih he same mass parameers as

28 22 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION PYTHIA (LO) CASCADE (LO) Version Evoluion scheme DGLAP CCFM m b [GeV] m c [GeV].5.5 Proon PDF CTEQ6L A Phoon PDF SaS2D - Renorm. scale µ R p 2 +(P 2 + P m2 q + m 2 q)/2 ŝ + Q 2 Facor. scale µ F p 2 +(P 2 + P m2 q + m2 q )/2 ŝ + Q 2 Lund a Lund b Peerson ɛ b.58 - Peerson ɛ c.69 - Table 2.: Overview of parameers and funcions used in he leading order QCD calculaions. used in PYTHIA. The facorizaion scale can be wrien as µ F = ŝ + Q 2.Hereŝrepresens he invarian mass of he q q subsysem and Q sands for is ransverse momenum. This choice of µ F is moivaed by he maximum angle allowed for any emission since he CCFM scheme is performed in an angular orderd region. The PYTHIA generaor provides he reamen of he final sae paron showers, he proon remnan and he fragmenaion. In CASCADE he same fragmenaion funcion as used in PYTHIA is applied, he Lund-Bowler funcion. The CASCADE Mone Carlo samples are produced o sudy sysemaic effecs coming from he choice of he underlying physics model. Two differen samples are generaed: charm and beauy ones. The esimaion of he ligh quark background is done wih he PYTHIA inclusive Mone Carlo sample. 2.9 QCD Predicions Perurbaive QCD calculaions a nex o leading order are available in Mone Carlo inegraion programs. In his analysis wo NLO predicions are compared o he measured cross secions and presened briefly in he following. FMNR The FMNR 4 program [38] implemens a fixed order calculaion in he massive scheme a nex o leading order precision. The predicions are herefore expeced o be valid in he lower p region. FMNR provides weighed paron level evens wih wo or hree ougoing parons. This is for example he heavy quark aniquark pair and in he case of hree parons a hird 4 Frixione, Mangano, Nason, Ridolfi

29 2.9. QCD PREDICTIONS 23 ligh quark. A comprehensive overview of he FMNR program is for example given in [39]. The b quark is evaluaed ino a b flavoured hadron by rescaling he hree-momenum of he quark using he Peerson fragmenaion funcion wih he parameer ɛ b =.69. To be able o produce a final sae conaining a muon as a produc of he decay of a beauy flavoured hadron, he program is exended. Boh direc and indirec decays of beauy flavoured hadrons ino muons are included using he JETSET [4] muon decay specrum. The k je algorihm is used o reconsruc paron level jes from he ougoing parons. The hadronisaion correcions in he FMNR calculaions are deermined using he PYTHIA programme in his analysis. The observables relaed o jes are calculaed on he one hand for he evens generaed wih PYTHIA using he final sae parons, and on he oher hand from he resuling hadrons. On his basis, a migraion marix for each observable is deermined, which describes he migraion from bins of paron level observables o bins of hadron level observables. To esimae he uncerainies of he hadron level NLO QCD predicions, he mass of he beauy quark m b =4.75 GeV is varied by ±.25 GeV. Addiionally, he renormalizaion and facorizaion scales µ r and µ f are varied independenly in he range µ /2 µ r,µ f 2µ f, using he consrain /2 µ r /µ f 2. The deviaions due o he beauy mass variaion and he larges deviaion due o he scale variaion in boh direcions are deermined in each bin on hadron level. For he oal model uncerainy, he deviaions are added up in quadraure, as recommended in [4]. For his analysis he proon srucure funcion is aken from CTEQ5F4 [42] and he phoon srucure funcion is calculaed by GRV-G HO [43]. The heavy quark masses are se o.5 GeV and 4.75 GeV for charm and beauy, respecively. A summary of he parameers for he NLO calculaions can be found in able 2.2. Due o echnical reasons, he FMNR calculaion is performed for he beauy measuremen only. The calculaion is done by Dr. Benno Lis. MC@NLO The MC@NLO program [44] was developed recenly and is currenly available for HER- WIG@NLO only. HERWIG is a Mone Carlo generaor [45] which sands for Hadron Emission Reacions Wih Inerfering Gluons. HERWIG is able o simulae hard lepon-lepon, lepon-hadron and hadron-hadron scaering as well as sof hadron-hadron collisions. The PYTHIA@NLO program is on he way and will be mos probably available for he publicaion of his analysis. The MC@NLO program is a Mone Carlo even generaor, which deermines he marix elemens a nex-o-leading order. In such a calculaion he siuaion becomes more complicaed han in he leading order picure, since so-called momenum reshuffling occurs. Afer he paron showering process each paron becomes a je, which makes a replacemen of he paron momena by je momena necessary. This has o be done carefully, since energy momenum mus be conserved and double couning has o be avoided. This complicaion and oher issues of he nex-o-leading order calculaion are aken ino accoun and implemened in he MC@NLO program developed in [44]. In [44] he calculaions are done for he case of heavy quarks in phooproducion. The HER- WIG@NLO predicions for he charm and beauy measuremen are calculaed by Tobias Toll for he analysis presened in his hesis and compared o he measured daa. The seings

30 24 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION FMNR (NLO) Version - HERWIG 6.5 Evoluion scheme angular ordering angular ordering m b [GeV] m c [GeV].5.5 Proon PDF CTEQ5F4 CTEQ6.6 Phoon PDF GRV-G HO m GRV-E Renorm. scale µ R 2 b + p2 m 2 b + p2 Facor. scale µ F µ R µ R Fragmenaion Peerson fragmenaion cluser fragmenaion ɛ b =.69 - Table 2.2: Overview of parameers and funcions used in he NLO QCD calculaions. for he calculaion are lised in able 2.2. The resuls can be found in chaper Properies of Charm and Beauy Hadrons Charm and beauy flavoured hadrons have a relaive large mass and lifeime. The lifeime is of he order O( psec) and hus measurable wih a precision verex deecor. These are remarkable properies in comparison o oher hadrons. Their masses, mean lifeimes and branching raios canno be calculaed heoreically. Therefore, hese properies are measured by experimen. The main experimenally deermined aribues of some b and c flavoured hadrons are lised in able 2.3. Decays of ground sae hadrons proceed via he weak ineracion. Theoreically he Cabbibo- Kobayashi-Maskawa (CKM) marix describes he change of he differen quark flavours. The ransiion probabiliy for he quarks i, j wih j i is given by he squared absolue value of he marix elemen V ij 2. In he dominan weak decays b cw and c sw + he corresponding marix elemens V cb and V cs are [46] V cb =.42 ±., (2.22) V cs =.4 ±.6. (2.23) The smaller measured value for V cb indicaes ha b flavoured hadrons have larger decay lenghs and lifeimes han c flavoured hadrons. In his analysis he semi-leponic decay B µx is sudied, which is depiced in figure 2.8. The b quark conained in he B hadron can eiher decay direcly ino cw and he W boson decays subsequenly ino a muon and a neurino (see figure 2.8 (a)). According o [46], he branching fracion for his decay is roughly %. In he case of an indirec decay (figure 2.8 (b)), he beauy quark decays ino a charm quark and a W boson. The charm quark decays hen ino a srange quark and a W boson, which in urn decays ino a muon and a neurino. The branching fracion for he indirec decay is abou 8% [46]. Two W bosons are produced

31 2.. RECENT RESULTS OF HEAVY QUARK PRODUCTION 25 quark mass lifeime decay lengh conen m q [GeV] τ [psec] cτ [µm] B d b ± ± B + u b ± ±. 49. Bs s b ±.6.47 ± Λ b udb ± ± D cū ±.7.4 ± D + c d ±.2.4 ± D s + c s ±.34.5 ± Λ + c udc ±.4.2 ± Table 2.3: Properies of heavy hadrons according o he resuls of he PDG group in 28 [46]. (a) b W c μ ν μ (b) b c s W f W μ f ν μ Figure 2.8: Diagrams for semi-leponic decays of beauy quarks. In (a) he direc process ino a charm quark is shown, while in (b) he indirec cascade process ino a srange quark via a charm quark is illusraed. in his cascade decay, which decay ino a fermion-anifermion pair. Thus in rare cases wo muons can appear in he final sae. 2. Recen Resuls of Heavy Quark Producion A comprehensive and nice overview of heavy quark measuremens a HERA can be found in [47], [48]. Here, a collecion of heavy quark measuremens in phooproducion using dije evens is presened. A firs, he agging mehods used a HERA for heavy quarks are summarized. Then, some ineresing resuls obained a HERA are presened briefly for charm and beauy phooproducion separaely. Tagging Mehods for Heavy Quark Producion A HERA mainly five basic analysis echniques are used o ag evens conaining heavy quarks. Usually several of hese agging mehods are combined. In he following mehods, single agging is used, which means, ha he decay paricles of one heavy quark are measured. A double agging is possible, bu no as efficien as he single agging. The full reconsrucion of he decayed hadrons conaining heavy quarks is mosly used for charm measuremens. Here he D meson is used very ofen, which is reconsruced via he so-called golden decay channel: D + D π s + (K π + )π s +. Since he branching raios for decay channels, which

32 26 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION can be reconsruced, is oo small and he beauy producion raes are very low, he full reconsrucion mehod is no used for beauy analyses. A very common agging mehod is using lepons, like muons or elecrons from semileponic decays of charm and beauy flavoured hadrons. These lepons have relaively large momena and can be idenified clearly. Anoher agging mehod is he p rel mehod. Here he relaive ransverse momenum of he lepon o he axis of he associaed je is exploied. Due o he large masses of beauy flavoured hadrons, i is possible o idenify evens conaining beauy quarks wih he p rel mehod clearly a saisical level. The single charm fracion canno be obained wih his mehod. The fourh agging mehod makes use of he large lifeime of heavy flavoured hadrons. Eiher he full reconsrucion of he charged decay racks a he secondary verex is performed or he disance of he charged racks o he primary verex is used. This mehod is able o disinguish beween evens conaining charm and beauy quarks. In general a leas one je is required in heavy quark analyses. This is necessary o esimae he direcion of he ougoing heavy quark, which is used by he lifeime and p rel mehod. In combinaion wih anoher heavy quark agging mehod a quark je can be found. Charm Phooproducion The charm quark was discovered a wo insiues a he same ime in November 974: he Sanford Linear Acceleraor (SLAC) [5] and a he Brookhaven Naional Laboraory (BNL) [5]. Boh experimens observed a narrow resonance a 3. GeV, which was inerpreed as a c c bound sae. This meson go he name J/Ψ o ake boh suggesions for is name ino Charm Charm [pb] obs /dx d 4 3 Daa Pyhia Pyhia res. Cascade NLO QCD had ep eccx H ejjx [pb/deg] /d( jj ) 2 Daa Pyhia Cascade NLO QCD had ep eccx ejjx d Daa/NLO x obs 8 jj ( ) / deg Daa/NLO x obs 5 5 jj ( ) / deg Figure 2.9: Cross secions for he process ep ec cx ejjx as a funcion of he observable x obs γ and he angular separaion of he wo jes δφ jes in he ransverse plane measured in [49].

33 2.. RECENT RESULTS OF HEAVY QUARK PRODUCTION 27 accoun. Since hen, charm producion was sudied a many differen colliders in various ineracions, e.g. a he Tevaron in p p ineracions. An overview of open charm and beauy resuls from he D and CDF experimens can for example be found in [52]. In he following, he discussion is focussed on recen HERA resuls. In [49] charm and beauy dije cross secions in phooproducion a high p are presened. Here he impac parameer of all racks wih respec o he primary verex is used o deermine he fracions of evens conaining charm and beauy evens. The agreemen of he charm cross secions in comparison o he nex-o-leading order pqcd calculaions is in general reasonably good. In conras o beauy in phooproducion, he charm cross secions as a funcion of he ransverse momenum is in good agreemen wih NLO calculaions. Only in he region of low x obs γ and low values of he azimuhal angular separaion of he wo jes δφ jes, he NLO predicion underesimaes he daa, as depiced in figure 2.9. The observables δφ jes and x obs γ are explained in deail in secion 5.4. Here, processes involving resolved phoons or higher order conribuions are expeced o conribue significanly. This observaion is also repored in oher analyses on independen daa ses from H [53] and ZEUS [54]. Therefore, i is ineresing o perform furher sudies in he region of resolved processes (x obs γ <.75), whichisdoneinhishesis. Beauy Phooproducion The beauy quark was discovered in 977 a he Fermi Naional Acceleraor Laboraory (FERMILAB) [55]. The Υ resonance a 9.5 GeV was observed, a b b meson. The producion dσ/dp [pb/gev] µ µ H -.55 < η <. µ ZEUS -.6 < η < 2.3 NLO QCD Had: µ -.55 < η <. µ -.6 < η < 2.3 dσ/dη [pb] µ 4 ep ebb X ejjµ X Q 2 < GeV 2.2 < y <.8 µ p > 2.5 GeV p je(2) > 7(6) GeV η je < 2.5 H ZEUS NLO QCD (ZEUS) NLO QCD (H) Q 2 < GeV 2 ;.2 < y <.8 p je(2) > 7(6) GeV; ηje < µ µ p [GeV] η Figure 2.: Comparison of he H and ZEUS analysis for ep eb bx ejjµx wih HERA I daa as a funcion of he ransverse momenum of he muon and is pseudorapidiy.

