Diploma Thesis. supervised by Prof. Dr. Christoph Grab Tutor: Michel Sauter

Transcription

1 ETHZ-IPP-29-7 ElasticJ/ψProductionatlowQ 2 athera Florian Hubr Diploma Thsis suprvisd by Prof. Dr. Christoph Grab Tutor: Michl Sautr Swiss Fdral Institut of Tchnology Zurich Fbruary 29

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3 Abstract In this diploma thsis th lastic J/ψ vctor mson photoproduction(p J/ψp)isstudidinthdcaychannlJ/ψ + withthh1dtctoratth lctronprotoncollidrhera.thdatafromthrunsofthyar27with anintgratdluminosityof62.4pb 1 arusd. InthistimHERAopratd withtrdiffrntprotonnrgise p calldhigh(92gv),mdium(575gv) and low(46 GV) with intgratd luminositis 45.5(high), 5.96(mdium) and 1.9pb 1 (low). Thkinmaticalrgionof t <1.2GV 2,whrtisthfour momntumtransfratthprotonvrtx,andq 2 <1GV(photoproduction)is usd.furthrthrangofthcntrofmassnrgyinthphotonprotonrst fram,w γp,isrstrictdto4gv <W γp <11GV(high),2GV <W γp < 8GV(mdium)and2GV <W γp <1GV(low). Thdiffrntialcross sctionasafunctionof t iswlldscribdbyanxponntial,dσ/d t b t, whichyildstob =4.4 ±.2(stat.). ThcrosssctionasafunctionofW γp is fittdbyapowrlaw,dσ/dw γp Wγp δ,andgivs δ =.66 ±.7(stat.). Kurzfassung In disr Diplomarbit wurd di lastisch J/ψ Vktormson-Photoproduktion(p J/ψp)imZrfallskanalJ/ψ + mitdmh1dtktorbim Elktron Proton Kollidr HERA studirt. Di Datn aus dr Laufzit vom Jahr 27mitinrintgrirtnLuminositätvon62.4pb 1 wurdnbnutzt.indisrzitarbittheramitdrivrschidnnprotonnnrgine p,gnannt hoch(92 GV), mittl(575 GV) und tif(46 GV) mit intgrirtn Luminositätn45.5(hoch),5.96(mittl)und1.9pb 1 (tif).dikinmatischrgion t <1.2GV 2,wobitdrVirrimpulsübrtragbimProtonVrtxist,und Q 2 <1GV(Photoproduktion)wurdbnutzt.AussrdmwurddrBrich drschwrpunktsnrgiimphotonprotonruhsystm,w γp,ingschränkt auf4gv < W γp < 11GV(hoch),2GV <W γp < 8GV(mittl)und 2GV <W γp <1GV(tif).DrdiffrntillWirkungsqurschnittalsFunktionvon t istgutbschribndurchinexponntialfunktion,dσ/d t b t, wlchszub = 4.4 ±.2(stat.)führt.DrWirkungsqurschnittalsFunktion vonw γp istbstimmtdurchinpotnzfunktion,dσ/dw γp Wγp,undrgibt δ δ =.66 ±.7(stat.).

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5 Contnts 1 Introduction 7 2 Thory KinmaticVariablsofElctronProtonScattring CharactrisationofJ/ψProduction ModlsforVctorMsonProduction RggThory RconstructionofthKinmaticVariabls CrossSctionandPhotonFlux Th H1 Dtctor at HERA ThHERAAcclrator ThH1Dtctor Tracking Calorimtry,MuonandForwardTaggrSystm H1TriggrSystm FastTrackTriggr(FTT) Mont Carlo Simulation DiffVMgnrator RwightMC ComparisonofMontCarlowithData Data Slction and Triggr DataSlction TriggrConditions Evnt Slction ExtractionofJ/ψcandidats H1TrackSarchAlgorithm(Findr) H1ElasticTrack-TrackJ/ψSarchAlgorithm(Findr) ElctronIdntification EvntSlction PhasSpacofthAnalysis... 36

6 6 Contnts 6.3 ExtractthNumbrofJ/ψ Efficincis GomtricAccptancandRconstructionEfficincy SlctionEfficincy CombindAccptancandSlctionEfficincy TriggrEfficincy Elastic Evnt Slction ForwardTagging UnfoldingProcdur ForwardTaggingEfficincis Cross Sction Calculation and Rsults SystmaticUncrtaintis Summary A Bin Cntr Corrction 73 B Kinmatical limit forq 2 75 C MinimalW γp 77 D Cross Sction Valus 79 E Photon Flux Factors 81 Bibliography 82 Acknowldgmnts 87

7 Chaptr 1 Introduction Th Standard Modl(SM) of particl physics, volvd and vrifid by many masurmnts, prsnts today th most accurat modl to dscrib th mattr and th fundamntal intractions of natur. Within this framwork two kinds of particls ar distinguishd frmions, which hav half-intgr spins, and gaug bosons with intgr spins. Frmions ar again dividd in two groups: lptons and quarks. Whras lptons, lik lctrons and positrons, ar dscribd as point lik particls, baryons, lik th stabl protons, wr found to hav an innr structur. Th HERA acclrator was build as an lctron proton collidr to xtnd th knowldg of this innr structur of protons and also to tst Quantum Chromo Dynamics(QCD), which dscribs th intraction of gluons, th slf intracting carrir particls of th strong forc, and quarks. For this purpos svral dtctors whr constructd to dtct th scattrd particls aftr th collision. On of this dtctors is H1, which has producd th data sampls usd in this thsis. At hadron hadron intraction th class of so calld diffractiv procsss wr found, which ludd th dscription of prturbativ QCD(pQCD) in phas spac rgions whr no hard scal,forxamplalargmomntumtransfratthlctron(q 2 )orthprotonvrtx(t), xist. Instad a phnomnological modl calld Rgg thory is usd. In this modl a so calld pomron, which only carris vacuum quantum numbrs, and thrfor is also colourlss, is usd as intracting particl. Diffractiv procsss also occur by p-scattring, which can b dscribd by th Vctor Dominanc Modl(VDM), for xampl by th xclusiv vctor mson production. Sinc in thphotoproduction(inthoryq 2 =,butxprimntallyq 2 <1GV 2 isusd)andatlow momntum transfr at th proton vrtx(low t ) rgion thr is no hard scal availabl, dscription by th Rgg thory will b prformd. In figur 1.1 th dpndnc of th lastic(th proton stays intact aftr th scattring) vctor mson(vm) photoproduction cross sction on th cntr of mass nrgy in th protonphotonrstframw γp isgivnforsvralvctormsons(γp γvmp). Butforth J/ψVMstillxistsagapbtwnfix-targtandarlirH1masurmnts.Thgoalofthis

8 8 Introduction thsisistofillthisgapbyusingh1datafrom27bcausinthistimpriodalsolowr cntr of mass nrgis ar availabl. Th xamind channl to rconstruction J/ψ vnts isj/ψ +. Th nxt chaptr givs an ovrviw of th thortical tools ndd in this thsis. Chaptr 3 introducs th H1 dtctor and its main parts, spcially th componnts important for this thsis ar discussd. Th fourth chaptr dals with th aspcts of Mont Carlo simulation and rwighting of thm. Th data usd for this analysis ar discussd in chaptr 5. Whr also th triggr conditions ar xplaind. Chaptr 6 dscribs stp by stp th sarch algorithms and cuts usd to slct J/ψ candidats and also th xtraction of th numbr of J/ψ vnts. Th nxt chaptr dals with aspcts of infficincis, such as gomtrical accptanc, rconstruction, slction and triggr fficincis. In chaptr 8 th procdur to sparat lastic from inlastic vnts is dscribd. And finally in th last chaptr th (diffrntial)lasticcrosssctionsofj/ψproductionasafunctionof t andw γp argivn. Som additional information ar givn in th appndics. 2 Accordingto[5]:onlyfixd-targtrsultsarshownwhichwrprformdonH 2 andd 2 targtsandwhich hav bn corrctd for contributions from proton dissociativ procsss.

