Sixth International Conference on Perspectives in Hadronic Physics May 2008

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1 Sixth Interntionl Conference on Perspectives in Hronic Physics 1-16 My 008 Diffrctive Hroprouction of +, - n Z0 osons t high energies. M.B. Gy Ducti High Energy Phenomenology Group GFPAE - IF UFRGS Brzil

2 Diffrctive Hroprouction of +, - n Z 0 osons t high energies (*) Mri Betriz Gy Ducti High Energy Phenomenology Group GFPAE - IF UFRGS, Porto Alegre etriz.gy@ufrgs.r (*) M. B. Gy Ducti, M. M. Mcho, M. V. T. Mcho, PRD 75, (007)

3 Outline Diffrctive Scttering Ingelmn-Schlein Moel Inclusive Cross Section Diffrctive Cross Section Multiple Pomeron Corrections Gp Survivl Proility (GSP) Khoze Mrtin Ryskin (KMR) Gotsmn Levin Mor (GLM) Tevtron Results LHC Preiction MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

4 This work Results from phenomenologicl nlysis of n Z hr iffrctive hroprouction t high energies Use of Regge fctoriztion pproch Consier recent iffrctive prton ensity functions extrcte y the H1 Collortion t DESY-HERA Multiple Pomeron exchnge corrections consiering gp survivl proility fctor Rtio of iffrctive to non-iffrctive oson prouction is in goo greement with the CDF n D0 t on centrl region Preiction for the future mesurements t the LHC MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

5 Motivtions Stuy of inclusive n iffrctive cross section: chrge guge oson + n - p + p p + ( eν )X neutrl guge oson Z 0 p + p p + Z 0 + ( e e )X Stuy of Pomeron trjectory Stuy of hr iffrctive process Investigtion of the effects from multiple Pomeron scttering in the centrl region phenomenology escries the iffrctive scttering Ingelmn-Schlein moel gp survivl proility fctor (GSP) Anlysis using recent prmetriztion for Pomeron structure function D(3) F ( xip, β, Q ) H1 Collortion MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

6 Introuction Diffrctive processes re wy of mplifying the physics progrm t proton colliers Inclusion of new chnnels serching for New Physics Investigtion of these rections gives importnt informtion on the structure of hrons n their interction mechnisms Diffrctive prouction of mssive eletrowek osons llows the stuy of the interply of the smll- n lrge-istnce ynmics within QCD In oson hroprouction, single iffrctive issocition cn occur chrcterize y the existence of lrge rpiity gp IP exchnge MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

7 Generl Aspects Expecte tht unitrity effects t high energies ffect the results of iffrctive cross sections Multiple-Pomeron contriutions reuce the iffrctive cross section Depenence on the prticulr hr process Tevtron energies ( s =1.8 Tev) suppression is in the rnge For LHC energy ( s =14 TeV ) suppression is in the rnge Aequte tretment of the multiple scttering effect is crucil for the reliility of theoreticl preictions of the cross sections for iffrctive processes MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

8 Diffrctive Process Discovere t DESY (HERA) collier (H1 n Zeus Collortion) Rpiity (y) gps no prticle prouction y 1 = ln E E + p p z z p z proton momentum p z Finl stte with sme quntum numers of initil stte Pomeron exchnge of vcuum quntum numers M = 80 GeV, M Z = 90.1 GeV MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

9 Diffrctive DIS t HERA Diffrctive Deep Inelstic Scttering (DDIS) contriutes sustntilly to the cross section ( 10% of visile low-x events) X Inclusive DIS: Proes prtonic structure of the proton Q : 4-momentum exchnge : γ p centre of mss energy x: frction of p momentum crrie y the struck qurk x IP : frction of p momentum crrie y the Pomeron (IP) X Diffrctive DIS: Proes structure of the exchnge color singlet Ingelmn-Schlein moel x β: frction of IP momentum crrie y the struck qurk β IP q ( p p') = q p Q Q Q Q X = = q ( p p') Q + M X x IP + + M x MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

10 Inclusive cross section (I) Hr iffrctive process, consiering the Ingelmn-Schlein moel Pomeron structure (qurk n gluon content) is proe Cross section for process in which prtons of two hrons (A n B) interct to prouce mssive eletrowek oson ( ± 0 / Z ) X A + B + proton u u q e +, e -,e + σ = x, x f / p ( x ) f / p ( x ) ˆ σ tˆ tˆ u u q +, -, Z 0 v e, v e,e - ntiproton x n x re the momentum frction of nucleons crrie y the prtons f i/h is the prton istriution function (PDF) of prton of flvor i =, in the hron h = A, B MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

11 Inclusive cross section (II) σˆ / tˆ gives the elementry cross section of the corresponing suprocess The cross section is the usul leing-orer QCD proceure to otin the non-iffrctive cross section Next-to-leing-orer contriutions re not essentil, since corrections to n Z prouction re smll High energies (m p << E) pseuo-rpiity θ η = lntg θ is the electron scttering ngle relte to the proton em irection MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

12 Energies n Mnelstn Vriles Totl Energy E e s 4 [ x ( 1+ cosθ ) + x ( 1 cosθ )] = Longituinl Energy Trnsversl Energy Mnelstn vriles of the process E E s 4 T [ x ( 1+ cosθ ) x ( 1 cosθ )] L = M = senθ ˆ ( p p ) = ( 1 cosθ ) tˆ = c uˆ = s = ( p + p ) = M sˆ sˆ ( p p ) = ( 1+ cosθ ) c cosθ = ± A 1 A A = M / E T c MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