34 28 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION of beauy quarks was sudied a differen colliders, for example in p p collisions a he Sp ps, in γγ ineracions a LEP, in p p collisions a he TEVATRON and in ep collisions a HERA. The large mass of he beauy quark provides a hard scale and hus pqcd calculaions are expeced o give reliable resuls. Therefore i was a surprise, ha early measuremens performed a LEP and he TEVATRON show large discrepancies beween he measured daa and he NLO predicions (see e.g. [56]). In he meanime, boh he measuremens and he NLO calculaions were improved, which lead o a much beer agreemen. This can be seen for example in a recen measuremen from he CDF experimen [57]. Here, he fixed order and he nex o leading log (FONLL) calculaion scheme is used. In he firs publicaion [58] on beauy phooproducion a HERA he meanwhile well esablished mehod of using semileponic decays of a beauy hadron inside jes from he hadronisaion of he beauy quark was presened. To enrich he beauy sample, a muon wih a high ransverse momenum was required. In his measuremen, he NLO predicion underesimaes he daa, which was also seen a oher experimens. Several analyses for beauy in phooproducion a HERA were performed in he las years. dσ/dp T b (pb/gev) H 99- b je H 99- b µ je ZEUS 96- b µ je ZEUS (prel) 5 b µ je H (prel) 6/7 b µ je ZEUS b e ZEUS 2 pb - b e H 97- b D* µ ZEUS 96- b D* µ ZEUS 4 pb - bb µ µ HERA dσ/dp b T (ep ebx) Q 2 <GeV 2,.2<y<.8, η b < 2 NLO QCD (FMNR) 2 µ = /4 (m 2 + p 2 T ) k T fac. (LZ J23 se ) <p T b > (GeV) Figure 2.: Several analyses for beauy in phooproducion performed a HERA from he H and he ZEUS experimen.

35 2.. RECENT RESULTS OF HEAVY QUARK PRODUCTION 29 A collecion of hese resuls is summarised in figure 2.. In a recen H measuremen wih HERA I daa [59] a leas wo jes accompanied by a muon associaed o one of hese jes are required. The exracion of he beauy fracion is done using a combinaion of he p rel and he lifeime mehod. A similar analysis in a slighly differen phase space was performed by ZEUS [6]. Here, only he p rel mehod is used o obain he fracion of beauy evens. Boh resuls of H and ZEUS agree reasonably in he overlapping region. The cross secions of boh measuremens as a funcion of he ransverse momenum p µ and he pseudorapidiy of he muon η µ are shown in figure 2.. For boh resuls he NLO calculaion is also ploed. In general a good agreemen for he daa and he NLO predicion [6] is observed excep for he firs p µ bin in he range 2.5 GeVo3.3 GeV of he H analysis. This discrepancy is also seen in he firs bin of he cross secion as a funcion of he ransverse momenum of he highes p je. Also a endency of a oo low NLO predicion in he very forward region for he muon is observed in boh he H and ZEUS analyses. To clarify hese discrepancies and o obain a deeper undersanding of beauy in phooproducion, i is ineresing o repea he above described measuremen wih a higher saisical precision as i is done in his hesis. I is hus possible o measure also double differenial cross secions. In his analysis, he regions of direc and resolved processes are invesigaed furher.

36 3 CHAPTER 2. HEAVY QUARK PHOTOPRODUCTION

37 Chaper 3 The Experimen This chaper gives an overview of he HERA acceleraor and a descripion of he mos relevan componens of he H experimen for he presened analysis. Furher deails abou he H deecor can be found in [62]. 3. The HERA Acceleraor From 992 o 27, he Hadron Elecron Ring Acceleraor (HERA) a he Deusches Elekronen Synchroron laboraory (DESY) in Hamburg, Germany, provided high energy elecron and proon beams. The beam collisions occurred a wo ineracion poins, namely a he experimens H and ZEUS. The wo fixed arge experimens HERA-B and HERMES respecively used one of he wo beams. HERA has a circumference of 6.3 km wih four experimen halls as picured in figure 3.. The proon ring is equipped wih superconducing magnes while he elecron ring consiss of normal conducing magnes. In he firs running period from 992 o 2, named HERA I, an inegraed luminosiy of 3 pb was colleced wih he H experimen. The accumulaion of luminosiy as a funcion of ime is illusraed on he righ-hand side in figure 3.. During he years 2 o 23 a luminosiy upgrade was performed. New focussing magnes were insalled close o he ineracion regions. This made a modificaion of he H deecor necessary. The HERA II running period from 24 o summer 27 provided an inegraed luminosiy of almos 4 pb for each H and ZEUS. In his period proons a energies of 92 GeV collided wih elecrons or posirons a energies of 27.6 GeV yielding a cenre-of-mass energy of s 39 GeV. 3.2 The H Deecor The H experimen is an asymmeric, muli-purpose deecor, which covers a solid angle of almos 4π. The deecor s weigh is approximaely 28 and is dimensions are 2 m 5 m m. Due o he higher energy of he proons and heir hadronic properies, he deecor is more insrumened o proon direcion. 3

38 32 CHAPTER 3. THE EXPERIMENT (a) (b) HERA Hall WEST (HERA-B) HASYLAB DORIS Hall NORTH (H) Hall EAST (HERMES) Elecrons / Posirons Proons Synchroron Radiaion H Inegraed Luminosiy / pb - Saus: -July elecrons posirons low E HERA-2 HERA- DESY PETRA Hall SOUTH (ZEUS) 5 5 Days of running Figure 3.: On he lef a schemaic illusraion of he HERA ring, is preacceleraors and is four experimen halls can be seen. The righ-hand side shows he inegraed luminosiy for he HERA I and HERA II phase colleced wih he H experimen. In figure 3.2 a cross secion of he H deecor is depiced. The ineracion poin of he elecrons coming from he lef and he proons enering he deecor from he righ, is defined as he origin of he righ handed coordinae sysem of H. The z-axis corresponds wih he fligh direcion of he proons. The region wih posiive z values is called he forward region, he one wih negaive values is ermed he backward region. The x-axis poins a he cenre of he HERA ring and he y-axis poins upwards perpendicular a he x and z-axis. In spie of he cylindrical shape of he H deecor, a spherical coordinae sysem wih he coordinaes (r, θ, φ) is ofen used. r sands for he radial lengh, θ denoes he polar angle measured wih respec o he posiive z-axis and φ is he azimuhal angle relaive o he posiive x-axis. Insead of θ he so-called pseudorapidiy η = ln(an(θ/2)) is ofen used. Someimes he x y or r φ plane is also labelled as he ransverse plane. For aking he differen characerisics of decay paricles ino accoun, H consiss of several subdeecors which are buil cylindrically around he beam pipe. The firs componen, he decay paricles have o go hrough, is he racking sysem, which is explained in secion Aferwards, hey pass he calorimeer which is described briefly in secion The rackers and he calorimery are surrounded by he superconducing coil and he iron reurn yoke. Insrumened wih limied sreamer ubes he laer one operaes as he cenral muon deecor which is presened in secion A oroid magne was insalled, o cover he forward region as well.

39 3.2. THE H DETECTOR elecrons proons Figure 3.2: Technical view of he H deecor. Legend can be found in able Tracking Deecors The Cenral Tracking Deecor (CTD) delivers rack and verex informaion of charged paricles in he range <θ<7, he cenral region of he deecor. I consiss of five radial componens (see figure 3.3) wihin a solenoidal magneic field of.6 T which causes curved racks, depending on he ransverse momenum of he paricle. The componens of he CTD are described briefly in he nex secions, as hey play an imporan role for his hesis. The very forward region is equipped wih he Forward Tracking Deecor (FTD), which is designed o measure racks in he region smaller han 2. Cenral Silicon Tracker (CST) In 995 he H experimen was equipped wih a verex deecor, he Cenral Silicon Tracker (CST). I provides precise racking and verex informaion in he cenral region, which is very imporan for his analysis. In 2 a luminosiy upgrade of HERA necessiaed a redesign of he CST owing o a modified shape of he beampipe. Deails concerning he redesign can

40 34 CHAPTER 3. THE EXPERIMENT No. Subdeecor Abbreviaion Tracking Deecors Forward Silicon Tracker FST 2 Cenral Silicon Tracker CST 3 Backward Silicon Tracker BST 4 Cenral Tracking Deecor CTD 5 Forward Tracking Deecor FTD Calorimery 6 Elecromagneic Spaghei Calorimeer em. SpaCal 7 Hadronic Spaghei Calorimeer hadr. SpaCal 8 Elecromagneic Liquid Argon Calorimeer em. LAr 9 Hadronic Liquid Argon Calorimeer hard. LAr Muon Sysem Cenral Muon Deecor (Insrumened Iron) CMD Forward Muon Deecor FMD Table 3.: Lis of subdeecors of he H experimen. A skech of he cenral racking deecor is given in figure 3.3. Ouer Cenral Je Chamber (CJC2) Cenral Ouer z Chamber (COZ) Inner Cenral Je Chamber (CJC) Cenral Inner Proporional Chamber (CIP) Cenral Silicon Tracker (CST) Figure 3.3: Radial view of he cenral racking deecors for he HERA II period.

41 3.2. THE H DETECTOR 35 be found in [63]. The CST iself was buil in a collaboraion of PSI, ETH and he Universiy of Zürich [64] and consiss of wo layers wih double-sided silicon srip sensors, which are described in [65]. The srip sensors are oriened in such a way, ha he p side allows a precise measuremen of rack poins in he coordinaes rφ. The srips on his side are parallel o he beam axis. The srip pich on he p side amouns o 5µm. The n side allows a measuremen of he z coordinae. Here he srips are oriened perpendicular o he beam axis wih a pich of 88 µm. The single hi resoluion in rφ amouns o µm [66]. The inner layer has 2 ladders and he ouer layer has 2 ladders, as illusraed in figure 3.3. Each ladder consiss of 6 sensors, alogeher he CST is equipped wih 92 silicon sensors on 32 ladders. Every ladder consiss of 2 half ladders (see figure 3.4) wih 28 srips per half ladder. These 64 half ladders and 892 srips can be read ou individually. The readou is performed by he APC 28 readou chip which was developed a PSI [67], [68]. The analog daa are hen digiized and processed. The CST is sensiive o charged paricles, which produce pairs of posiive and negaive charge carriers when crossing a half ladder. A difference of elecrical poenial beween boh sides of he sensors leads o a drif of he charge carriers, which are hen read ou. The signals are classified in he hi finding algorihm [69] and a cluser candidae is defined, if one or several neighbouring srips wih signals a leas one sigma above he noise level are found. For each cluser candidae, he sum of he srip significances is calculaed, defined as raio beween he signal and he respecive noise RMS value. A cluser is acceped as hi if he summed significance is a leas five. The hi posiion is approximaed by he cener of graviy of he srip signals belonging o he cluser. The cener of graviy is calculaed separaely for he p and n side. For he nex sep, in he algorihm hree dimensional space poins have o be found by combining he clusers of boh sides. There are wo kind of his: his which are linked o a good rack are called signal his and hose which could no be linked are called background or noise his. The signal his are linked o a reconsruced rack provided by he cenral je chamber, which is described briefly in secion Cenral Inner Proporional Chamber (CIP) The Cenral Inner Proporional Chamber (CIP) is a muliwire proporional chamber wih wires parallel o he beam, arranged in five layers. The CIP surrounds he CST and covers he range 2.7 cm<z<4.3 cm and he angular region <θ<69. The readou is performed by 96 readou pads arranged in a projecive geomery. The spaial resoluion of he CIP in z amouns o.5 cm. The polar accepance of he CIP allows a rejecion of proon induced background wih a rue or apparen verex posiion ouside he H deecor a -5 cm o -2 cm. Informaion on he even iming, he rack mulipliciy and he significance of he even verex are delivered o he cenral rigger logic.

42 36 CHAPTER 3. THE EXPERIMENT CST Half Ladder p-side: carbon fiber rail rφ-srips 25 µm implan pich 5 µm readou pich aluminium wire bonds 34 mm vias meal- o meal-2 z-srips 4.4 mm 88 µm pich 64 readou lines on 2nd meal layer n-side: APC28 amplifier and pipeline chip Decoder chip Ceramic Hybrid 22 mm Kapon cable Figure 3.4: The p and n side of a CST half ladder. Cenral Je Chamber (CJC) The Cenral Je Chamber (CJC) is he main racking device of he H deecor, since he basic charged rack idenificaion and rajecory measuremen relies on his deecor. The CJC is divided ino wo pars: he inner (CJC) and he ouer je chamber (CJC2). The inner chamber is locaed beween he CIP and he COZ while he ouer one is insalled around he COZ. They cover an polar angle range of <θ<7 beween a radius of 2 cm and 85 cm. The CJC consiss of 3 drif cells conaining 24 sense wires, while he CJC2 has 6 drif cells wih 32 sense wires. To be able o measure he curved racks, he sense wires srung parallel o he beam axis are iled by 3 in he radial direcion. This makes sure ha paricles from he ineracion verex raverse more han one drif cell, which avoids drif ambiguiies due o mirror rack segmens. In he rφ plane, a resoluion of 3 µm is achieved. The resoluion in z amouns o 22 mm and is larger han in rφ, sincehez posiion is deermined by charge division. Cenral Ouer z Chamber (COZ) The Cenral Ouer z Chamber (COZ) complemens he CJC info by providing a precise measuremen of he z posiion. I has a resoluion of 35 µm and covers he polar angle range 24 <θ<57. The COZ is locaed beween he CJC and CJC2 as shown in figure 3.3 and has a cylindrical shape. I consiss of 24 idenical rings wih a lengh of 9 cm in z direcion (L COZ =2.6 m). Each of hese rings is divided ino 24 drif cells in φ and conains four sense wires and hree pairs of poenial wires srung perpendicular o he beam line.