9 Figur 1.1: Ovrviw of th dpndnc of th lastic cross sction of svral vctor mson productionandofthtotalphotonprotoncrosssctiononthcntrofmassnrgyinth photonprotonrstframw γp inthphotoproductionrgion.thfiguristaknfrom[1]. Th grn triangls originat from fix-targt xprimnts; for J/ψ thy ar xtractd from[2, 3] 2.ThrdcirclsrprsntthH1masurmnts;forJ/ψthyarxtractdfrom[4]and th rd star masurmnt point is coming from[5]. Th blu triangls rprsnt th Zus masurmnt; for J/ψ thy ar xtractd from[6]. 9

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11 Chaptr 2 Thory 2.1 Kinmatic Variabls of Elctron Proton Scattring Anlctronproton(p)scattringprocss(p Xor ν X)isinladingordrdscribdby xchangingaphoton(γ),z -orw ± -boson.anxchangofaphotonorz -bosoniscalld anutralcurrnt(nc)procss,whrasbyachargdcurrnt(cc)procssaw ± bosonis xchangd.butccprocsssarhighlysupprssdatlowq 2 [7],thrforonlyNCar lft in th rgion whr th analysis is don. Additional th contribution from γ-xchang tothnccrosssctiondominatsthz -procss,bcausofthlargz -mass,thusinth following only lctromagntic intraction is considrd in th lctron vrtx. Agnricpscattringvntisshowninfigur2.1. Thincominglctron 1 withmomntumkxchangsavirtualphotonwithmomntumqandlavswithamomntum ofk. Prprsntsthmomntumofthincomingproton,P X thmomntaofthoutgoing particls producd by th bursting proton. Sinc ths 4 momnta ar not Lorntzian invariant, th following variabls ar usd to dscrib th scattring procsss: ThphotonvirtualityQ 2 q 2 = (k k ) 2. Thsquardcntrofmassnrgyinthlabsystms (k +P) 2 4E E P bynglctingthmasssofthprotonandlctron. ThsquardcntrofmassnrgyinthprotonphotonrstframW 2 γp (P +q) 2 ys Q 2 bynglctingthmasss.ymansthinlasticityandisdfindasy P q P k.2 Thsquardmomnttransfratthprotonvrtxt (P X P X )2. InthlimitQ 2 GV 2 thphotonbcomsral,thatisthrasonwhyq 2 iscalld virtuality. This is similar to th procss whr a ral photon would scattr with th proton, thrforthisprocssiscalldphotoproduction. Inthopposit,ifQ 2 GV 2,thistyp ofintractionisnamdlctroproductionordpinlasticscattring(dis).sincq 2 isproportionalto1 cos Θ,with Θ thanglbtwnthincomingandscattrdlctron(outgoing lctron in figur 2.1), th dirction of th scattrd lctron trajctory is going to th cntral rgionofthdtctorwithincrasingq 2. 1 AtHERAbothlctronsandpositronswrusd. 2 Q 2,yandthBjorknx= Q2 2P k arrlatdaccordingthformulaq2 =xys.

12 12 Thory (k) Q 2, ν (k ) s W γ,z,w ± (q) γp p(p) t X(P X ) Figur 2.1: Gnric Fynman diagram for p scattring. Th 4-momntum vctors of th particls ar put in parnthss. Exprimntally a cut has to b applid, to distinguish th rgions from ach othr. In this thsisvntswithq 2 <1GV 2 arcalldphotoproductionvnts. 2.2 Charactrisation of J/ψ Production Th classification of vnts producing a J/ψ can b don from diffrnt viwpoints. In this thsis th xprimntal sid is usd, instad of a thortical argumntation. Exprimntally two procsss ar visibl in th dtctor. First th inlastic J/ψ production γp J/ψX (sfigur2.2(a) 3 and(b)),whrxrprsntsallothrparticlsproducdbythintraction. Scond th lastic J/ψ production γp J/ψp, whr th proton stays intact(s figur2.2(c)). For lastic(and partially also for inlastic) J/ψ production th proton and photon xchang a vacuum quantum numbr objct. Th bhaviour of this intrmdiat stat is spcifid in th thory usd to dscrib th scattring procss. In Rgg thory this objct isapomron(p),inladingordrqcdadoublgluon(gg)andinhighrordrsofqcd a gluon laddr. In thory oftn a slightly diffrnt procss classification is don. A procss is calld diffractiv 4 ifavacuumquantumnumbrobjctisxchangd. Thisprocsscaninlading ordr b illustratd by figur 2.2(b). Unfortunatly th dfinition of a diffractiv procss is not uniqu, somtims additional or vn othr critria ar usd. For som xampls s[9].thrforandbcausofthdtctorrspons,thprotonissplittingupornot,in this thsis th abov classification, which sparats vnts only in th classs of lastic and 3 ThadditionalgluonhastobthrbcausofcolourandparityconsrvationandthfactthataJ/ψis colourlss. Without such a gluon no colour singlt J/ψ could b producd. But a non colour singlt stat of a c and c, whras thy ar hadronizing sparatly, is still possibl, it is calld opn charm production. ThorticallypossiblisalsoaJ/ψformdbyacolourocttc cpair,inthiscasthadditionalgluon(g) would not b ndd. But this procss is dominatd by th colour singlt production[8]. 4 Thtrmdiffraction,asitisusdinopticalwavthory,isnotoutofplac. Inddforhadronhadron intractionthsambhaviourasforopticalwavswasshowntobvalid(s[9]andmordtaild[1]).

13 2.3 Modls for Vctor Mson Production 13 (k) (a) (k ) (k) (b) (k ) (k) (c) (k ) γ(q) J/ψ g X(P X ) p(p) X 1 p(p) γ(q) P,gg J/ψ X(P X ) p(p) γ(q) P,gg J/ψ p(p ) Figur 2.2: Gnric lading ordr Fynman diagrams for inlastic(a) and(b), and for lastic (c) J/ψ production. inlastic vnts, is usd. 2.3 Modls for Vctor Mson Production Du to prturbation thory on can dscrib th photon as suprposition of a bar photon stat γ B andofaq qstat,cratdbyfluctuationofthphoton.ifthvirtualityissmall thnthfluctuationislonglivdandoncanlookatitasavctormson. Thrfora photoncanbwrittnas γ = Z 3 γ B +c α h, whr h isahadronicstat[11]andmusthavthsamquantumnumbrsasthphoton (J CP =1 ). Z 3 =1 c 2 αisnddtogtthproprnormalisationand αmansth lctromagntic coupling constant. It was shown that, if th targt particl is a hadron for xamplaproton,thnthhadronicstatofthphotonwilldominatthprocssandth intraction is similar to proton proton intraction[9]. Inthnon-prturbativVDM(VctorDominancModl)modl 5 onassumsthatonlyth hadronicpartintractswithahadronictargtandthatthhadronicstatofthphotonisa suprposition only of vctor msons. Sinc in this thsis only J/ψ ar considrd, on can stc α h = f J/ψ V J/ψ.Withthlctricchargandf J/ψ aconstant. Thrfor in this modl th γp intraction is similar to hadron-hadron intraction. By incrasingq 2 (ort,orp t )thvirtualitywillincrastooandthusonxpctsthatth dscriptionof γpscattringwillfailinthhighq 2 (andt,p t )rgion[11]. Butonth othr sid th dscription by prturbation quantum chromodynamics(pqcd) should b appropriat. Thrfor both modls supplmnt ach othr in ths two sparatd rgions. 5 ActuallythVDMmodlonlyconsidrdthvctormsons ρ, ω, φsincthoswrthonlyonknown atthattim.ifthhavirvctormsonsj/ψand Υartaknintoconsidrationaswll,onspaksofth gnralisd vctor dominanc modl(gvdm or GDM). For simplicity in this thsis it will rfrrd as VDM.