43 3.2. THE H DETECTOR Calorimery The H deecor is equipped wih wo main calorimeers: he liquid argon calorimeer in he forward and cenral region and he spaghei calorimeer, which covers he backward domain. Due o he fac ha in phooproducion he incoming elecron is scaered under a small angle escaping deecion he calorimeers are used o deec he absence. Boh calorimeers are used for he reconsrucion of he hadronic final sae. In addiion, he liquid argon calorimeer is used for he idenificaion of muons and elecrons e.g. from semileponic decays of heavy quarks. The following secions give a brief overview of he wo calorimeers. Liquid Argon Calorimeer (LAr) The Liquid Argon Calorimeer (LAr) covers he forward and he cenral region beween 4 <θ<53 of he H deecor and is described in deail in [7]. The inner elecromagneic par (ECAL) uses lead absorbers while he ouer hadronic secion (HCAL) consiss of seel absorbers. Boh deecor componens use liquid argon as acive maerial. Therefore he calorimeer is enclosed by a cryosa. The LAr is divided ino eigh wheels along he z-axis and each of hem is segmened ino eigh ocans in φ, as illusraed in figure 3.5. To avoid long ravel disances hrough a layer, he absorber and deecor layers are oriened in such a way, ha he impac angle of paricles coming from he ineracion poin is larger han 45. Therefore he deecor and absorber layers are insalled perpendicular o he beam axis in he forward region while he layers in he cenral region are parallel o he beam axis. The response for hadronic showers is roughly 3% smaller han for elecromagneic ones. The LAr is a calorimeer of non compensaing ype. The compensaion is obained during he reconsrucion, using sofware algorihms. Following [7] he energy resoluion of he LAr calorimeer is σ(e e ) E e σ(e π ) E π. % for he ECAL and Ee [GeV] (3.).55 2% for he HCAL. Eπ [GeV] (3.2) Spaghei Calorimeer (SpaCal) The Spaghei Calorimeer (SpaCal) covers he backward region of he H deecor beween 53 <θ<74.5 and is described in deail in [72]. I is divided ino an elecromagneic secion and a hadronic par, while boh use lead as absorber and scinillaing fibres as deecor maerial. The elecromagneic par consiss of 5 quadraic lead absorber cells which have an acive volume of cm 3 corresponding o approximaely 27.5 radiaion lenghs X.These cells conain scinillaing fibres which are pairwise arranged in submodules, where eigh of hem build a module. The fibres have a diameer of.5 mm and direc he ligh hrough

44 38 CHAPTER 3. THE EXPERIMENT Figure 3.5: The lef-hand side shows a laeral view of he upper half of he Liquid Argon calorimeer while on he righ he cross secion of a wheel in he barrel is illusraed. ligh mixers o Phoomuliplier Tubes (PMT). The hadronic secion is build similar o he elecromagneic par, bu has nearly hree imes larger edge lenghs. The cell deph corresponds o one ineracion lengh and herefore almos all elecrons are sopped in he elecromagneic par of he SpaCal. The hadronic par is mainly used as a veo agains hadrons, which fake a scaered elecron Muon Sysem The muon sysem of he H deecor is divided ino wo pars, he Cenral Muon Deecor (CMD) and he Forward Muon Deecor (FMD). The FMD covers he polar angle range 3 <θ<7 and is no used in his analysis. The CMD is embedded in he iron reurn yoke of he superconducing coil and is divided ino 64 modules which are illusraed in figure 3.6. I consiss of four subdeecors (see figure 3.6), he Forward EndCap (FEC), which covers he range 5 <θ<35, he forward and backward Barrel (BAR, 35 <θ<3 ), and he Backward EndCap (BEC), which is designed o deec muons in he range 3 <θ<75. The endcaps consis of an inner (modules 6-) and ouer par (modules 54-59). The modules are composed of en iron layers, each wih a hickness of 7 cm. There are nine gaps in beween hem, which are insrumened wih limied sreamer ubes, which are filled wih a mixure of Argon and Isobuane (< %). They have a cross secion of 9 9mm 2 and heir insides are coaed by graphie o ac as a cahode. A double layer of sreamer ubes is insalled in he gap beween he fourh and he fifh iron layer only. Addiionally, hree layers of sreamer ubes are placed on boh sides of he iron reurn yoke, he so-called muon boxes. In oal, he CMD has 6 layers. Spaial resoluion along he wire-axis is achieved hrough he ouer wo layers of he muon boxes and he double layer in he middle. They are read ou via srip elecrodes, insalled perpendicular o he sense wires. The resoluion of hese layers is σ 4 mm perpendicular

45 hgi 3.2. THE H DETECTOR 39 and σ 2 mm parallel o he sense wires. The measuremen of he momenum is raher poor wih only he CMD informaion and gains values of dp/p 3% [73]. 6 3 Souh 7 Backward Barrel x y z Forward Barrel A B C D 3 25 E A B C D Backward Endcap E Forward Endcap 39 4 Norh x y 3 25 z h g i Iron Srips Pads Srips and Pads Figure 3.6: On he lef an overview of he 64 modules of he cenral muon deecor is illusraed. The righ-hand side shows a module and is layers in more deail Triggering a H The H rigger sysem selecs ineresing physics evens and rejecs background evens aiming for he smalles dead ime possible. A a collision rae of.4 MHz, a recording of all evens would be impossible as he deecor can only be read ou a a rae of 5 Hz. The rejeced background evens arise mainly from ineracions of he proon beam wih he beam pipe (beam wall) or residual gas as well as from beam halo and cosmic muons. The four level rigger sysem was opimized o suppress background evens efficienly wih minimal dead ime. Only he second and hird rigger level produce dead ime. The firs rigger level does no induce dead ime iself. The fourh rigger level operaes as a filer, reducing he amoun of daa wrien o ape for he offline analyses. In he following secion, he four levels of he H rigger sysem are described briefly. Furher informaion can be found for insance in [74]. The rigger elemens of he required subriggers used in his analysis are presened.

46 4 CHAPTER 3. THE EXPERIMENT Level The decision of he firs rigger level (L) is based on he informaion of several subdeecors of H and akes 2.3 µsec, which corresponds o 24 bunch crossings. The daa coming from he subdeecors is wrien o pipelines and he daa aking coninues during he deerminaion of he rigger decision. A his level no dead ime is inroduced. Upon a posiive rigger decision, a signal is sen o sop he pipeline and o read ou he curren even. The readou of he daa akes abou msec, leading o 5% dead ime a 5 Hz. The subdeecors provide 256 Trigger Elemens (TEs) in oal, which are combined o up o 92 SubTriggers (STs) in he Cenral Trigger Logic (CTL). The TEs are based on signals coming from he muon sysem as well as from he cenral racker and energy deposiions in he calorimeers. To be able o conrol he accep rae of L and o opimize he usage of he available bandwidh some of he subriggers are prescaled. A prescale facor of n means, ha only every n-h posiive decision is aken ino accoun. Therefore, he prescaled subriggers collec only a fracion of he luminosiy. The presened analysis requires subriggers which are prescaled wih average prescale facors unequal, bu close o one. Level 2 The second rigger level (L2) analyses he informaion from he differen subdeecors in more deail and is decision is available afer 2 µsec. L2 is used o ighen he oupu raes of he L subriggers from khz down o 5 Hz. Three rigger sysems are implemened, namely he Topological Trigger (L2TT), he Neural Nework rigger (L2NN), and he Fas Track Trigger (FTT). L2TT and he L2NN combine informaion coming from he rackers, calorimeers, and he muon sysem. Level 3 The hird rigger level (L3) sared is operaion a he beginning of 26. I was planned from he early sages of H and before is acivaion, he informaion of L2 was direcly delivered o L4. The hird rigger level provides a parial even reconsrucion based on he rack informaion from level 2, he muon sysem and he calorimeer. The level 3 rigger provides 48 rigger elemens o he cenral rigger logic, which verifies he TE condiions and rejecs he even, if he condiion is no fulfilled. I is kep hough, if a subrigger does no have any level 3 condiion. This rigger level mus ensure a maximum oupu rae of 5 Hz. Level 4 The fourh rigger level (L4) provides a full reconsrucion of he riggered even afer confirming he decisions of he former levels. For reducing he amoun of wrien daa o ape, background finders rejec unwaned evens like cosmic muons or residual gas or beam pipe evens. % of hese evens are kep and used for monioring he background finders. The evens ha remain, which are of physics ineres, are caegorized ino classificaion bis, based

47 3.2. THE H DETECTOR 4 on he presence of a hard scale, such as a high Q 2,highp rack, high p je or missing E. If he even fulfills one of he laer requiremens or passes one of he final sae finders, i is acceped wihou prescale. If his is no applicable, i is downscaled and receives a L4 even weigh. The class of ineres for his hesis is number 6, which sands for heavy flavour physics. Afer full reconsrucion on L4, he evens are wrien o so-called Physics Oupu Tapes (POT) wih a rae of roughly 2 Hz, which conain he full even informaion (5 kb/even). A fracion of informaion mos relevan for analysis is wrien o Daa Summary Tapes (DST), which is usually sufficien for physics analyses (2 kb/even).

48 42 CHAPTER 3. THE EXPERIMENT

49 Chaper 4 Even Reconsrucion The signal exracion of heavy quarks used in his hesis explois he long lifeime and he large mass of hadrons conaining heavy quarks. The lifeime is derived from he reconsruced impac parameer, while he mass is exploied using he relaive ransverse momenum of he seleced muon candidae o he axis of he associaed je. This chaper presens he main aspecs of he even reconsrucion, which are applied o he objecs enering hese disribuions. In secion 4., he reconsrucion of muon candidaes is described briefly. Secions 4.2 and 4.3 conain relevan aspecs of he rack reconsrucion. The racks are basically measured wih he CJC and he measuremen is improved using he CST informaion. In secion 4.4, he uning of he CST simulaion is presened. This secion also conains a discussion of he CST efficiency and conribuions o he rack resoluion. The following secions concenrae on he reconsrucion and calibraion of hadronic final sae objecs and jes. In he las secion of his chaper, he used rigger elemens and heir efficiencies are discussed. 4. Muon Idenificaion and Reconsrucion Muons are idenified in he H experimen by hree subsysems: he racking sysem, he LAr and he muon deecors. The main idenificaion uses reconsruced racks in he CMD. Muon racks are classified by heir qualiy Q µ = Q iron + Q cal, which is he sum of he qualiy deermined in he CMD Q iron and he qualiy of he rack in he LAr calorimeer Q cal.the deerminaion of he single qualiies is explained in he following. In his analysis, he informaion of he insrumened iron is used o idenify muon candidaes. The informaion of he LAr is no used, bu described here for compleeness. Only a few hadrons are able o reach he CMD and are wrongly idenified as muons. Therefore, he puriy of he muon idenificaion in he muon deecor is very high. Muons in he Insrumened Iron The energy losses of muons in he deecor originae mainly from ionisaion a here considered energies. The energy loss due o Bremssrahlung is negligible, since he cross secion for 43

50 44 CHAPTER 4. EVENT RECONSTRUCTION H Iron Tracks ρ < cm z < cm number of hi layers 3 number of firs hi layer 5 number of las hi layer 2 link probabiliy > 4 Table 4.: Selecion crieria for H Iron Tracks. Bremssrahlung is proporional o he inverse of he squared paricle mass. Based on he fac, ha he muon mass is roughly 2 imes larger han he elecron mass, Bremssrahlung is heavily suppressed for muons wih respec o elecrons. According o he Behe-Bloch equaion, muons are minimal ionising a energies of abou 3 MeV. To be able o reach he cenral muon sysem, he momenum of he muon has o be greaer han.5 GeV. Inhe insrumened iron, muons lose roughly 9 MeV per iron plae. To allow he reconsrucion of a rack, he muon has o raverse several iron plaes. Therefore, he energy of a muon has o be larger han 2 GeV o be deeced in he insrumened iron wih an efficiency larger han 5% [75]. The H reconsrucion sofware HREC performs a rack fi over all his in he CMD o idenify muons in he insrumened iron. These racks are also called ouer racks. They are required o link o an inner rack, since he momenum and angle resoluion of racks reconsruced in he insrumened iron is no sufficien for his analysis. Inner racks are reconsruced using he cenral and forward racking sysem. The linking beween inner and ouer racks is performed by HREC. Here, only ouer racks are used, which fulfil cerain qualiy crieria lised in able 4.. The ouer racks are required o have his in a leas hree ou of 6 layers of he muon sysem. The firs hi should appear wihin he firs five layers, while he las hi is required o be a leas in he second layer. The disance of closes approach dca of he ouer rack o he even verex has o be smaller han one meer in cylindrical coordinaes (ρ, z ). Inner racks, which mach ouer racks in he polar and azimuhal angle are seleced. These seleced inner racks are exrapolaed ino he muon sysem. Muliple scaering and energy losses due o ionisaion are aken ino accoun assuming ha he inner rack is a muon. Afer he linking procedure is done, he compaibiliy of each rack pair is performed. For his purpose a χ 2 value is calculaed, which depends on he rack momena, heir polar and azimuhal angles and he derivaives of boh angles. The inegral of χ 2 gives he linking probabiliy P µ link (χ2 ), which needs o be larger han P µ link (χ2 ) >. for iron muon candidaes in his analysis. A qualiy of Q iron = is assigned o a muon candidae in he CMD, if i fulfils all cus lised in able 4.. Muons in he LAr Elecrons generae elecromagneic showers and are absorbed in he firs layers of he liquid argon calorimeer. Hadrons produce showers conaining an elecromagneic and a hadronic

51 4.. MUON IDENTIFICATION AND RECONSTRUCTION 45 componen and are sopped as well in he LAr. Whereas muons are Minimal Ionising Paricles (MIPs), which have an average energy loss of abou de/dx MeV/cm in lead. They can be idenified in he LAr via heir uniform energy deposiion wihin a narrow cone, since hey do no produce showers. The high granulariy of he LAr wih roughly 45. cells makes i possible o use his signaure for muon idenificaion. To be able o reach he LAr, he muon racks need a minimal ransverse momenum of 8 MeV. The algorihm KALEP [76], [77], which is performed in he H even reconsrucion, searches for he above described signaure of MIPs in he LAr calorimeer. Four discriminaors are deermined, which are based on he summed energy of he calorimeer cells and on he opology of he responding cells. These four discriminaors are used o define he qualiy of each muon rack. Muon Reconsrucion Efficiency Exensive sudies of he efficiency o reconsruc muons in he LAr and in he insrumened iron were performed in [78] and in [75]. The invesigaions in [78] are for low p measuremens and [75] invesigaes higher p regions. In his analysis, a muon candidae in he insrumened iron wih a ransverse momenum of a leas p µ > 2.5 GeV is required, which corresponds o he higher p region. Therefore, he resuls of [75] are used. I is found, ha he reconsrucion efficiency of muon candidaes in he insrumened iron are well described by he Mone Carlo simulaion (solid line) above p µ > 2.5 GeV as depiced in figure 4.. On he lef hand side he efficiency o find a muon in he insrumened iron wih a ransverse momenum larger han p µ > 2.5 GeV as a funcion of he polar angle θ is shown. The efficiency gains values around roughly 8%. In figure 4. (b) he raio of he daa efficiency over he simulaion efficiency is ploed. Boh figures are aken from [75]. Based on hese sudies, no correcion facors for he simulaion in his hesis are applied. efficiency (a) p > 2.5 GeV ε DATA /ε MC Θ in degrees Θ in degrees (b) Figure 4.: Efficiency o idenify muon candidaes in he insrumened iron for p µ funcion of he polar angle θ. Boh figures are aken from [75]. > 2.5 GeVasa

52 46 CHAPTER 4. EVENT RECONSTRUCTION 4.2 Impac Parameer Evens conaining heavy quarks show an experimenal signaure, which can be used o disinguish hem from evens conaining only ligh quarks. As described in secion 2., beauy and charm flavoured hadrons have lifeimes of he order O( psec), which lead o a resolvable disance beween racks originaing from he decay and he primary verex. The decay process and he corresponding variables are shown in figure 4.3 in he rφ-plane. A heavy hadron is produced a he primary verex which lies inside he beam spo. The long lifeime enails a ravel of usually a few hundred micromeers in he lab frame for he hadron (cf. able 2.3). The decay of he hadron ino charged paricles produces a decay verex, which is also called he secondary verex. The ravelling disance beween he primary and he secondary verex is referred o as he decay lengh. In he rφ-plane, he displacemen of he rack can be quanified via he so-called impac parameer δ, which denoes he closes disance beween he paricle s rajecory and he primary verex. To approximae he fligh direcion of he hadron, a je-based reference axis is used. A sign for he impac parameer is inroduced, which akes he je conaining he muon as a reference. If he angle β beween he axis of he associaed je and he line, joining he primary verex o he poin of closes approach of herack,islesshan9, hen he sign is posiive. If β is larger han 9, i is negaive. A schemaic illusraion of he sign convenion is shown in figure 4.2. The widh of he impac parameer disribuion reflecs he finie rack and verex reconsrucion resoluions. Evens wihou lifeime informaion have a reconsruced specrum of δ which is symmeric around zero, while evens wih decays of long-lived paricles are expeced o have an asymmeric disribuion wih an excess a posiive impac parameers. The region of large posiive impac parameers is expeced o be dominaed by muons from decays of beauy flavoured hadrons. 4.3 Track Reconsrucion The rack reconsrucion is based on informaion from he cenral racking deecors. The goal is he reconsrucion of he rajecory and he deerminaion of five rack parameers κ, φ, θ, dca, z a he verex. This is achieved by performing a fi o he measured his < /2 = + > /2 = je primary verex je primary verex rack rack Figure 4.2: Sign convenion of he impac parameer δ wih respec o he angle β.

53 4.3. TRACK RECONSTRUCTION 47 je axis r plane decay racks secondary verex decay lengh beam spo dca impac parameer primary verex Figure 4.3: Schemaic view of he impac parameer in he rφ plane. in he CJC. The uniform magneic field parallel o he z-axis bends he racks of charged paricles in he rφ-plane. Due o he Lorenz force he bending radius is proporional o he srengh of he magneic field and inverse proporional o he ransverse momenum of he charged paricle. The fligh rajecory can be described by a helix. I can be parameerized in H coordinaes as a funcion of he arclengh s: x(s) =dca κ sin(φ )+ κ sin(φ + κs), (4.) y(s) = (dca κ cos(φ ) κ cos(φ + κs)), s (4.2) z(s) =z + s co(θ). (4.3) The azimuhal angle φ describes he fligh direcion of he paricle in he ransverse plane wih respec o he posiive x-axis as depiced in figure 4.4. I is measured a he poin of closes approach o he z-axis, which is defined as saring poin of he helix (s = ). In he zs plane he rack rajecory is a sraigh line which crosses he z-axis a he poin z.the angle θ beween he rajecory and he z-axis describes he fligh direcion wih respec o he posiive z-axis. The curvaure κ is he inverse of he bending radius r and has a posiive sign for negaive charged paricles and vice versa. The disance of closes approach dca sands for he minimal radial disance of he rack o he origin (, ) in he rφ-plane. If he origin lies

54 48 CHAPTER 4. EVENT RECONSTRUCTION y rack s rack r= (,) primary verex x z z dca Figure 4.4: The rack parameers κ, φ,θ,dcaand z in he rφ- andzs-plane. inside he circle, which describes he rack, he signs of dca and κ are equal. If he origin lies ouside, he sign of dca is chosen opposie o he one of κ CST improved Tracks The momenum resoluion and he precision of he rack rajecories measured by he CJC is improved by adding he CST informaion. The CJC racks are associaed (linking) o CST his and he deerminaion of he improved rack parameers is done via a CJC-CST combined rack fi. This renders possible o resolve primary and secondary verices of long lived heavy hadrons, which is crucial for his analysis. The selecion of he racks required in his analysis is discussed in chaper 5. The Track Fi The linking of CST his and non-verex fied CJC racks is done in he rφ- andzs-plane separaely using he H sofware CSTLIN [79]. This permis o use p-side (rφ) informaion only o obain improved rφ rack parameers of he CST improved racks. The rack fi is divided ino wo seps: firs, a circle fi in he rφ-plane is performed which deermines κ, dca and φ. Second, a sraigh line fi is done in he zs-plane o deermine θ and z. The inpu for he circle fi are he rack parameers of he non-verex fied CJC racks, which are sored in he BOS bank DTNV. Furher inpu are seleced CST his. For each CJC rack and all possible suiable combinaions of p-side his from boh CST layers, he circle rack fi is applied. This circle fi minimizes a χ 2 funcion [79] depending on he rφ rack

55 4.4. TUNING OF THE CST SIMULATION 49 parameers obained by he CJC and heir covariance marix. Furhermore, he disance of he rack circle and he CST his in he inner and ouer layer as well as he corresponding error of he disance are included. The CST hi combinaion and corresponding rack fi is chosen, which gives he smalles χ 2 of he rack fi. Soluions wih a maximum number of CST his are preferred as long as hey have a reasonable χ Primary Verex Reconsrucion The usage of he impac parameer requires a precise knowledge of he Primary Verex (PV) posiion in he plane ransverse o he beam axis. For each run, he average coordinaes x beam and y beam of he ep ineracion poin (beam spo) are defined by using he informaion of many evens conained in he run. The Run Verex (RV) is obained by a leas-squares fi. This fi minimizes he overall disance of closes approach of racks o he run verex. I uses only well-measured non-verex fied CST improved racks wih high ransverse momena. This run verex is used as saring poin for an even-wise primary verex fi o seleced racks. The primary even verex fi is performed by he H sofware CSPRIM [8] wihin wo seps. A firs, he deerminaion of he verex posiion in he xy plane is done. As second sep, he z coordinae is reconsruced from seleced racks which are mached o he xy verex posiion. In his analysis, he fi of he primary even verex is performed afer excluding he seleced muon rack candidae, which comes from he secondary verex. This fi is based on CST improved non-verex fied racks. Only racks are used, which are compaible wih he run verex wih wo sandard deviaions. 4.4 Tuning of he CST Simulaion In his secion, he uning of he CST Mone Carlo simulaion is described [8]. The CST iself is presened in secion The Mone Carlo simulaion of he CST should provide a descripion of all relevan aspecs of he daa, such as efficiency, resoluion, mulipliciy and disribuion of dead channels. The simulaion should also provide a reasonable descripion of he noise presen in daa. For his ask, he occupancy and he noise ampliude in he simulaion are adjused o he daa. Tuning of he Signal o Noise Raio There are wo kind of his: his which are linked o a good rack ge named signal his, and hose which could no be linked are called background or noise his. The significance or signal o noise raio for signal and noise his before he uning shows a discrepancy beween daa and Mone Carlo simulaion as can be seen in figure 4.5 (a). The daa used here, was colleced a he beginning of 26 by he H deecor. For geing a beer agreemen of daa and Mone Carlo simulaion he significance disribuion is fied for boh hi ypes. For he background, a sum of wo exponenials is used. For he signal his, a Landau disribuion is added o he background funcion. Afer fiing he daa, he parameers of hese fis are used o conver he significances of he simulaion. This is done separaely for each of he

56 Number of His Number of His Number of His Number of His 5 CHAPTER 4. EVENT RECONSTRUCTION -2 (a) Before Tuning Daa MC Signal His Enries Mean RMS χ / ndf / 36 Prob 4.92e-5 norm.462 ±. p ±.46 mpv 9.57 ±.6 sigma ±.47-2 (b) Afer Tuning Enries Mean RMS χ / ndf / 36 Prob 4.92e-5 norm.462 ±. p ±.46 mpv 9.57 ±.6 sigma ±.47-3 Noise His Signal/Noise Signal/Noise Figure 4.5: Signal o noise raio of boh hi ypes on one half ladder side for 26 daa (doed black line) and Mone Carlo simulaion (doed blue line) in comparison. Figure (a) shows he Mone Carlo simulaion before he uning and in (b) he uning resul is illusraed. The solid lines represen he used fi funcions. The same uning procedure was performed for all 64 half ladders separaely. 64 half ladders, because heir disribuions are significanly differen. Afer his adjusmen, he Mone Carlo simulaion describes he daa much beer han before as shown in figure 4.5 (b). Descripion of Dead Channels Each of he 64 half ladders has an individual number of dead channels. To check which of he 64 channels of each half ladder do no work properly or are dead, he so-called cener of (a) Before Tuning (b) Afer Tuning MC simulaion MC simulaion Channel Number Channel Number Figure 4.6: Disribuion of he cener of graviy of his in unis of srip numbers of one half ladder side in he Mone Carlo simulaion. Figure (a) shows he cener of graviy for one half ladder before he uning. No dead channels can be seen in ha plo while (b) depics he resul of adding dead channels.