14 14 Thory 2.4 Rgg Thory RggthoryisavrysuccssfulthorytodscribhadronhadronscattringA +B C +D.ItconnctsthspinJandthsquarmassm 2 forparticlswiththsam intrnal quantum numbrs, such as isospin, strangnss, baryon numbr and so forth. As dscribd in th last sction according to th VDM γp intraction is similar to hadron-hadron intraction,thrforitisalsopossibltousrggthoryforpscattringinlowq 2 domain. Th first hadron hadron intractions studid, lik π p ρp procsss, could wll b dscribdbythxchangofapion.butforothrprocsss,lik πp πp,thxchang ofapionisnotallowd,bcausofg-parityviolation.usingaρinstadofaπispossibl and showd a good agrmnt with th data[7]. Thrfor it was proposd th xchang of a so calld rggon, which is quivalnt to th xchang of particls with diffrnt spins (sfigur2.3). 6 R = J = 1 + J = Figur 2.3: A rggon xchang can b sn as th xchang of many particls with diffrnt spins J. ThRggthoryassumsthatthrxistboundstatswithangularmomntumJ B, massm B andrsonancswithj R andm R.Thboundstatscratapolatt=t B M 2 B, thrsonancsatt=t R M 2 R im RΓofthpartialwavamplitudf j (t)forj=j B and j =J R,rspctivly.Nowitispossibltointrpolatf j (t)btwnthintgrvalusjto gtf(j,t),whrlcanbcomplx,anddmandthatf(j,t) =f j (t).thnitispossiblto intrprtthsquncofthpolsasasinglmovingrggpolwithl = α(t)[7]. Th function α(t)iscalldrggtrajctorywith α(t i ) =J i.oncanthnwritthconnction btwn thm as J =R(t j ). Asanxamplinfigur2.4(a)thtrajctoryfor ρisgivnandin2.4(b)thsocalld 6 Agnralrasonwhysinglparticlxchangcannotdscribtwo-bodyscattringinthhighnrgyrgion is th fact, that th transition amplitud T(s,t) s s J, whrsandtarthmandlstamvariabls(s = (p A +p B ) 2 = (p C +p D ) 2 andt = (p A p C ) 2 = (p B p D ) 2 ),violatsth(martin-)froissartboundforj>1andthrforunitarity[9]. Th(Martin-)Froissart thormsays,thatthtotalcrosssctioninthhighnrgyrgionhastoblimitdby whrcisaconstant. σ cln 2 s fors,

15 2.4 Rgg Thory 15 (a) (b) Figur2.4: (a)th ρtrajctoryxtractdfromthraction π p π n[7]. (b)chw- FrautschiplotshowsdiffrntRggtrajctorisinthJ-M 2 plan. Chw-Frautschi plots, which shows diffrnt trajctoris. It is rmarkabl that th Rgg trajctoris ar linar. Thrfor it is possibl to xprss α by α(t) = α + α t. WiththusofthRggtrajctoryitispossibltowritthtransitionamplitudforth two-body scattring as T s (s,t) s α(t) andifthfullcalculationistaknintoaccountoncandriv[7] dσ dt = γ(t) ( ) s 2(α 1) s 2 2α tlns s, (2.1) s whrs isjustanarbitraryscalingfactorand γ(t)isrlatdtothrsiduoff(j,t). In th tim of cration of th Rgg thory th nrgis usd for scattring xprimnts wr small compard to th cm nrgy usd at HERA. Fits for diffrnt trajctoris gav α.5and α 1GV 2.Thrforitwasxpctdthatthtotalcrosssction,givnby σ tot s α 1,woulddcraswithhighrnrgy.Butthiswasnotthcas.Soanwobjct calldpomron(p)withvacuumquantumnumbrsandatrajctory α P (t) = α P () + α P t wasintroducdwith α P () >1inordrtodscribthdata. Ifafitisdonofthtotal γpcrosssctiononfindsthtrajctory α P (t) = t, whichwasprdictdbydonnachiandlandshoffbforthstartofhera[9] 7. 7 Toxtndthfitrangalsoarggonxchangbsidapomroncouldtakintoaccount.Thcrosssction canthnbyparamtrisby σ tot = XW α P() 1 +YW α R() 1. ThisladstofitparamtrsX =.677,

16 16 Thory 2.5 Rconstruction of th Kinmatic Variabls Inpscattringprocsssthusualscattringvariabls (y,q 2,x)canbdtrmindby 5 diffrnt standard mthods using xprimntally accssibl obsrvabls. This stp is normally calld rconstruction. (An ovrviw and a comparison of th diffrnt mthods canbfoundin [12]). InthisthsisthlctronmthodisusdtocalculatQ 2 by Q 2 =4E E cos2 Θ 2, (2.2) whre ande mansthnrgyofthincomingandscattrdlctronand Θ thangl of th scattrd lctron with rspct to th proton dirction. To calculat y a modifid Jacqut Blondl mthod is usd, whr y mh = (E p z) ψ 2E. (2.3) (E p z ) ψ mansthnrgyminusthzcomponntofthj/ψmomntum.thmomntum diffrnc of th incoming and outgoing proton t is rconstructd by t p 2 ψ,t, (2.4) whrp ψ,t isthtransvrsmomntumcomponntofthj/ψ. Thisformulaisvalidfor small t andforsmallq 2. Itisassumdthatthmasssarngligiblcompardtoth nrgis(m,m E,E andm p,m p E p,e p ).Ascanbsninquation2.4,normallyis t <,thrformostofthtimnottbut t willbusd,togtpositivvalus. 2.6 Cross Sction and Photon Flux Th inlastic diffrntial p cross sction in DIS can b writtn(in lading ordr, Born cross sction) as d 2 σ p [ dydq 2 =4πα2 y 2 ] Q 4 xf 1 + (1 y)f 2, x whrasthf i F i (y,q 2 )fori 1,2manthprotonstructurfunctionsand αrprsnts thlctromagnticcouplingconstant.thparityviolatingstructurfunctionf 3 isngligiblinthrgionq 2 m 2 Z [13].IfthlongitudinalstructurfunctionF L (y,q 2 ) =F 2 2xF 1 isintroducd,ongtsforthcrosssctionbyliminatingf 1 infavouroff L d 2 σ p [ dydq 2 =4πα2 (1 y+.5y)f2 Q 4.5y 2 ] F L. x Y =.129, α R =1.88and α R () =.5475forthtotal γpcrosssction.

17 2.6 Cross Sction and Photon Flux 17 For historical rasons and for th fact that th thortical prdictions normally ar givn for th γp cross sction, th p cross sction will b transformd. Following th standard approachandusingthwizsäckr-williamsapproximation[14,15,16]atlowq 2 inwhich thincominglctronissnasa bunchofphotons,onmaywritthpcrosssction inagnralformas d 2 σ p dydq 2 = FT γ (y,q 2 )σ T γp + F L γ(y,q 2 )σ L γp, whr F T γ (y,q 2 )and F L γ(y,q 2 )rprsntthtransvrsandthlongitudinalphotonflux and σ T γp and σl γp thtransvrsandlongitudinal γpcrosssctionswith σ γp = σ T γp + σ L γp.in this approximation on gts Thusth γpcrosssctionis F T γ (y,q 2 ) = ε(y) = FL γ(y,q 2 ) F T γ (y,q 2 ) = α ( 1 y+.5y 2 ) πyq 2 1 y 1 y+.5y 2. d 2 σ p dydq 2 FT γ (y,q 2 )σ T γp [1 +Rε], withr= σl γp. σγp T Itisusdthat ǫ 1,whichmansthatallphotonsartransvrs 8. Thrforthcross sction is d 2 σ p dydq 2 FT γ (y,q 2 )σ γp. Finally th total γp cross sction in th visibl kinmatical rgion is givn by intgrating ovryandq 2 σ γp( y, Q 2 ) σ p Φ T γ 8 Thisapproximationisrasonabl,bcausthkinmaticalrgionisrstrictdtoW γp 11GV,dutoth vntslction(schaptr6).thismanswithq 2 <1GV 2 andw γp = ys Q 2 thaty.25andthus ε.96.in[4]p.34rismasurdanditfollowsthatforq 2 <1GV 2 thatr.1.thrforain d 2 σ p dydq 2 FT γ (y,q 2 1 +Rε )σ γp, 1 +R }{{} A isa.996.thusbyusinga =1,whichisqualto ε =1,thintroducdsystmaticuncrtaintybythis approximation is xpctd to b small compard to th total systmatic uncrtainty.