57 Number of Evens 4.4. TUNING OF THE CST SIMULATION 5 Number of Evens (a) 3 Daa Before Tuning (b) Afer Tuning 2 MC Number of His Number of His Figure 4.7: Occupancy of one half ladder side for 26 daa (poins) and Mone Carlo simulaion (solid line) in comparison. Figure (a) shows a very high occupancy for he ununed simulaion while in (b) a good descripion of he daa can be seen. Again, his plo is done for one of he 64 half ladders. graviy of a cluser for he signal his is sudied. Before uning, he simulaion did no have any dead channels a all. Srips wih more han 5% deviaion of signal his, compared o he average occupancy of he respecive half ladder, are marked as dead in he Mone Carlo simulaion. The resul is exemplarily shown for one of he 64 half ladders in figure 4.6 for he Mone Carlo simulaion. The daa is no shown here. Adjusmen of he Occupancy For a beer descripion of he elecronic background, an adjusmen of he occupancy is necessary. The occupancy is defined as he number of noise his per half ladder per even. In he simulaion, he occupancy is oo high before uning, which can be seen in figure 4.7. The noise ampliude is rescaled using he parameers sored in he bank CSNP, which sands for CST Noise Parameer. In his bank, all parameers conribuing o he noise ampliude are sored. This rescaling in he significance disribuion leads o a very good agreemen wih he daa. CST Efficiency Afer he uning procedure, a saisfacory descripion of he efficiency is obained. The oal CST rack finding efficiency includes he CST hi efficiency, he CJC-CST linking efficiency and losses due o inacive pars of he CST. The oal CST efficiency is defined as he fracion of racks measured by he CST wih Plink CST >. andncst his over all CJC racks. The linking probabiliy and he number of CST his are ploed in figure 4.2. Boh variables ploed wih he daa (poins) are reasonably described by he simulaion (solid line). These efficiency sudies are done using he final selecion cus as lised in able 5.3. The average CST rack finding efficiency amouns o roughly 7%. The oal CST efficiency is ploed as a funcion of he ransverse momenum of he muon rack in figure 4.8 (a) and

58 52 CHAPTER 4. EVENT RECONSTRUCTION (a) (b) CST efficiency H daa 6/7 PYTHIA CST efficiency H daa 6/7 PYTHIA µ p [GeV] µ θ [deg] Figure 4.8: The oal CST rack finding efficiency as a funcion of p µ (a) and θµ (b). The seleced muon racks are required o have a leas CST hi and a CJC-CST linking probabiliy of a leas %. in is polar angle in figure 4.8 (b). The Mone Carlo simulaion (solid line) describes he daa (poins) reasonably well in boh cases. To ake he remaining uncerainy of he Mone Carlo descripion ino accoun, an sysemaic error of 3% is esimaed for he oal rack finding efficiency. Before uning, he efficiency of he Mone Carlo simulaion was abou % higher han in he daa. The improvemen is mainly due o he above described correcions of he signal o noise raio in he simulaion. The efficiency is almos independen of he wo variables shown here and he disribuions are almos fla. The CST efficiency per half ladder is illusraed in figure 4.9 for daa (a) and he simulaion (b). The daa is modelled reasonably well by he simulaion, since he above described uning is done for each half ladder separaely. Boh disribuions are almos fla and show an efficiency of roughly 7%. The Mone Carlo simulaion end o be slighly higher han he daa. (a) (b) CST Efficiency H daa 6/7 CST Efficiency PYTHIA Half Ladder Number Half Ladder Number Figure 4.9: The oal CST rack finding efficiency as a funcion of he half ladder number for daa (a) and Mone Carlo simulaion (b). The seleced muon racks are required o have a leas CST hi and a CJC-CST linking probabiliy of a leas %.

59 4.4. TUNING OF THE CST SIMULATION Resoluions In his analysis, he resoluion of he impac parameer plays an imporan role. I has o be small enough, o be able o disinguish beween racks coming from long lived hadrons and racks of he zero lifeime combinaorial background. In addiion, a small sysemaic error is desirable, which is only possible if he impac parameer resoluion is well described. In figure 4., he various conribuions o he impac parameer are illusraed schemaically. The inrinsic resoluion of he CST for racks wih wo his amouns o 2 µm. This resoluion is due o uncerainies on he inernal alignmen of he CST wih respec o oher deecor componens. Muliple scaering effecs depend on he ransverse momenum of he rack and originae from he beam pipe and he firs layer of he CST. The conribuion is measured o be 7 µm/p [GeV]. Requiring one hi in he CST leads o a slighly worse resoluion. If he hi is in he ouer layer, he resoluion becomes a facor of wo worse [83], [84] Figure 4.: Schemaic view of he conribuions o he impac parameer resoluion. Made by PD Dr. Olaf Behnke [82] and slighly modified o illusrae he HERA II condiions.

60 54 CHAPTER 4. EVENT RECONSTRUCTION Conribuions from he primary verex fi depend on he reference poin of he impac parameer measuremen. To disenangle hese conribuions, he resoluion is sudied separaely for he run verex and he primary even verex as reference for he impac parameer. Primary Verex Resoluion The beam posiion is precisely known [83] and amouns o 26 e : σ x =8µm and σ y =2µm (4.4) 26/27 e + : σ x =92µm and σ y =23µm in x and y for he wo differen run periods, respecively. The maximal size of he primary even verex errors is given by he size of he ellipical beam spo. In figure 4. (a) and (b) he calculaed errors on he radial posiion of he primary even verex are depiced. The uncerainies on x PV and y PV are dominaed by he beam exensions due o small errors on he run verex parameers, which were obained wih high saisics when averaging over many evens. A comprehensive overview of he verex deerminaion and even reconsrucion wih he CST is for example given in [69]. The disribuion of σ(x PV ) gains values up o (a) (b) Tracks 3 2 Tracks 4 3 H daa 6/7 PYTHIA σ(x ) [cm] PV (c) σ(y ) [cm] PV (d) Tracks 5 Tracks x PV -x RV [cm] y -y [cm] PV RV Figure 4.: Calculaed errors on he primary verex posiion in x (a) and y (b), respecively. In figure (c) and (d) he difference of he reconsruced primary verex and he run verex are ploed. Shown are he daa (poins) and he PYTHIA predicion (solid line) in comparison.

61 4.4. TUNING OF THE CST SIMULATION 55 8 µm, which reflecs approximaely he widh of he beam spo in x. The primary even verex error in x of he daa (poins) is well modelled by he PYTHIA predicion (line). Figure 4. (b) shows he even verex error in y. The small beam spo size in y can hardly be resolved. The agreemen beween daa and he PYTHIA simulaion is reasonable. In figure 4. (c) and (d), he difference of he reconsruced primary verex and he run verex is depiced. While he projecion in x shows a well agreemen beween daa and he Mone Carlo simulaion, i is described reasonably in y. The disribuions have a RMS of 6 µm inx and of 7 µm iny. These values have o be compared o he beam spo size. Boh disribuions of he daa in y, figures 4. (b) and (d), are no described perfecly, ye sill reasonably, by he Mone Carlo simulaion. This ows o a non perfec simulaion of he beam il in he Mone Carlo. The beam il conribues o he error of he run verex and is herefore also migraed o he calculaion of he primary even verex error. The beam il in y is larger han in x and has herefore a higher impac on he calculaed errors in y. The beam spo size in y is already very small and he same holds for he calculaed primary even verex error. Thus he non perfec descripion of he daa in y by he simulaion has a negligible effec. Track Resoluion The rack resoluion can be invesigaed using he linking probabiliy Plink CST of CJC racks and CST his. This quaniy measures he accuracy of he covariance marix of he rack parameers direcly. The linking probabiliy is defined as P CST link (χ2,n)= e.5.5n d. (4.5) 2 N Γ(N/2) χ 2 Here χ 2 is aken from he combined fi of CJC racks and CST his in he rφ plane. The variable N is he number of degrees of freedom, which sands for he number of linked CST his. The linking probabiliy Plink CST is he probabiliy of having a larger χ2 value as obained by he minimizaion algorihm. The disribuion of Plink CST should be fla beween and if a good descripion of he rack resoluion is given. Exensive invesigaions concerning he undersanding of he rack linking probabiliy were performed in [82]. The covariance marix of he CST rack parameers consiss of wo pars: he inrinsic par and conribuions from muliple scaering. Boh pars are correced o achieve a good agreemen beween daa and Mone Carlo simulaion. For he inrinsic par correcion facors of f rφ =.35 and f rz =. are obained from he daa for he rφ plane and he rz plane, respecively. The Mone Carlo is hen smeared by help of hese parameers, since he rack resoluion in he Mone Carlo was oo opimisic before uning. Addiionally a correcion facor f MS =.22 for he muliple scaering is deermined in [82] for racks wih a ransverse momenum of p >.3 GeV. Following [49], his facor is chosen o be f MS =.9 o avoid an overesimaion. Since he ransverse momenum of he muon rack in his analysis is p > 2.5 GeV, muliple scaering effecs are negligible for he rack resoluion. The choice of hese hree parameers is proper, as he linking probabiliy is well modelled by he PYTHIA predicion as depiced in figure 4.2 (b). Here, all analysis

62 56 CHAPTER 4. EVENT RECONSTRUCTION (a) (b) Evens 8 6 Evens 6 H daa 6/7 PYTHIA CST His N CST P link Figure 4.2: The number of CST his (a) in he analysed sample and he CJC-CST linking probabiliy (b) in he rφ plane. The verical line in (b) represens he cu a %. Daa (poins) and he PYTHIA predicion (line) in comparison. cus are applied (able 5.3), besides he cu on he linking probabiliy iself o show he full disribuion. The analysis cu is locaed a Plink CST >. and represened by he verical line in figure (b). The number of CST his in figure 4.2 (a) shows a good agreemen for he daa and he PYTHIA predicion. For his disribuion, all analysis cus are applied (able 5.3) including he cu on he linking probabiliy. Impac Parameer Resoluion The resoluion of he impac parameer consiss of conribuions from he rack resoluion, he beam spo and he primary verex resoluion. In order o separae conribuions from he primary verex fi, he run verex and he primary even verex are used as reference in he impac parameer definiion separaely. Due o echnical reasons, he analysed daa and Mone Carlo samples for hese sudies conain idenified muons. The impac parameer wih respec o he run verex is sudied firs. For racks wih a ransverse momenum of minimum 2.5 GeV and a leas one CST hi, he Gaussian widh of he impac parameer disribuion dca RV as a funcion of he azimuhal angle φ of he rack is ploed in figure 4.3 (a). The disribuion represens he measured impac parameer resoluion of he daa (full poins) in comparison o he Mone Carlo simulaion (open poins). The resoluion values are beween 9 2 µm, depending on he rack direcion in φ. Replacing he run verex wih he primary even verex in he impac parameer definiion, he φ dependence is decreased. This is illusraed in figure 4.3 (b). Here, he gaussian widhs of he impac parameer, wih respec o he primary even verex as a funcion of he azimuhal angle φ, is shown. The disribuion is almos fla and dominaed by he rack resoluion, which is also fla. A mean resoluion of 8 µm is achieved in boh, daa and Mone Carlo simulaion.

63 4.5. RECONSTRUCTION OF THE HADRONIC FINAL STATE 57 (a) (b) ) [cm] σ(dca RV.2.5. H daa 6/7 PYTHIA ) [cm] σ(dca PV.2.5. H daa 6/7 PYTHIA φ [deg] φ [deg] Figure 4.3: The gaussian widh of he impac parameer wih respec o he run verex dca RV in (a) and wih respec o he primary even verex dca PV in (b) as a funcion of he azimuhal angle φ of he rack. The Daa (full poins) and he Mone Carlo simulaion (open poins) are shown in comparison. 4.5 Reconsrucion of he Hadronic Final Sae In his secion, he reconsrucion of he Hadronic Final Sae (HFS) is described briefly. The reconsrucion is performed by he Hadroo2 [85] algorihm. The informaion of he rack measuremen and he calorimeer is used as he inpu of he algorihm o reconsruc he kinemaics of he paricles forming he hadronic final sae. The Hadroo2 algorihm creaes HFS paricles, combining he informaion coming from he racks and clusers. Boh informaion are mached and a double couning of energies is avoided. Their relaive resoluions are compared o decide, wheher racks or clusers are aken for he consrucion of HFS objecs, for keeping he bes measuremen. The exac precision of he calorimeer is unknown due o possible conribuions of neural paricles. Thus he average relaive error σ expecaion E LAr expeced for he calorimeer measuremen is esimaed as ) expecaion ( σe = σexpecaion E LAr =.5. (4.6) E LAr E rack Erack The rack measuremen is favoured for he creaion of he HFS paricle if he comparison ( σe ) ( E < σe rack E ) expecaion LAr is rue or if he rack energy is below he cluser energy (4.7) E rack <E cylinder.96 σ cylinder E. (4.8)