18 18 Thory whr Φ T γmansthintgratdphotonflux Φ T γ = ymax y min dy Q 2 max Q 2 min dq 2 F T γ. (2.5) ThintgrationrangofyisdirctlylinkdtothW γp rang(sabov)whichisdtrmindbythphasspacofthanalysis. ThupprQ 2 boundaryforphotoproduction canbchosnxprimntallyandissttoq 2 max =1GV 2,butthlowronisgivnby Q 2 min = y2 1 y m2 (sappndixb),whichisvalidforlarglctronmomntumscompardto lctron mass. Th valus of th intgratd photon flux ar givn in appndix E.

19 Chaptr 3 Th H1 Dtctor at HERA This chaptr givs a vry brif ovrviw of th HERA acclrator and th H1 dtctor. Th parts rlvant for this analysis of th dtctor ar dscribd in mor dtails othrs ar omittd.foranarlyfulldscriptionofthh1dtctors[17,18,19]. 3.1 Th HERA Acclrator Th HERA(Hadron Elktron Ring Anlag) acclrator th only p-collidr vr built was locatd at DESY(Dutschs Elktron Synchrotron). Th opration priod is dividd intwomainphass,calldheraiandheraii,andnddin27. Btwnthstwo priods a luminosity upgrad was installd. Th intgratd luminosity of HERA I and II arshowninfigur3.1.sincduringthattimnocollisionstookplac,itwasalsousdto mak som modifications at th dtctors, for xampl th Fast Track Triggr for H1 was installd. In this thsis only run priods from HERA II ar considrd, thrfor th trm HERAwillmanHERAII,ifnothinglsisnotd. ThmainringofHERAhadacircumfrncofabout6.3kmandcontainsthtwosparatdbampipsforthacclrationofthlptons 1 andprotons.thnrgyofthlptons was27.6gv.atheraiithprotonswrnominallyacclratdto92gv 2.Atthnd of HERA II opration, aftr a short brak for modifications of about two wks, collisions withprotonnrgisof46gvand575gvwrprformd. Thmainrasonwasto dirctlymasurthlongitudinalstructurfunctionofthprotonf L [2]. Thparticlbunchswrsparatdbyatimintrvalofabout96ns,whichcorrspondto a frquncy of 1.4 MHz. Th bams wr colliding at two points whr th xprimnts H1andZEUSwrlocatd.AtthothrtwostraightpartsofHERAthfix-targtxprimnts HERMES and HERA-B wr stationd. A schmatic ovrviw of HERA and its pr-acclrators is shown in figur Sinclctronsandpositronswrusdasparticlsforacclratingthywillbrfrrdaslptons. 2 ForHERAIitwas82GV

20 2 Th H1 Dtctor at HERA H1 Intgratd Luminosity / pb -1 Status: 1-July lctrons positrons low E HERA-2 HERA-1 Hall NORD (H1) Hall NORTH (H1) Hall nord (H1) HERA Hall WEST (HERA-B) Hall WEST (HERA-B) Hall oust (HERA-B) HASYLAB DORIS Hall OST (HERMES) Hall EAST (HERMES) Hall st (HERMES) Elktronn / Positronn Elctrons / Positrons Elctrons / Positons Protonn Protons Protons Synchrotronstrahlung Synchrotron Radiation Rayonnmnt Synchrotron DESY Days of running Figur 3.2: A schmatic ovrviw of HERA Figur 3.1: Intgratd luminosity for HERA Iand its pr-acclrators. and II. 3.2 Th H1 Dtctor PETRA Hall SÜD (ZEUS) Hall SOUTH (ZEUS) Hall sud (ZEUS) ThH1dtctorwaslocatdinthNorthhallofthHERAringandwasbuiltbyacollaboration of about 4 physicists from ovr 4 countris. Du to th diffrnt momnta of th collidingprotonsandlptonsthdtctorwasbuiltasymmtricallyalongthz-axis 3.This mans that th componnts in th forward and backward dirction ar not idntical. For anovrviwofmost 4 partsofthh1dtctorsfigur3.3. Th dtctor was consistd of diffrnt subsystms. Th first and most closly placd to th bam pip was th tracking systm, its sub-dtctors wr constructd to masur as prcis as possibl th trajctory of th chargd particls producd by th collision. Th applid magntic fild producd a bnt trajctory which allowd to xtract th momntum. Th tracking systm was surroundd by th calorimtry dtctors. In th forward and cntral dirction a liquid argon dtctor was placd, which primary assignmnt was to masurd th nrgy of th particls. Th lctromagntic part usd lad, th hadronic stl as absorbr plats. In th backward rgion a spaghtti calorimtr was usd mainly to dtct th scattrd lctron, which is ssntial to idntify DIS procsss. Thy all wr nclosd by a suprconducting magnt, which producd a fild of 1.16 T. Th nxt layr containd th muon dtctor and th iron rturn yok, both usd to rturn th stramlins 3 ThoriginofthH1coordinatsystmissituatdinthnominalintractionpoint. Thz-axisisorintd along th dirction of th incoming proton. Th positiv z-dirction is calld forward, th ngativ backward dirction.thx-axispointstothcntrofthheraring,andthusthy-axisdirctsupwards.toxprss th dirction of particls normally Θ(angl btwn th trajctory of th particl and th positiv z-axis) and φ(angl btwn th x-axis and th projction of th trajctory into th xy-plan) ar usd. 4 InthisanalysisthForwardTaggingSystm(FTS)wasusdtoo,butsincthnarstFTSdtctorcomponntwaslocatd26mfromthintractionpointthyarnotvisiblinfigur3.3.

21 3.2 Th H1 Dtctor 21 of th magntic fild lctrons protons Figur3.3:AschmaticviwofthH1dtctor Tracking Th tracking systm in th H1 dtctor consists of thr dtctor groups Forward Tracking Dtctors(FTD), Cntral Tracking Dtctors(CTD) and Backward Tracking Dtctors(BTD). InthisthsismainlythCTDarusd.Foranovrviwofthtrackingsystmss[17,18]. Th innrmost dtctor in th cntral rgion is th Cntral Silicon Trackr(CST) with an angularcovragof3 < Θ <15 andconsistsoftwolayrsofdoubl-siddsilicon dtctors. Th CST is nclosd by th Cntral Innr Proportional Chambr(CIP) which is a multiwir proportional chambr. Th main tracking dtctor of H1 is th Cntral Jt Chambr(CJC)whichissplitintwoconcntricpartsCJC1andCJC2.ThCJC1contains3, thcjc26azimuthalcllswithanangularcovragof2 < Θ <16 (sfigur3.4). Btwn thm th Cntral Outr z-drift Chambr(CIZ) and th Cntral Outr Proportional Chambr(COP) ar situatd. InthforwarddirctionthForwardMuonDtctor(FMD)(3 < Θ < 17 )islo-