64 58 CHAPTER 4. EVENT RECONSTRUCTION Here E cylinder and σ cylinder E =.5 E rack denoe he elecromagneic (hadronic) energy of he clusers and is error wihin a cylinder of 25 cm (5 cm) around he exrapolaed rack. The energy wihin his cylinder is removed up o he rack energy o avoid double couning. Possible flucuaions of boh measuremens are aken ino accoun and poenially remaining cluser energy due o neural paricles or from anoher rack is exrapolaed in he same region of he calorimeer [85]. If (4.7) urns ou o be false and he rack energy E rack is wihin 2σ of E cylinder,bohrack and cluser measuremen are considered o be compaible. In ha case, he calorimeric measuremen is used o reconsruc he HFS paricle candidae. Afer reamen of all racks, he remaining clusers are considered o be massless. They originae from neural hadrons wih no corresponding rack, or from charged paricles wih a badly measured rack. The rack measuremen gives beer resuls up o 2 GeV for forward racks, 25 GeV for cenral racks and abou 3 GeV for combined ones. If he energy deposied in he cenral region is above 25 GeV, he calorimeric measuremen is beer. 4.6 Je Reconsrucion Measuring direcly he final sae quarks and gluons coming ou of he hard ineracion would be he bes way o analyse phooproducion evens. Bu, due o he fac ha hese parons carry colour, i is no possible, since hey produce paron showers and finally recombine o colour single saes - he colourless hadrons. They are he measurable final sae paricles, collimaed around he direcion of he originaing paron. These groups of hadrons are called jes. Jes are measured by he deecor and reconsruced wih he objecive of achieving direcion and energy of he original parons. Je Finding Algorihm Clusering algorihms define jes by merging paricles ogeher o so-called pseudoparicles in an ieraive procedure. These pseudoparicles are he consiuens of he final je and are assigned o he je in an unambiguous way. Clusering algorihms are mainly used for e + e experimens. They are boh collinear and infrared safe. Recombinaion Schemes Recombinaion schemes are procedures o deermine he momenum four vecor of he je on basis of he momenum four vecors of merged je paricles. The Snowmass Convenion [86] provides he basic recombinaion schemes. These are he p -weighed and he covarian E scheme. The firs one resuls in massless jes while he second one leads o massive jes. In his analysis, jes are reconsruced using he inclusive k -clusering algorihm [87] in he laboraory frame. This scheme makes use of he p -weighed recombinaion scheme and provides herefore massless jes. The p -weighed scheme is defined as follows:

65 4.7. CALIBRATION OF THE HADRONIC FINAL STATE 59 p je = i η je = i φ je = i p,i (4.9) p,i (p,i η i ) (4.) p,i (p,i φ i ). (4.) 4.7 Calibraion of he Hadronic Final Sae In secions 4.5 and 4.6, he reconsrucion algorihms were presened. An addiional calibraion of jes and he complee hadronic final sae is applied o improve he reconsruced quaniies of he je and he hadronic final sae. In his secion, he calibraion is described briefly and a cross-check, using a DIS neural curren dije sample, is performed. The consequences for he sysemaic error on he hadronic energy scale is discussed a he end of his secion. The energy of a hadronic shower is no fully measurable and leads o a sysemaic deviaion from he rue value. Therefore, he measured energy is significanly smaller han he energy carried by he hadron, which iniiaed he hadronic shower. In order o correc his effec, a calibraion is performed. In H, differen calibraion mehods for differen purposes exis. The Ieraive mehod [88], [89] includes all calorimeer clusers in he even and gives hus a global calibraion of hadronic energy measuremens. The High P Je Calibraion [85], [9] considers only clusers, which belong o he reconsruced je. I is developed for high Q 2 evens (Q 2 > GeV 2 ) and for jes wih ransverse momena above GeV. The Low P HFS Calibraion [9] is useful for evens where he oal ransverse momenum of he hadronic sysem is lower han GeV. This mehod is based on an ieraive mehod for hadronic sysems wih low ransverse momena, and on a Low P Je Calibraion mehod which is developed for jes wih ransverse momena below GeV. In his analysis, a combined calibraion mehod is applied. Here, he paricles belonging o he reconsruced jes are calibraed wih he Low and High P Je Calibraion, while he remaining paricles are calibraed wih he ieraive mehod. The oal ransverse momenum of he iniial sae a HERA is zero, since he elecron and proon beams are colliding head-on. Considering momenum conservaion, he oal rans- NC DIS Dije Sample E e > 4 GeV Q 2 e > GeV 2 y e >.5 4 GeV <E P z < 7 GeV z vx < 35 cm Number of jes > Table 4.2: The selecion cus for he neural curren DIS dije even sample.

66 6 CHAPTER 4. EVENT RECONSTRUCTION (a) (b) > da h /p <p.2.8 Daa Mone Carlo (MC)> bal (daa)/p bal.2.8 no calibraed <p.6 (c) [GeV] e p.6 (d) e p [GeV] > da h /p <p.2.8 Daa Mone Carlo (MC)> bal (daa)/p bal.2.8 calibraed <p [GeV] e p [GeV] e p Figure 4.4: The mean balanced ransverse momenum beween he hadron and he elecron as a funcion of he elecron s ransverse momenum before (op) and afer (boom) calibraion. verse momenum of he final sae has o be zero as well. Therefore, he ransverse momenum of he scaered elecron needs o be balanced by he ransverse momenum of he hadronic final sae in he laboraory sysem. This balanced ransverse momenum p bal is defined as wih p had p bal = phad p da, (4.2) being he oal ransverse momenum of he hadronic sysem. The observable p da sands for he ransverse momenum of he ougoing lepon, obained by he double angle mehod. This mehod explois he scaering angle of he ougoing lepon and he effecive angle of he hadronic sysem. The double angle mehod is ideal o es he calibraion of he calorimeer, because i is almos independen of he energy scale iself. The agreemen of daa and simulaion is checked wih a neural curren DIS dije sample. The applied selecion cus are summarized in able 4.2. The daa was aken in he years 26/27 and is compared o he DJANGO Mone Carlo simulaion. The disribuion of he balanced ransverse momenum is ploed before calibraion and aferwards. The balanced ransverse momenum as a funcion of he elecron s ransverse momenum p e is depiced in figure 4.4, before and afer he calibraion is applied o daa and simulaion.

67 4.8. TRIGGER ELEMENTS AND THEIR EFFICIENCIES 6 (a) (b) > da h /p <p.2.8 Daa Mone Carlo no calibraed (MC)> bal (daa)/p bal <p (c) 5 5 γ [deg] h.6 (d) 5 5 γ h [deg] > da h /p <p.2.8 Daa Mone Carlo (MC)> bal (daa)/p bal.2.8 calibraed <p [deg] γ h [deg] γ h Figure 4.5: The mean balanced ransverse momenum beween he hadron and he elecron as a funcion of he hadronic angle before (op) and afer (boom) calibraion. Addiionally, he raio p bal (daa)/p bal (MC) is ploed. Afer he calibraion, he disribuion of p bal becomes more fla and is shifed from 9% o higher values close o one for he daa. The disribuion for he DJANGO Mone Carlo lies slighly above he daa. The agreemen beween daa and simulaion is improved as well afer he calibraion is performed. Figure 4.5 illusraes he same quaniies as a funcion of he hadronic angle γ h. In he forward and backward region he response for hadrons is low. Afer he calibraion, he agreemen beween daa and simulaion is improved. The applied calibraion improves he agreemen beween daa and he simulaion. In all regions of p e and γ h he disagreemen is smaller han 2%. Therefore, an uncerainy of he hadronic energy scale of ±2% is used for esimaion of he sysemaic error of he hadronic energy scale. 4.8 Trigger Elemens and heir Efficiencies In his analysis, he phooproducion riggers s9 or s23 are required. These riggers are sensiive o signals coming from he CMD and he CTD (cf and 3.2.). Their condiions on he firs rigger level differ in ha s9 riggers evens deeced in he barrel of he muon sysem and s23 riggers signals in he endcap of he CMD:

68 62 CHAPTER 4. EVENT RECONSTRUCTION L(s9) :Mu Bar FTT mul Tc > FTT mul Td > CIP Sig > L(s23) :Mu ECQ FTT mul Tc > 2 CIP Sig >. The L2 and L3 condiions for s9 and s23 are he same: L2 : FTT Tc g (since 6..26) L3 : L3 V7[3] (since ). Boh rigger phooproducion evens. In he following, he rigger elemens of s9 and s23 are described briefly and heir efficiencies are invesigaed. Muon Trigger Elemens The rigger elemen Mu Bar demands his in wo ou of he four rigger layers of he muon barrel. The requiremen of he muon endcap rigger elemen Mu ECQ consiss of several condiions: Mu ECQ = Mu BOEC Mu 2 BIoOEC Mu FOEC. (4.3) The backward inner endcap Mu BIEC and he backward ouer endcap Mu BOEC as well as he forward ouer endcap Mu FOEC demand his in hree ou of he five rigger layers. In he forward inner endcap Mu FIEC four ou of five layers are required o avoid he idenificaion of high energeic hadrons from he proon remnan, as muons. If wo rigger signals in he forward or backward endcap occur he elemens Mu 2 BIoOEC or Mu 2 FIoOEC reurn a posiive decision. FTT Trigger Elemens The FTT rigger elemens are based on informaion coming from he CJC. Three ou of he four FTT layers are locaed in he CJC, while he fourh layer is siuaed in he CJC2. The FTT provides online rigger decisions on he firs hree rigger levels. On level he rack curvaure κ /p rack and he azimuhal angle φ rack a a rack radius of 2 cm are deermined. As he rigger decision has o be made wihin 2.3 µsec, a fas calculaion is performed which compares he measured hi paerns of he FTT wih precalculaed paerns. The rigger decision is based on he couned FTT racks above a cerain p hreshold (cf. able 4.3). On level 2 a similar, bu more precise paern idenificaion han on level is performed. This decision delivers angular and momenum resoluions, which are close o hose of he final reconsrucion. The second rigger level of he FTT is available since November 26. The decision on L3 is based on he FTT L2 racks and on informaion from oher subsysems, e.g. he CMD. For he subriggers, used in his analysis, he L3 FTT elemen requires a leas one rack which poins o one of he riggering modules in he CMD. Thus a maching of muon racks is performed, which is acive since December 26.

69 4.8. TRIGGER ELEMENTS AND THEIR EFFICIENCIES 63 FTT Elemen FTT mul Tc>n FTT mul Td>n FTT Tc g L3 V7[3] Definiion n L FTT racks above 4 MeV n L FTT racks above 9 MeV A L2 FTT rack above 47 GeV muon maching on L3 Table 4.3: Lis of used FTT rigger elemens and heir definiion. z Verex Trigger Elemens The z verex rigger elemen CIP Sig consrains he z posiion of he verex in order o rejec background evens, which are far away from he nominal ineracion poin (cf. secion 5.3). The informaion of he CIP is used o build he rigger decision. Reconsruced racks are exrapolaed o he z axis and hen ploed as a z verex disribuion. The significance S of his disribuion S = Ncen rk Nbwd rk + N fwd rk, (4.4) which is deermined using he number of racks in he forward (Nfwd rk ), cenral (N rk cen )and backward (Nbwd rk )regionofhez axis, is used as well for he rigger decision. The requiremen of CIP Sig> indicaes more racks coming from he cenral region han from he backward and forward region. Trigger Efficiencies In his secion, he efficiencies of he required subriggers s9 and s23 are deermined. For he cross secion measuremen he rigger efficiency as calculaed from he daa is used. To deermine he efficiency of a subrigger, monior riggers are used ha do no conain any (a) (b) Trigger Efficiency.5 L: Mu_Bar Mu_ECQ H daa 6/7 PYTHIA b Trigger Efficiency.5 L: Mu_Bar Mu_ECQ H daa 6/7 PYTHIA b μ p [GeV] - η μ Figure 4.6: Efficiencies of he L muon rigger elemens Mu Bar Mu ECQ as a funcion of p µ and η µ (b). The PYTHIA simulaion (solid line) in comparison o he daa (poins). (a)

70 64 CHAPTER 4. EVENT RECONSTRUCTION (a) (b) Trigger Efficiency.5 L: FTT_mul_Tc > H daa 6/7 PYTHIA b Trigger Efficiency.5 L: FTT_mul_Tc > H daa 6/7 PYTHIA b (c) μ p [GeV] (d) - η μ Trigger Efficiency.5 L: FTT_mul_Td > H daa 6/7 PYTHIA b Trigger Efficiency.5 L: FTT_mul_Td > H daa 6/7 PYTHIA b (e) μ p [GeV] (f) - η μ Trigger Efficiency.5 L2: FTT_Tc_g_ H daa 6/7 Trigger Efficiency.5 L3: muon maching H daa 6/7 PYTHIA b PYTHIA b μ p [GeV] μ p [GeV] Figure 4.7: Trigger efficiencies of he FTT rigger elemens as a funcion of p µ [(a),(c),(e),(f)] and η µ [(b),(d)]. The PYTHIA simulaion (solid line) in comparison o he daa (poins). of he rigger elemens from he analysed rigger. The rigger efficiency is deermined for daa and Mone Carlo separaely a he rigger elemen level o be able o compare i. Each rigger elemen is invesigaed separaely. The Mone Carlo simulaion provides he firs hree rigger levels and he FTT elemens are simulaed. The rigger efficiency ɛ rigger is calculaed by he fracion of evens ha are riggered by boh, he monior and he analysis rigger N signal monior, relaive o all evens riggered by he monior rigger N monior :

71 4.8. TRIGGER ELEMENTS AND THEIR EFFICIENCIES 65 ɛ rigger = N signal monior. (4.5) N monior The subriggers s9 and s23 are sensiive o signals coming from he CMD and he CTD (cf. secion and 3.2.). The subrigger s9 is sensiive o evens wih muons in he CMD barrel and s23 o evens wih muons in he CMD endcaps. Boh riggers selec evens ha conain cenral racks above a cerain momenum hreshold (able 4.3) and a reconsruced CIP-verex. No independen phooproducion riggers are available and hus he invesigaion of he rigger efficiency is carried ou using evens ha were independenly riggered by he SpaCal. These DIS evens have a similar hadronic final sae and a scaered elecron in addiion. Accordingly, he cus are removed, which resric he sample o he phooproducion regime. The rigger efficiencies for Mu Bar Mu ECQ are shown in figure 4.6 as a funcion of he ransverse momenum of he muon and is pseudorapidiy. The poins correspond o he daa, while he solid line represens he PYTHIA Mone Carlo simulaion. The simulaed efficiency underesimaes ha of he daa, especially in he backward region and a high p. The rigger efficiencies of he FTT elemens are shown in figure 4.7 as a funcion of p µ and η µ. The poins correspond o he daa while he solid line illusraes he PYTHIA predicion. On level he daa efficiency is very close o % and nicely described by he Mone Carlo simulaion. On level 2 and 3, he daa has an efficiency of more han 8% and is again in very good agreemen wih he simulaed efficiencies. In figure 4.8 he rigger efficiency of CIP Sig is shown. The efficiency in he daa (poins) reaches nearly % and is well described by he PYTHIA simulaion (solid line) in all variables. Trigger Efficiency of s9 and s23 The oal rigger efficiency for he subriggers s9 s23 is shown in figure 4.9. The muon rigger elemens Mu Bar Mu ECQ dominae he efficiencies of he subriggers s9 and (a) (b) Trigger Efficiency.5 L: CIP_Sig > H daa 6/7 PYTHIA b Trigger Efficiency.5 L: CIP_Sig > H daa 6/7 PYTHIA b μ p [GeV] - η μ Figure 4.8: Efficiency of he z verex rigger elemen CIP Sig on L. The daa (poins) shows an efficiency of nearly % and is compared o PYTHIA (solid line). In (a) he efficiency is ploed as a funcion of p µ and in (b) as a funcion of η µ.

72 66 CHAPTER 4. EVENT RECONSTRUCTION (a) (b) Trigger Efficiency.5 s9 s23 H daa 6/7 PYTHIA b Trigger Efficiency.5 s9 s23 H daa 6/7 PYTHIA b μ p [GeV] - η μ Figure 4.9: Trigger efficiency for he subriggers s9 s23 as a funcion of p µ The daa (poins) in comparison o he PYTHIA simulaion (solid line). (a) and η µ (b). s23. The daa (poins) and he simulaed Mone Carlo are in good agreemen. The rigger efficiencies are checked for boh, he beauy and he charm Mone Carlo simulaion and only he simulaed efficiencies for evens conaining beauy are shown here. The charm simulaion gives very similar resuls.

73 Chaper 5 Even Selecion In his chaper, he procedure o selec he phooproducion dije sample is presened. I sars wih a selecion of periods wih sable deecor condiions and coninues wih he selecion of phooproducion heavy quark evens. Aferwards, background evens from cosmic rays and oher sources are discussed. Finally, he correlaion beween reconsruced and generaed variables is sudied. The disribuions presened in his chaper conain a comparison of he daa and he PYTHIA simulaion. The disribuions of beauy, charm and ligh quarks are scaled wih heir fracions and normalised o he daa. The fracions are obained by he 2-dimensional fi as explained in chaper 6. The sum of hese hree quark conribuions is hen compared o he daa. 5. Daa Sample The daa sample analysed in his hesis, was recorded wih he H deecor in he years 26 and 27 and corresponds o an inegraed luminosiy of 79.8 pb. Before auumn 26 proons of 92 GeV energy were collided wih elecrons and aferwards wih posirons of 27.6 GeV energy. The differen lepon charges are no expeced o have an impac on his analysis and he wo run periods are analysed ogeher. The inegraed luminosiies for he differen run ranges are lised in able 5.. Run Selecion In order o selec evens for he analysed physics process, several selecion seps are performed. A firs, runs wih good and medium qualiy are seleced. Each run is required o have an inegraed luminosiy of a leas. nb. The relevan deecor componens lised in able Run Period Run Range Luminosiy [pb ] 26 e /27 e Table 5.: Run ranges analysed in his hesis and he corresponding inegraed luminosiies. 67

74 68 CHAPTER 5. EVENT SELECTION Subdeecor Inner Cenral Je Chamber Ouer Cenral Je Chamber Liquid Argon Calorimeer Time-of-fligh Sysem Luminosiy Sysem Cenral Inner Proporional Chamber Spaghei Calorimeer Cenral Muon Deecor Cenral Silicon Tracker Fas Track Trigger HV symbol CJC CJC2 LAR TOF LUMI CIP SPAC IronClusers CST FTT Table 5.2: Lis of relevan subdeecors wih swiched on high volage. 5.2 mus be fully operaional and heir High Volage (HV) is required o be on. They have o be in he read ou as well. Some run ranges are known as problemaic. In some cases, he FTT sofware on L or L2 was wrongly loaded or a power glich of L2 occurred. The year 24 is compleely excluded, since no CST informaion is available, which is crucial for his analysis. 25 is excluded as well due o a very problemaic period of he CST. Only 2/3 of he half ladders were operaional. A bug concerning he wires which connec neighbouring srips, reduced he hi efficiency and degraded he resoluion. The wires were crossed, which caused an inerchange of he signals coming from neighbouring srips. This bug is no fully fixed for he recorded daa of 25, bu he crossed wires were correced in 25 o be fully operaional for he las.5 years of daa aking. In 25 anoher problem occurred: he beampipe ouched he CST, which caused a movemen in every lumi fill when he magnes were ramped up. Even during a fill, he posiion of he CST was no compleely sable. Therefore, only he daa aking periods 26 and 27 are analysed since he CST had is bes operaional period. Only a small number of runs in hese years is excluded due o failures of some CST half ladders. 5.2 Heavy Quark Selecion in Phooproducion In his secion, he selecion of even candidaes wih heavy quarks in phooproducion is discussed. The selecion conains kinemaic cus, a requiremen of a muon candidae and a dije selecion. In able 5.3 an overview of he selecion cus is given Kinemaic Selecion In phooproducion, he virualiy of he exchanged phoon is small and he elecron is scaered under very small angles, escaping deecion in he main H calorimeers. Phooproducion evens are seleced requiring ha here is no elecron candidae found in he calorimeers wih an energy of more han 8 GeV. The SpaCal accepance resrics he virualiy of he phoon o Q GeV 2.

75 5.2. HEAVY QUARK SELECTION IN PHOTOPRODUCTION 69 (a) (b) Evens 8 H daa 6/7 PYTHIA sum PYTHIA b 6 PYTHIA c PYTHIA uds 4 Evens y h -2 2 z Verex [cm] Figure 5.: The inelasiciy in (a) and he z verex disribuion in (b) for daa (poins) and PYTHIA (lines) in comparison. As he kinemaic quaniies of he scaered elecron are no accessible, one has o use he hadrons o deermine he kinemaic variables wih he Jacque-Blondel mehod (JB) [92]. The cu on he inelasiciy y JB helps o rejec Deep Inelasic Scaering (DIS) background evens, which migh sill be in he sample due o inefficiencies of he elecron finder. The inelasiciy is defined as y JB = (E pz ) 2E e. (5.) Here, E and p z are he energies and he z-componens of he momena of he hadronic final sae paricles, while E e denoes he lepon beam energy. The definiion (5.) shows ha DIS evens can be found a high inelasicies since he (E p z ) conservaion leads ypically o values of wice he beam energy (E p z )=2E e =55.2 GeV. Therefore, he upper limi of y JB is resriced o y JB <.8, aking also he accepance of he muons ino accoun. To ensure a complee reconsrucion of he final sae, evens in he very forward region have o be discarded leading o an inelasiciy of.2 <y JB <.8. Figure 5. (a) shows he inelasiciy for he daa (poins) and he PYTHIA Mone Carlo simulaion (see legend) afer applying all selecion cus. The simulaed inelasiciy shows a good agreemen wih he daa Muon Selecion The muon idenificaion and reconsrucion is presened in secion 4.. In he following, he applied selecion cus are discussed. In his analysis, a muon candidae idenified in he insrumened iron is required. To ensure a reconsrucion efficiency larger han 6%, a ransverse momenum of a leas 2.5 GeV is demanded [75]. This cu also removes evens wih large muliple scaering. Muliple scaering effecs are proporional o /p, as explained in secion The ransverse momenum of he muon candidae is depiced in figure 5.2

76 7 CHAPTER 5. EVENT SELECTION Evens 3 2 (a) H daa 6/7 PYTHIA sum PYTHIA b PYTHIA c PYTHIA uds Evens 3 2 (b) (c) 5 p µ [GeV] (d) 5 p µ [GeV] Evens 4 Evens µ φ [deg] - µ η Figure 5.2: The ransverse momenum p µ in (a) and (b), he azimuhal angle φ µ in (c) and he pseudorapidiy η µ in (d) of he seleced muon candidae for daa (poins) and PYTHIA (lines) in comparison. All cus discussed in his secion are applied. (a) and (b) wih linear and logarihmic scale. The daa is well modelled by he PYTHIA simulaion. The analysed range is.3 <η µ <.5, corresponding o an angular range 25 <θ µ < 5, which is an exension of he forward and backward region compared o he previous measuremen [59]. The θ µ cus are moivaed by he angular accepance of he CST. In figure 5.2 (c) and (d), he disribuion of he pseudorapidiy and he azimuhal angle of he muon are presened. The PYTHIA simulaion underesimaes he daa in he very forward region η µ >.2 and overesimaes i in he region.4 <η µ <.2. The underesimaion in he very forward region can be explained by an increase of he ligh quark conribuion in he daa. In general, he angular disribuions of he daa (poins) are modelled reasonably by he simulaion. If more han one muon candidae is found, he one wih he highes p is aken. This happens very rarely: more han one muon candidae is found in less han % of he seleced evens. To provide a high puriy of he muon sample, furher selecion cus are applied. The rack measured wih he CMD is herefore required o have his in a leas four ou of he 6 layers of he muon deecor. The number of hi layers in he insrumened iron is depiced in figure 5.3 (a). The PYTHIA simulaion is shifed o he lef. To reduce he number of

77 5.2. HEAVY QUARK SELECTION IN PHOTOPRODUCTION 7 fake muons coming from misidenified hadrons, he disance beween he las and he firs hi layer is required o be larger han hree, as ploed in figure 5.3 (b). Again, he simulaion overesimaes he daa a low values and underesimaes i a high values of he layer disance. In he backward region (3 <θ µ < 5 ), he disance beween he his in he las and firs layer is required o be a leas 8 layers, since he calorimeer (BBE) is insrumened wih less han wo hadronic ineracion lenghs. This causes an increase of background coming from hadrons, which are misidenified as muons. In figure 5.3 (d) a comparison of hadrons misidenified as muons wih (doed line) and releasing (solid line) he above described cus on he layer of he muon sysem is shown. The increase of hadrons in he backward region wihou he cus is clearly visible. Boh disribuions are obained from a PYTHIA Mone Carlo sample conaining only misidenified hadrons, which survive all oher applied analysis cus lised in able 5.3. The disribuions shown in figures 5.3 (a) and (b) are no perfecly modelled by he simulaion. This is mos probably due o a no perfec descripion of he deecor and is performance in he CMD Mone Carlo simulaion. In he scope of his analysis i is crucial, ha he reconsrucion efficiency in he insrumened iron is well modelled by he simulaion. This is he case, as was shown in [75]. Because he shown disribuions do no effec he deecor correcions in he measuremen and he shown quaniies are only used o rejec misidenified hadrons, no furher seps are aken. The linking probabiliy of he ouer o he inner muon rack is required o be a leas % and is shown in figure 5.3 (c). Here, he simulaion provides a good descripion of he daa Je Selecion Jes are reconsruced in he laboraory frame using he inclusive k clusering algorihm as described in secion 4.6. In his analysis, evens conaining a leas wo jes wih ransverse momena of p je(2) > 7(6) GeV wihin he pseudorapidiy range η je < 2.5 are seleced, aking he angular accepance of he deecor ino accoun. In he leading order QCD picure, hese wo jes resul from he hadronizaion of wo heavy quarks. The mehods, used o exrac he heavy quark fracion (see chaper 6), demand a sufficien precision of he reconsruced direcion of he jes. This is only provided for jes wih a sufficienly high ransverse momenum, which moivaes he selecion crieria of p je(2) > 7(6) GeV. If several jes are found, he wo highes p jes are aken. The seleced muon candidae is required o be associaed o one of hese wo jes and he associaion is provided by he je algorihm. In he following, he je, which conains he muon candidae, is called muonje while he oher one is called oher je. The indices and 2 denoe he ordering in ransverse momena and give no hin if he je conains he muon candidae or no. Figure 5.4 shows he ransverse momena of he wo highes p jes. A good agreemen beween he daa (poins) and he PYTHIA predicion is achieved. In figure 5.5 (a) and (b) he number of HFS paricles per je of he highes and second highes p je are shown. Figure 5.5 (c) and (d) presen he azimuhal angular disribuions for je and je2, respecively. The hisograms (e)-(h) illusrae he pseudorapidiies for je, je2, muonje and he oher je. In all cases, he simulaion describes he daa reasonably well. The Mone Carlo simulaion is normalised o he number of enries and scaled wih he quark conribuions obained by he