22 22 Th H1 Dtctor at HERA catd[21] Calorimtry, Muon and Forward Taggr Systm Thnrgyofparticlsismasurdbythcalorimtrysystm.InH1itconsistsoftwomain calorimtrs. In th forward and cntral rgion a Liquid Argon(LAr) dtctor covrs th angl4 < Θ <153.ThLArconsistsoftwoparts,thinnronussladabsorbrsand dtct lctromagntic showrs whilst hadronic showrs usually pntrat into th outr part which uss stl absorbrs[17, 18]. In th backward dirction a Spaghtti Calorimtr(SpaCal) with lad-scintillating fibrs ismainlyusdtodtctthscattrdlctron(153 < Θ <177.5 )[22,19]. Inthforwarddirctionatz =4.9mthPLUGcalorimtrissituatd. Itconsistsof a lad absorbr followd by four layrs of scintillators and has an angular covrag of 1.2 < Θ <3.2. Fardownthbampipatz =26,28,53and92mthfourstationsofthForward Taggr Systm(FTS) ar locatd, ach contains four scintillators arrangd around th bam pip. 3.3 H1 Triggr Systm ThbunchcrossingatHERAhasafrquncyof1.4MHz,howvrthintrstingprocsss wr only producd with about 1 khz. Th rmaining part is causd by background procsss.stillthh1radoutfrquncyismuchlowr(5hz)andthmaximaltapwrit spd,ofabout2mb/s,isvnlowr.thusthvntsactuallytostordontaphavto b slctd as fficint as possibl and th background has to b rjctd. This is prformd by th triggring systm, which is hirarchically dsignd in 4 lvls. This mans, that only vntspassdthfirstlvltriggr(l1)willbconsidrdinthscondlvl(l2)andonly vntsaccptdbythl2triggrarpassdtoththirdon(l3).thsamistruforth fourth lvl(l4) triggr. ThL1triggrisdsigndtomakafirstclassification,thrforitisimportantnotto losanyvnt.itwasbuiltwithoutanydadtimandwithonly2.3 µstorturnadcision. Tomakthispossiblthinformationfromvrybunchcrossingwithinth2.3 µs which corrspond to about 23 bunch crossings wr hold in a piplin. 256 triggr lmnts from diffrnt sub-dtctors ar combind in th cntral triggr logic to 128 sub-triggrs, i. for vry sub triggr xist a collction of conditions. But th output frquncy of som L1 sub-triggrsmaystillbtoohigh,bcausthl2inputislimitdbyabout1khz.thrfor vrysub-triggrhasalsoasocalldprscalfactorn,whichmansonlyvryn th vnt, that fulfils th sub-triggr conditions, is allowd to pass to th nxt lvl. A sub-triggr is calld raw sub-triggr, if an vnt satisfis all conditions. If it also passs

23 3.4 Fast Track Triggr(FTT) 23 th prscal condition thn it is calld actual sub-triggr. Ifatlastonactualsub-triggrisgivnforanvntthnth L1Kp signalissntand thvntistransfrrdtol2. Atthispointthdadtimbginsbcausthstoringof vnts in th piplin is stoppd. ThL2lvliscomposdofthrpartsallprovidingL2triggrlmnts.Thfirston uss a nural ntwork, th scond on combins information from tracking, calorimtry andfromthmuonsystmsandiscalldtopologicaltriggr. Andththirdon,thFast Track Triggr(FTT), is basd on th tracking information with a high spatial rsolution comparabltothonavailablofflin[9].thl2has2 µsavailablforcalculationandifan L2 triggr condition is satisfid, th rad out of th dtctor starts, othrwis vrything is clardandthpiplinfroml1isfilldagain. ThL3lvlcanhandlaninputratofabout2Hzandhasanoutputfrquncyof circa5hz.during1 µsithastimtoconfirmorrjctthdcisionmadinl1andl2. IncasofnotaccptingthvntbyL3thdtctorradoutisstoppdandthdatatakingisrstartd.L3ussthFTTnvironmntandwasdsigndtolookforspcificdcay channls(s blow). Th fourth triggr lvl(l4) dos not contribut anymor to th dad tim. Aftr th vntispassdtol4,thl1piplinfillingisrstartd. ThrforL4isworkingasynchronoustothHERAclock.Thislvlisnothandldbyhardwarasthprviousons, but by softwar running on a PC farm. Sinc th full rconstruction information is availabl,somadditionalrductionofthvntfrquncytoatapoutputofabout1hzis don by rjcting background and downscaling diffrnt vnt classs, which lads to L4 scaling factors calld L4Wights. passing L4 ar writtn on tap and ar accssibl for an offlin analysis. 3.4 Fast Track Triggr (FTT) By th upgrad to HERA II th luminosity was incrasd. Thrfor it was ncssary to build nw triggrs which ar abl to rjct th growing amount of background vnts and slctwithhighprcisionthintrstingphysics,spciallyinthrgionoflowq 2 whr nocalorimtrtriggrcouldbusd[23]. ThFastTrackTriggr(FTT)isabltorconstruct final stats from tracks on triggr lvl, thrfor it is an accurat instrumnt to look forhavyflavourphysics,liklasticvctormsonproductionord dcays(ofintrstis thdcayintokaonsandpions(d D π (Kπ)π),thsocalld goldnchannl ), spcially in th photoproduction rgion of th phas spac. ThFTTprovidstriggrsonL1toL3lvl. OnL1andL2lvlthFTTusssollyth

24 24 Th H1 Dtctor at HERA CJC1 CJC Figur3.4: ThfourCJClayrsusdforthFTTarcolourdorang. Evrylayris composd of thr sub layrs.(takn from[23]) information from th CJC to rconstruct th trajctory of particls. On L1 it uss four layrs withthrwirsach(sfig.3.4),tocalculatthtracksinthrφ-plan(onlypoorinformation about th z-axis is dtrmind). Thrfor cuts on th transvrs momntum ar prcis, compard to arlir triggrs. On L2 th granularity of th track rconstruction is improvd, du to th tim availabl for a dcision. Also bttr z-rsolution is achivd on thislvl.thrforatthispointprcisinformationofp t andz-vrtxarusabltomak adcision. OnL3thinformationfromthCJCandfromothrsub-dtctorsarcombind. ThL3 provids a partial vnt rconstruction including invariant mass and particl idntification. ThrforitispossibltotriggronD orinlasticj/ψvntswithlarg t. Formor information s[9]. ForthMontCarloSimulation(MC)(schaptr4)thrsponsofthFTTtriggrhas to b simulatd. This is don by th FTT mulation softwar(fttemu), which is running aftr th H1SimRc program, whras this packag simulats th rspons of th rmaining dtctor units.

25 Chaptr 4 Mont Carlo Simulation Mont Carlo(MC) simulations ar widly usd in particl physics for divrs rasons. Th first is to compar thortical modls with masurmnts. Th scond is to dtrmin fully inclusiv quantitis such as cross sctions. This can b don.g. by xtrapolation of quantitis masurd in a limitd visibl rgion of th phas spac to th full phas spac. An othr application of MC is th dtrmination of accptanc and fficincis. Extrapolations usd in th simulation can lad to wrong bhaviour of a variabl, thrforitisssntialtomakcrosschcks,tobuildupconfidncinthsimulation. For this analysis MC simulation ar usd in thr placs. First, as mntiond abov, to calculat th accptanc, scond to calculat th triggr fficincis and third for th sparationoflasticandinlasticvnts.althoughthusofmcatthfirstandlastpointis invitabl, it is not for th triggr fficincy, bcaus it also can b dtrmind from data. Howvr th us of MC is rasonabl bcaus of statistical issus.(mor dtails ar givn blow.) Th program structur usd for MC simulation in H1 is th following Gnrator: ar gnratd randomly according to som thortical distributions. Which distribution in what variabl is usd dpnds on th physical modl in th vnt gnrator program. In this thsis th DiffVM gnrator is usd. Th output of th gnrator ar vnts with spcifid 4-vctors. Simulation of th dtctor rspons: Th passag of th gnratd vnts through th dtctorandthintractionwiththmatrialwillbsimulatd.inh1thisisdonby H1SIM. Evnt rconstruction: Th rspons of th dtctor du to th intraction of th particlsiscalculatdbythprogramh1rec,whichisthsamforgnratdasfor ral masurd vnts. Th programs H1SIM and H1REC ar combind in on, calld H1SIMREC. Triggr simulation: Whras th ordr of th first thr stps is common for particl physics vnt simulations, th FTT simulation(fttemu) and calculation basd on th