78 72 CHAPTER 5. EVENT SELECTION (a) (b) Evens 2 Evens 4 H daa 6/7 PYTHIA sum PYTHIA b 3 PYTHIA c PYTHIA uds µ N layer (c) (d) Las - Firs Muonlayer Evens 3 Evens µ P link - MC: Hadrons MC: Hadrons afer cus η μ Figure 5.3: Number of hi layers in he muon deecor in (a), disance of las and firs hi layer in (b), linking probabiliy of he ouer o he inner muon rack in (c) and hadrons misidenified as muons (d). The Daa (poins) are shown in comparison o he PYTHIA simulaion. 2-dimensional fi as explained in chaper 6. All selecion cus discussed in his secion are applied and lised in able 5.3. Je Profiles A useful ool for geing insighs o he characer of he seleced dije evens is he ransverse energy flow around he je axis. The energy flow is visualized by so-called je profiles which illusrae he disance in η and φ beween he objecs of he hadronic final sae and he je axis. This disance is weighed by he ransverse energy of each objec. In oher words, he je profile shows he angular energy disribuion around he je axis. Figure 5.6 (a) presens he je profile in he region η <, where η = η obj η je. The poins correspond o he daa and he solid line illusraes he sum of he differen quark conribuions in PYTHIA, which describes he daa very well. The peak around zero originaes from paricles of he je iself, while he increase of he energy flow o ±π is caused by he paricles of he second je. Figure 5.6 (b) illusraes he je profile in he region φ <, wih φ = φ obj φ je. Again he agreemen beween daa and PYTHIA is very good. The shape of he disribuion shows

79 5.3. BACKGROUND STUDIES 73 (a) (b) Evens H daa 6/7 PYTHIA sum PYTHIA b PYTHIA c PYTHIA uds Evens (c) je p [GeV] (d) je p [GeV] Evens 2 Evens je2 p [GeV] je2 p [GeV] Figure 5.4: The ransverse momena of he highes [(a),(b)] and second highes [(c),(d)] p jes for he daa (poins) and PYTHIA predicion in comparison afer all cus. an asymmery o higher values of η, which indicaes a higher energy flow in he direcion of he proon remnan. In figures 5.7 and 5.8, he je energy flow is illusraed in bins of p je and x obs γ as a funcion of φ and η. In all cases, he PYTHIA simulaion models he daa very well. 5.3 Background Sudies Afer applying he cus discussed in he las secion, he even sample consiss of candidaes for heavy quarks in dije evens conaining a muon. The sample conains also background evens like cosmic or fake muons, which are explained in he nex wo secions, including selecion cus o reduce heir conribuion. Background, coming from non ep evens, is eliminaed consraining he posiion of he reconsruced primary verex wihin a cerain range of he z posiion of he nominal verex. This rejecs evens coming from collisions of saellie bunches wih nominal bunches. Thus, he primary verex is required o be reconsruced close o he nominal ineracion poin z vx < 35 cm. Figure 5. (b) presens he z verex disribuion. Since he variable z vx is generaed oo broad (no shown) in he PYTHIA simulaion, i is reweighed in erms of he generaed z verex. The daa (poins) is well described by he reweighed simulaion.

80 74 CHAPTER 5. EVENT SELECTION (a) (b) Evens H daa 6/7 PYTHIA sum PYTHIA b PYTHIA c PYTHIA uds Evens HFS (c) N /je 2 HFS (d) N /je2 Evens 4 3 Evens (e) - φ je [deg] (f) - φ je2 [deg] Evens Evens (g) -2-2 η je (h) -2-2 η je2 Evens 2 5 Evens η µje -2-2 oher je η Figure 5.5: Conrol disribuions of je quaniies for daa (poins) and PYTHIA (lines) in comparison. For je, he number of HFS paricles (a), azimuhal angle (c) and he pseudorapidiy (e) are shown. The same quaniies are ploed for je2 in (b), (d) and (f), respecively. The η disribuions for he muonje and he oher je are presened in (g) and (h). All cus discussed in his secion are applied.

81 5.3. BACKGROUND STUDIES 75 (a) (b) <E > - H daa 6/7 PYTHIA η < <E > - φ < obj je Φ -Φ -2 2 obj je η -η Figure 5.6: The ransverse energy flow around he je axis as a funcion of he disance beween he angles of he objec and he je axis. (a) shows he disance in azimuhal angles φ obj φ je and in (b) he disance in pseudorapidiies η obj η je is illusraed. The referring je is he one wih he highes p,namelyje. Cosmics Muons from cosmic rays are a naural source of background evens as nearly of hem reach every square meer of he earh s surface per minue. Thus, hey are equally disribued in ime and in he deecor, which is a convenien propery o remove hem. The iming informaion of he CJC rack mus be consisen wih he average even ime o make sure ha he deeced signal does no come from a cosmic muon. As a cosmic muon flies sraigh hrough he deecor, i preends o be wo muons wih a back o back opology. This feaure is used as well o rejec hem performing a maching beween wo muon racks. Since a pure cosmic even has only wo racks he number of cenral racks is resriced o a leas hree racks Ncen racks 3. A las sep o rejec cosmic evens is o consrain he signed impac parameer δ (cf. secion 4.2) o a cerain range as he cosmic muons are disribued equally in he deecor. The following cus are applied in his analysis o reduce background from cosmics: The iming informaion of he CJC racks mus be consisen wih he average even ime wihin 3 σ, which corresponds o 2.8 nsec. Evens are rejeced if a second muon is found, which fis he oher muon candidae in he opposie hemisphere in φ and p. The signed impac parameer mus lie in he range. <δ<. cm. These cus rejec 3% of he seleced evens.

82 76 CHAPTER 5. EVENT SELECTION (a) (b) <E > - H daa 6/7 PYTHIA 7 < p φ < je < GeV <E > 7 < p η < je < GeV - -2 (c) -2 2 obj je η -η (d) -2 2 obj je φ -φ <E > - < p φ < je < 4 GeV <E > - < p η < je < 4 GeV -2-3 (e) -2 2 obj je η -η -2 (f) -2 2 obj je φ -φ <E > - 4 < p φ < je < 25 GeV <E > - 4 < p η < je < 25 GeV obj je η -η obj je φ -φ Figure 5.7: The ransverse energy flow around he je axis as a funcion of η (lef column) and φ (righ column) for differen regions of p je. The daa (poins) in comparison o he PYTHIA simulaion (solid line). Fake Muons Anoher imporan source for background evens in his analysis are he so-called fake muons. Hadrons or heir decay producs, which reach he muon sysem, can be wrongly idenified as muons from heavy quark decays for hree reasons: sail hrough: A hadron, which reaches he muon deecor in case i suffers no hadronic ineracion wih he calorimeer is no srong is a so-called sail hrough hadron. Here, he hadron acs like a minimum ionising paricle. According o [76], he maximum

83 5.3. BACKGROUND STUDIES 77 (a) (b) <E > - H daa 6/7 PYTHIA φ < obs x γ <.75 <E > η < obs x γ < <E > - (c) -2 2 obj je η -η φ < obs x γ >.75 <E > (d) -2 2 obj je φ -φ η < obs x γ > obj je η -η obj je φ -φ Figure 5.8: The ransverse energy flow around he je axis as a funcion of η (lef column) and φ (righ column) for differen regions of x obs γ. The daa (poins) compared o he PYTHIA (solid line). probabiliy for his reaches.6% as a funcion of he polar angle. depends on he hadronic ineracion lengh and he ravel disance. The probabiliy punch hrough: A punch hrough hadron ineracs wih he calorimeer, bu does no deposi is enire energy since he radiaion lengh of he calorimeer is oo small. The energy leaking, passing some of he iron layers, could cause he misidenificaion of his hadron as a muon. infligh decay: Some ligh hadrons, like pions or kaons, have decay channels wih muons in he final sae. Pions have a branching fracion of almos % o decay ino a muon and a neurino, while he kaons show a fracion of roughly 65% [46]. If one of hese hadrons decays inside he deecor, he resuling muon could reach he muon deecor. Here, i migh be misidenified as a muon, which originaes from a heavy quark decay. The backward par of he LAr calorimeer (BBE) in he region 4 <θ<6 is insrumened wih less han wo hadronic ineracions lenghs in fron of he muon deecor. This causes an increase of wrongly idenified hadrons as depiced in figure 5.3 (d). To reduce he number of misidenified hadrons, he cu on he disance beween he firs and he las hi layers is ighened in he backward region. Here he disance is required o be a leas eigh

84 78 CHAPTER 5. EVENT SELECTION Phoon Virualiy Q 2 [GeV 2 ] < 2.5 Inelasiciy y Trigger s9 s23 Muon Selecion associaed o one Je Transverse Momenum p µ [GeV] > 2.5 Pseudorapidiy η µ #MuonLayerN µ layer (BEC) 4( 8) Iron Link Probabiliy P µ link >. #CSTHisNCST his CST Link Probabiliy Plink CST >. Je Selecion Pseudorapidiy η je Transverse Momenum p je [GeV] > 7 Transverse Momenum p je2 [GeV] > 6 Table 5.3: Summary of he applied cus. The cus defining he kinemaic range are in bold leers. layers, which rejecs 35% of he evens according o a PYTHIA Mone Carlo sample, which conains only misidenified hadrons. Requiring a larger disance beween he firs and las hi layers increases he puriy and keeps he single iron layer efficiency consan. If he number of layers iself would be increased, hese condiions would no be fulfilled [78]. The conribuions of sail hrough and punch hrough hadrons are aken ogeher in he following. According o he inclusive Mone Carlo simulaion he conribuion of hadrons, which reach he muon deecor, is 24%. The conribuion of infligh decays o he fake muon background is found o be 3.7%. Even Yield Figure 5.9 shows he even yield of he daa sample. All analysis cus presened in secion 5.2 are applied. The number of evens per pb increases a approximaely run number 477 slighly. This sep is observed by several independen analyses and he source is no clarified a presen. The average number of evens per pb is approximaely 5 before he sep and 6 aferwards. Selecion Summary The daa sample analysed in his hesis conains 993 evens afer applying all cus discussed above (cf. able 5.3). In figure 5., a ypical dije even conaining a muon is depiced, which is one of he analysed evens in his hesis. Figure 5. illusraes a schemaical view of he H deecor in he rz and xy plane and is ploed using he program HRed [93]. The LAr energy of he wo seleced jes is also shown.

85 5.4. DIJET EVENT OBSERVABLES 79 - evens / pb Runnumber 3 Figure 5.9: Even yield for he phooproducion dije sample conaining a muon (s9 s23). The number of evens per pb are shown as a funcion of he runnumber. 5.4 Dije Even Observables As explained in secion 2.5, processes in he kinemaic region of phooproducion can be direc or resolved in he LO QCD picure. The relaive fracion depends on he energy of he phoon, which comes from he elecron and ineracs wih parons of he proon. The measuremen of dije evens enables o invesigae several quaniies, which are relaed o he heavy quark producion mechanism. The following consideraions are based on he assumpion, ha he wo highes p jes describe he kinemaics of he ougoing parons. In he case of a direc process, he ougoing parons are a heavy quark pair. If i is a resolved process, he wo ougoing parons can be a heavy quark and anoher paron, like for example a ligh quark or agluon. The observable x obs γ represens he fracion of he phoon energy, which eners he hard ineracion. I is hus feasible o disinguish beween direc and resolved processes. Based on he above menioned assumpion, i is esimaed using x obs γ = je (E p z)+ je2 (E p z) had (E p, (5.2) z) where E sands for he energies and p z for he z-componens of he paricles conained in he wo jes in he numeraor and in he denominaor he sum runs over all deeced hadronic final sae paricles. Wih his definiion he range of x obs γ is resriced o <x obs γ. In he direc process he phoon eners he hard ineracion compleely and hus a x obs γ of roughly one is expeced. In ha case, he hadronic final sae consiss of only he wo hard jes and he proon remnan in he forward region, which makes an insignificanly small conribuion o he denominaor in (5.2). In resolved processes x obs γ becomes smaller due o he conribuion of he phoon remnan o he hadronic final sae, which increases had (E p z ). Conribuions from nex-o-leading order processes can also lead o smaller values of x obs γ, since a hird je, iniiaed by he addiional hard ougoing paron, is produced. To summarize, he observable x obs γ is sensiive o he resolved phoon srucure and conribuions from higher

86 8 CHAPTER 5. EVENT SELECTION 2 Jes: p > 7(6) GeV, -2.5 < η < 2.5 Muon: p > 2.5 GeV, -.3 < η μ <.5 μ e p R μ RUN Even 5463 Z LAr energy [GeV] φ (degrees) Je2 Je - -2 η 2 Y X Figure 5.: Schemaical rz and xy view of he H deecor showing a ypical even ou of his analysis. The LAr energy of he wo seleced jes is also illusraed.