26 26 Mont Carlo Simulation information supplid by th FTT is don subsquntly to abov stps, du to historical rasons. 4.1 DiffVM gnrator Th DiffVM gnrator[24] simulats diffractiv procsss in th framwork of Rgg phnomnology and in th Vctor Dominanc Modl. Inthismodlavirtualphotonwillbmittdbythincominglctron.Inthisthsisth photons ar producd according to Wizsäckr-Williams Approximation[14, 15, 16]. Th virtual photon fluctuats into a virtual vctor mson(hr a J/ψ) and th vctor mson intracts diffractivly with th incoming proton by xchanging a pomron. Thrarmanyoptionswhichcanbchosn,s[24]. InthisthsisbothlasticandinlasticMCarusd.Normallythyrfrrdtoaslasfor lasticandinlasforinlasvnts. 1 Th cross sction dpnds on t according to ( ) dσ dt las = dσ dt ( ) W 4ε bt t=,w=w W (4.1) forlasticvnts. Itisaslightlymodifidvrsionofquation2.1 2,whichisprdictdby th Rgg Thory. For inlastic vnts, th distribution ( ) dσ dt inlas = dσ dt ( 1 b ) n ( ) W 4ε t=,w=w n t W wastakn. Thvariabl 1 + εisthconstantpartinthpomrontrajctorya P (t) α P () + α P t =1 + ε + α P t. 4.2 Rwight MC A MC simulation gnrats vnts according to a distribution which is givn by a crtain modl blivd to dscrib th undrlying physics of th masurmnt. Oftn this modl has som paramtrs which cannot b calculatd by this thory and thrfor hav to b masurd. 1 Thoptioninthgnratorstringfilisnamdas Choicoflasticorinlasticprotonvrtx. 2 Hrthcntrofmassnrgyinth γpsystmw γp isthrlvantnrgyscal,thrforsinquation.2.1 hastobrplacdbyw γp.

27 4.2 Rwight MC 27 Thdfinitionofthcrosssctionisgivninquation9.1and9.2. Tocalculatit,svral tims(sparation of lastic from inlastic vnts, accptanc, rconstruction, triggr fficincy and fficincy du to som additional cuts; s th corrsponding chaptrs) th usofmcisndd.butthsquantitisitslfardpndingonthparamtrsusdto gnrat th cross sction. To solv this loop dpndncs an itrativ procdur is usd in this thsis. Procss b[gv 2 ] n W ε α P lastic inlastic Tabl 4.1: Paramtr valus for DiffVM gnrator for lastic and inlastic sampls. FirsttwoMCsampls,onforlasticandonforinlastic,argnratdforachnrgy rgionaccordingtothparamtrsgivnintabl4.1. ThcrosssctionfordataandMC ar calculatd, whras MC is usd for th missing quantitis in th data cross sction dtrmination. Thn thy ar dividd. Bcaus th fficincis and th branching ratio ar th sam thy ar canclling, thus th rwighting distributions for th diffrntial cross sctions ar R las = Nlas data L data / Ndiffvm(las) and R L inlas = Ninlas data diffvm(las) L data / Ndiffvm(inlas) L diffvm(inlas). Anxamplofth t -rwightingdistributionsr las forlasticandr inlas forinlasticar givn in figur 4.1(a) and(b). Ths rwighting distributions ar fittd and th xtractd rwightparamtrsarusdtorwightthmcsampls.thsamisdonforw γp inan additional stp. R las R inlas t [GV ] t [GV ] Figur4.1:Examplofthlastic(a)andinlastic(b)rwightingfunctionsR las andr inlas asfunctionof t forthhighnrgypriod. Thlinrprsntsthfitwhichisusdto dtrmin th rwight paramtrs. An additional turn is not ndd bcaus th scond rwighting functions ar almost

28 28 Mont Carlo Simulation flat. Thcrosssctioninquation4.1showsthatitdpnds,accordingtothmodl,on t andw γp.butinthisthsisonlyondiffrntialcrosssctionarcalculatdandthrfor thrwightprocdurcouldonlybdonin t andw γp sparatly.ofcoursthisintroduc an rror but th fits of th rwight distributions show that thy still convrg. That wasxpctdbcaus εisstimatdtobsmall[7]. 4.3 Comparison of Mont Carlo with Data TolgitimatthatthproducdandrwightdMCcanbusd,infigur4.2and4.3 th comparison btwn data and MC is shown in diffrnt variabls(s caption of th figurs) as an xampl for th low nrgy rgion. Th grn histograms rprsnt th lastic MC, th blu th inlastic ons. Th gry histograms ar formd by stacking th twomchistograms.thrdpointsarthdata.thcutsusdforthisplotsargivnin tabl6.2. Additionalthcut2.9GV <m + <3.15GVisusd,torducbackground. (Thdfinitionofm + isgivninquation6.1). Ascanbsninthfigurs,thrisstillbackgroundinthdatasampls(diffrnc btwnthgryhistogramandthrdpoints).thisisdutothfactthatnobackground MCwasusd.NvrthlssthshapofMCanddatasmstoagrandthrforth dcision to us ths rwightd MC is justifid. Apossiblwaytosubtractthbackgroundisthsidbandmthoddscribdin[25,26].

29 4.3 Comparison of Mont Carlo with Data 29 7 (a) 6 Data DiffVM inlas (b) Data DiffVM inlas DiffVM las DiffVM las+inlas DiffVM las DiffVM las+inlas P t,j/ψ t [GV ] (c) Data DiffVM inlas DiffVM las (d) Data DiffVM inlas DiffVM las 12 DiffVM las+inlas 12 DiffVM las+inlas W γ p W γ p () Data DiffVM inlas DiffVM las DiffVM las+inlas 5 Data 4 (f) DiffVM inlas DiffVM las DiffVM las+inlas Θ J/ψ [ ] Φ T [ ] Figur 4.2: Comparison btwn Mont Carlo and data for th low nrgy priod as functionsofthtransvrsmomntumofth J/ψ, Pt,J/ψ, (a), t (b),w γp (c: quidistant binning,d:binningusdinanalysis),thtaanglofthj/ψ, Θ J/ψ,()and φanglsofboth tracks, φ T,(f).Thgrnhistogramrprsntsthlastic,thbluthinlasticMCvnts; stackdthygivthgryfilldhistogram.thrdpointsarthdata.

30 3 Mont Carlo Simulation 25 (a) Data DiffVM inlas DiffVM las DiffVM las+inlas P t,t (b) Data DiffVM inlas DiffVM las DiffVM las+inlas P t,low (d) Data DiffVM inlas 12 DiffVM las DiffVM las+inlas Θ T 1 () Data DiffVM inlas 8 DiffVM las DiffVM las+inlas Θ low (f) Data DiffVM inlas 1 DiffVM las DiffVM las+inlas Θ high [ ] [ ] [ ] (c) Data DiffVM inlas DiffVM las DiffVM las+inlas P t,high Figur 4.3: Comparison btwn Mont Carlo and data for th low nrgy priod as functionsofthtransvrsmomntumofbothtracks,p t,t,(a),thtransvrsmomntumofth smallr(largr)p t,p t,low (P t,high ),(b,c),ththtaanglofbothtracks, Θ T,(d)andththta anglofthsmallr(largr) Θ, Θ low (Θ high ),(,f).thgrnhistogramrprsntsthlastic, th blu th inlastic MC vnts; stackd thy giv th gry filld histogram. Th rd points ar th data.

31 Chaptr 5 Data Slction and Triggr First th data usd for th J/ψ masurmnt ar dscribd, aftrwards a short ovrviw ovr th triggr conditions is givn. 5.1 Data Slction Thdatastudidinthisthsiswrtaknfromthyar27,whichcorrspondtoth runrangfrom492559to ThndisschduldbythshutdownofHERA.In this run priod HERA was oprating with positrons of 27.6 GV nrgy. Th protons wr acclratduptothrdiffrntnrgisof92gv,575gvand46gv,calldhigh, mdium and low nrgy priod, rspctivly. Th luminosity and th run rangs for th diffrnt nrgis ar givn in tabls 5.1. dsignation proton nrgy run rang intgratd luminosity [pb 1 ] man prscal factor for s59 high mdium low Tabl 5.1: Luminosity, run rangs and man prscal factors for th thr diffrnt nrgy priods. Inthsrangsonlyrunswithatlast.1nb 1 luminosityandmdiumorgoodquality ar takn into account. Additional a fw run rangs ar xcludd, du to problms with som sub-dtctors in that tim. Furthrmor only runs ar slctd, with a rad-out of th dtctorcomponnts(cjc,cip,lar,plug,fmd,fts,spacal 1,TOFandLUMI),ndd for this thsis, wr on. 1 ThSpaCaldtctorisrqustd,bcausitisnddforthtriggrfficincystudy.

32 32 Data Slction and Triggr 5.2 Triggr Conditions ToslctlasticallyproducdJ/ψvntsinthdcaychannlJ/ψ +,i..dcayinto twochargdtracks,thsub-triggrs59isusd. ThL1andL2triggrconditionsfors59 ar givn in tabl 5.2. Th CIP conditions ar for background rjction, whras th FTT conditions ar fulfilld, if two opposit chargd tracks, with transvrs momntum abov ththrshold(givninthtabl),armasurdinthcjc.nol3conditionsarusdfor th s59 triggr. triggr lvl condition L1 L2 (CIPsig>1&&(CIPmul<6)&&(FTTmulTa<5)&&(FTTmulTd> )&& vto conditions (FTT mul T==2)&&(FTT Qtot==4) Tabl 5.2: L1 and L2 triggr conditions for th s59 subtriggr.(no L3 triggr conditions for s59xist.) In th following th sparat triggr conditions will brifly xplaind. Mor information aboutthcipargivnin[27]andforthfttin[9]. for L1 CIP sig> 1: This condition is usd for background rjction. It rquirs, that thnumbrofcntraltracks,n ctr,islargrthnthnumbrofbackward,n bkw, andforward, N fwd,tracksinthz-vrtxhistogramofthcip.itiscoddin N ctr >k(n bwd +N fwd )withk=1forcipsig>1[28]. CIPmul<6:Rprsntsthdmandtolimitthmaximalnumbroftracksto3 and thrfor rjcts background mostly coming from non p-intractions[9]. Th formulaforcalculationisn ctrl +N bkw +N fwd <MforCIPmul<mulandwith (mul M) = {(1 ), (2 2), (3 6), (4 1), (5 2), (6 3), (7 1),... }[28]. FTTmulTa<5:Thnumbroftrackswithatransvrsmomntumabov1MV snbythfttis4orsmallr. FTTmulTd>:AtlastonFTT-trackhasatransvrsmomntumabov9MV. andforl2 FTT mul T==2: Calls for xactly two FTT-tracks with a transvrs momntum largr than 8 MV. FTTQtot==4: OnlyvntswiththsumofchargsofallFTT-tracksisqualto zro, ar not rjctd.

33 Chaptr 6 Evnt Slction To masur th diffrntial lastic photoproduction cross sction, th numbr of lastic J/ψ vntswithinthkinmaticalrgionq 2 <1GV 2 asafunctionofthbinningvariablis ndd. This is don in thr stps. First diffrnt sarch algorithms, which in H1 ar calld findrs,arapplid.inadditionsomcutsarusdonthfullsampl,togtamasspak forthj/ψvnts.thscondstpwillbtofitthsdistributionswithacombinationof signalandbackgroundfunctions,inordrtogtthnumbrofj/ψvnts. Andthlast stp will contain th sparation of lastic from inlastic vnts. Thfirsttwostpswillbillustratdinthischaptr,thlastwillfollowinchaptr Extraction of J/ψ candidats SincitisnotpossibltodtctaJ/ψdirctlydutoitstooshortliftim,onisforcdto lookforitsstabldcayproducts.inthisthsisthlasticlptondcaychannlj/ψ + ischosn. Thusthgoalistoidntifythlctronsandpositronsfromthisdcayasfficint as possibl and rduc th background. Thrconstructionofparticlscanbsparatdintwoclasssandisdondutoth apparanc in th sub-dtctor units. If th informations from th tracking systm ar usd, thn th particl is lablld with slctd track or for short with track. Altrnativly on attachs th rconstruction of a crtain particl with clustr, if th information is basd onthcalorimtrydtctors.eachclassussdiffrntsarchalgorithms 1,calldfindrsin H1, to giv information about momntum, nrgy and charg. But no particl idntification isdonatthispoint. Looking for two dcay products and hav two distinguishing proprtis, track and clustr, lads to thr implmntd combinations of J/ψ findrs within th H1 softwar framwork: both dcay particls ar rconstructd by tracks(track-track), both by clustrs(clustr-clustr) and th combination of on track and on clustr(track-clustr). Dpnding on th phas 1 ThsarchalgorithmusdtofindaslctdtrackislocatdinthclassH1CratSlTracksandisbasdon thlwsttrackfindrtchniqu,s[29]orlookdirctlyintothclass. Forclustrsthfindrclass H1CratPartEm is usd.

34 34 Evnt Slction spac,onisintrstdin,spciallythw γp rgion,thproprcombinationisusd. In AppndixCthW γp rgionisillustratdaccordingtoththrcombinations.inthisthsis onlytrack-trackvntsarconsidrd,whichgivaccsstothlowstrgionofw γp H1 Track Sarch Algorithm (Findr) Th usd tracks ar standard H1 tracks, also calld slctd tracks or for short sltracks. Vrtx fittd tracks ar dividd in thr groups(cntral, forward and combind), ach with its owncuts.thnamsarhistoricallybasdonthtargion,butarchangdinthrlas usdforthisanalysis(h1oo3.3.1).thismanscntraltracksmustsatisfy1 < θ <179, forward6 < Θ <25 andcombind1 < Θ <3. Additionalcutssuchasminimal momntum, minimal transvrs momntum, track lngth and numbr of hits in th CJC ar also rquird. Sinc for th usd cntral tracks, th thta cut is almost maninglss, th othr cuts will b dcisiv. Thy ar primary rsponsibl for a quality of th rconstructd trajctory. Thdtaildcutsargivnintabl6.2. Othrsourcsofthissubjctcanb found in[3] or in th H1TrkFindr packag H1 Elastic Track-Track J/ψ Sarch Algorithm (Findr) Basdonthslctdtracks,thJ/ψsarchalgorithm,calldH1lasticJ/ψfindr 3,is usdtolookforlasticj/ψcandidatsbyapplyingthcutslistdintabl6.1. Ththta rgionofthtracksischosnsuchthatonlytracksarusdwhicharinthaccptancof thcjc.thtransvrsmomntumofachtrackndstoxcdththrsholdat.8gv. Thtracksmusthavoppositcharg,othrwisthsourcofthmcouldnotbanutral J/ψ. AndthrconstructdmassofthJ/ψhastoblargrthn1.5GVandsmallras 15GV.Rconstructdmassmans,thatthmassofthJ/ψiscalculatdbyth4-vctors ofthtracks,whrasthyarcomputdonthmasshypothsisofanlctronoramuon 4. Still at this point no particl idntification of th tracks is don Elctron Idntification SincnoparticlidntificationisapplidonthtrackorlasticJ/ψfindr 5,thJ/ψcandidat sampl still contains a lot of background vnts. Ths vnts ar mainly th composition of two pions which coincidntly fit into th mass window. Th H1SoftLptonID packag provids a mthod which calculats th probability of th particl bing an lctron or a 2 ForanlasticJ/ψ + analysiswithtrack-clustrandclustr-clustrs[4];thraralsothlastic channlsj/ψ µ + µ studid. 3 ImplmntdinthH1FindJPsiclass. 4 Thparticlidntificationforanlctronoramuonhastobdonaftrwards. Atthispointbothmass hypothssartaknintoaccount.thfulfillingofonofthmisnoughtoaccptthvnt. 5 Thinlasticandthtrack-clustrJ/ψfindronthothrsidusaparticlidntification.

35 6.1 Extraction of J/ψ candidats 35 nam of th cut variabl cut condition Thtaofatrack/clustr 2 < Θ <165 transvrsmomntumofatrack p t >.8GV Charg tracks must hav opposit charg rconstructdmasswindow 1.5GV <m,m µµ <15GV numbroftracks N tracks =2 Tabl 6.1: Cuts applid in th H1 lastic track-track J/ψ findr EMLP Figur 6.1: Distribution of th ElctronMLPDiscriminator(EMLP) variabl for an lctron nrichd sampl. Th probability that a track is causd by an lctron is incrasing towards +1.ForthisplotJ/ψcandidatsartaknwithallcutsdscribdintabl6.2butwithout thcutemlp >.ToshowthbhaviourofthisvariablforontrackthcutEMLP >.95 isapplidforthothron,tomaksurthatthistrackisanlctron.thdataartakn fromthhighnrgypriodof27. pion and givs th variabl ElctronMLPDiscriminator(EMLP) back. Th variabl runs from 1(pion)to +1(lctron).Itisbasdonanuralntworkwith7inputvariabls.Dtails aboutthinputparamtrsandthmthodscanbfoundin[31,32]. ThdistributionofthEMLPvariablisshowdinfigur6.1foranlctronnrichdsampl.ForlasticJ/ψcandidatsdcayingintotwotracks,EMLP >.95isdmanddforth firsttrack,inordrtonrichj/ψ + vnts.thnthemlpvaluisplottdforth scondtrack 6. ForthwholanalysisthcutEMLP >isusd. 6 Thrarvntswhichlayblow 1(undrflowvnts).Thsvntsarxtrapolatdtoflyinacrackand thusdonotliinthgomtricalaccptancofthdtctor. ThrforthyarcutoffbythEMLP.S sction 7.1.

36 36 Evnt Slction Evnt Slction Toimprovthqualityofthvntsinthsampl,additionalcutsarapplid. Firstth numbroftracksarrstrictdtoonlytwo 7.Thrforthpossibilityofinlasticvntsis rducd to thos with dcay products flying along th bam pip and thrfor cannot b dtctd by th tracking systms. Scondthvrtxoffstinthz-dirctionislimitdby z Vtx <35cm. Trackswhichar fittd too far away from th nominal intraction point, can indicat som troubl by th fitting procdur. Inadditionanothrcutonavariablcalldlasticityisusd.Thdfinitionis z = (E p z) ψ (E p z ), HFS but sinc th numbr of tracks, from which th kinmatic variabls of th J/ψ ar calculatd, is alrady rstrict to only two, this variabl is not vry rstrictiv and has an fficincy narly by1%(stabl7.5). Finallyththtaanglofthtracksisrstrictdto θ <14.Thiscutisnddbcausth lctron pion sparation at largr thtas is dcrasing, du to th fact th EMLP is rstrictd to th LAr accptanc. AsummaryofthmaincutsusdinthisthsistoslctthlasticJ/ψ + candidatsisgivnintabl Phas Spac of th Analysis In this analysis thr diffrnt cntr of mass nrgis, 32, 25 and 225 GV, which corrspondtoththrdiffrntprotonmomntums92,575and46gv,aratheraforth first tim availabl. From this it follows, that, compard to arlir masurmnts, which onlyhaddatafromprotonmomntumsat92gv(rspctivly82gvforherai),th phasspacwithinthaccptancofthdtctorisxtnddtowardslowrw γp valus. ThrfornwmasuringpointsarxpctdatthlowrndofW γp andrducingth gap btwn th arlir H1 masurmnts and th fixd targt xprimnts. In Appndix C thminimalrachablvalusforw γp withinthaccptancarcalculatd. Thnxtstpisthdcisionaboutthbinningofthcrosssctions.Ofcoursonwould liktohavasmanybinsaspossibl,butonalsohastolookatthnumbrofvntslft fromthprviouscuts. Th t andw γp binsarchosn,suchthatthstatisticalandth stimation of th systmatic rror ar of th sam ordr of magnitud. Howvr th total numbrofvntsaralsotaknintoaccount,suchthatnoughbinsarlftforafit. In 7 Actuallythconstrainttotwotracksisonlyapplidifthscattrdlctron,itslfisnotidntifidasatrack. Ifthisisthcas,thrtracksarallowd.Schaptr7.4.

37 6.3 Extract th Numbr of J/ψ 37 kinmatical rgion virtuality Q 2 <1GV 2 cntral track dfinition transvrsmomntum thtaangl numbrofcjchits track lngth radiusoffirsthit dca valu a p t >7MV 1 < Θ <179 N CJC R lngth 1cmfor Θ 15 R lngth 5cmfor Θ >15 R start 5cm dca 2cm lastic track-track J/ψ findr thtaofatrack 2 < Θ <165 transvrsmomntumofatrack p t >.8GV charg tracks must hav opposit charg rconstructdmasswindow 1.5GV <m,m µµ <15GV numbroftracks N tracks =2 slction cuts numbroftracksw/oscattrdlctron N tracks,w/oscatlc =2 z-vrtx z Vtx <35cm lctron pion sparation EMLP > cntral tracks lasticity z >.95 thtaofthtracks Θ <14 a Thdca valuisthdistancofthclosstapproachofnon-vrtxfittdtracktothvrtxofthistrackin th r-phi-plan. Tabl 6.2: Ovrviw of th applid cuts for lastic J/ψ candidats. tabl6.3thbinninginthvariabls t andw γp ardisplaydforththrnrgis.sinc inthhighnrgydatasamplisaboutafactorof1morstatisticsavailabl,thaninth mdiumon,itwaspossibltousthrafinrbinning. 6.3 Extract th Numbr ofj/ψ An Exampl of an invariant mass distribution for vnts slctd by th J/ψ findr and satisfying cuts in tabl 6.2 is shown in figur 6.2. Th invariant mass is calculatd according

38 38 Evnt Slction highnrgyrunpriod(protonnrgye p =919GV) Variabl numbr of bins Bin dgs Unit t 11 [,.5,.1,.15,.2,.3,.4,.55,.7,.9,1.2] GV 2 W γp 11 [4,5,6,7,8,9,1,11] GV mdnrgyrunpriod(protonnrgye p =575GV) Variabl numbr of bins Bin dgs Unit t 7 [,.5,.1,.2,.3,.5,.8,1.2] GV 2 W γp 5 [2,4,5,6,8] GV lownrgyrunpriod(protonnrgye p =46GV) Variabl numbr of bins Bin dgs Unit t 7 [,.5,.1,.2,.3,.5,.8,1.2] GV 2 W γp 7 [2,35,45,52,6,7,8,1] GV Tabl 6.3: Ovrviw of th usd binning to calculat th cross sction in th variabls t andw γp forththrprotonnrgisusdinthisthsis. to th formula m + = 2m 2 +2 p 1 p 2 (1 cos(θ )), (6.1) whrm isthlctronmass,p i thmomntaofthtwofoundtracksand θ thangl btwn ths tracks. Bsids th xpctd mass pak around 3.1 GV, also a broadr background distribution is visibl. Todtrminthdiffrntial t andw γp crosssction,itisncssarytodtrminan invariant mass distribution for ach bin dscribd in tabl 6.3. Ths distributions ar fittd to xtract th numbr of J/ψ vnts dcaying into two lctrons. Ascanbsninfigur6.2thpakshapisnotsymmtric.Onthlftsid,thsocalld radiativ tail is visibl, du to nrgy loss of th lctrons in th tracking dtctors causd by brmsstrahlung. A Gaussian or a Brit-Wignr distribution can thrfor not b sufficint for a dscription, bcaus thy us a constant paramtr, sigma(σ) for a Gaussian, to control thbhaviourofthshap.instadamodifidgaussian[25]isusdforthsignal.ituss, compard to a normal Gaussian, an additional paramtr r, which controls th dclining onthradiativtailsid.thnwvariablsigma σ isdfindby σ = σ +r [ m m ψ ( m m ψ )].