13 hr scle in which the PDFs re evolve - inclusive cross section = p p t X Z p p x f x f x x x, / / ˆ ) ] / [ ˆ( ), ( ), ( σ µ µ σ 1 ˆ 6 ) ( ) (, / / Γ = A u M s G V x f x f E F p p T η e σ Totl ecy with Γ =.06 GeV Fermi Constnt G F = x 10-5 GeV - V is the Mtrix CKM element = M µ Generl cross section for n Z - inclusive cross section MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

14 + inclusive cross section + inclusive cross section σ V ) 6 sγ F = E T f / p ( x ) f ( x / p η e +, M A G tˆ 1 µ = M tˆ [ ] A + ( 1) = E M A T Totl ecy with Γ =.06 GeV G F = x 10-5 GeV -, V is the CKM Mtrix element + - epenence in t chnnel epenence in u chnnel MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

15 Diffrctive cross sections 1 ˆ 6 ) ( ) ( ) (, / / Γ = A u M s G V x f x f E x g x F p IP T IP IP η e σ 1 ˆ 6 ) ( ) ( ) (, / / Γ = + A t M s G V x f x f E x g x F p IP T IP IP η e σ f /IP is the qurk istriution in the IP prmetriztion of the IP structure function (H1) g (x IP ) is the IP flux integrte over t + iffrctive cross section - iffrctive cross section MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

16 Z 0 Diffrctive cross sections Z 0 iffrctive cross section σ x x x x = IP, IP x x f ( x IP ) f / IP ( x, µ ) f / p Z πc ( x, µ ) 3 GF M s Z ˆ( σ ZX ) tˆ f /IP is the qurk istriution in the IP g (x IP ) is the Pomeron flux integrte over t f ( x IP ) = 0 f / ( x, t) t IP p IP Z C qq' 1 / e sin θ + 4 e q q sin 4 θ θ is the einerg or wek-mixing ngle Sme result of H1 with LO Pomeron structure function (STIRLING 96) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

17 Pomeron flux fctor x IP epenence is prmetrize using flux fctor IP trjectory is ssume to e liner f BIPt IP / p ( xip, t) = AIP α IP ( t) 1 xip e α ( t) = α (0) + α' IP IP IP t B IP,, α IP their uncertinties otine from the fits to H1 forwr proton spectometer (FPS) t min Normliztion prmeter x IP is chosen such tht x t x IP = IP. f = 1 t IP/ pt cut t is the proton mss min mpxip /(1 xip) t GeV cut = 1.0 is the limit of the mesurement MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008 t

18 Pomeron structure function Pomeron structure function hs een moele in terms of light flvor singlet istriution Σ(z) Consists of u, n s qurks n ntiqurks n gluon istriution g(z) z is the longituinl momentum frction of the prton entering the hr suprocess with respect of the iffrctive exchnge (z = β ) for the lowest orer qurk-prton moel process n 0 < β <z for higher orer processes Qurk singlet n gluon istriutions re prmetrize t Q 0 zf i / IP ( z, Q 0 ) = A z i (1 z) B i C i 0.01 exp (1 z) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

19 Pomeron structure function Experimentl etermintion of the iffrctive PDFs involves the following cuts β < 0.8, M X > GeV; Q < 8.5GeV Qurk singlet istriution, t requires inclusion of prmeters A q, B q n C q Gluon ensity is wekly constrine y t which re foun to e insensitive to the B g prmeter FIT A - Gluon ensity is prmetrize using only A g n C g prmeters (Q 0 = 1.75 GeV ) This proceure is not sensitive to the gluon PDF n new justment ws one with C g = 0 FIT B - Gluon ensity is simple constnt t the strting scle for evolution (Q 0 =.5 GeV ) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

20 Pomeron structure function Prmeter Vlue α IP 0.06 GeV 0.06 Vlues of fixe prmeters (msses) n their uncertinties, s use in the QCD fits. B IP α IR (0) α IR B IR m c m α (5) 8 (M Z ) ± ± 4,5 ± ± GeV 0.10 GeV GeV 0.GeV 0.5GeV 0.00 α IP n B IP (strongly nti-correlte) re vrie simultneously to otin the theoreticl errors on the fits (s well s α IR n B IR ). Remining prmeters re vrie inepenently. Theoreticl uncertinties on the free prmeters of the fit re sensitive to the vrition of the prmetriztion scle Q 0 DESY My 006 MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

21 Qurk n gluons istriutions Totl qurk singlet n gluon istriutions otine from NLO QCD H1. DPDF Fit A, Rnge < z < 0,8, corresponing pproximtely to tht of mesurement. Centrl lines re surroune y inner errors ns corresponing to the experimentl uncertinties n outer error ns corresponing to the experimentl n theoreticl uncertinties In this work, we use FIT A. Similr results re otine with FIT B MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

22 Gp Survivl Proility (GSP) Lrge Rpiity Gp Currently suject of intense theoreticl n experimentl interest GAP region of ngulr phse spce evoi of prticles Survivl proility fulfilling of the gp y hrons prouce in interctions of remnescent prticles < S > = A( s, ) P s A( s, ) ( s, ) A(s,) is the mplitue (in the prmeter spce) of the prticulr process of interest t center-of-mss energy P S (s,) is the proility tht no inelstic interction occurs etween scttere hrons s MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

23 KMR - GSP (*) Khoze-Mrtin-Ryskin Eur. Phys. J. C. 6 9 (00) The survivl proility of the rpiity gps (ssocite with the Pomeron, represente y the oule verticl line) Clculte * single iffrction (SD) * centrl iffrction (CD) * oule iffrction (DD) FPS or cl enotes forwr photon spectrometer or clorimeter, n correspons to the etection of isolte protons, or to events where the leing ryon is either proton or N* (symoliclly, two lines emerging from the vertex) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

24 KMR moel t epenence of elstic pp ifferentil cross section in the form exp (Bt) pion-loop insertions in the Pomeron trjectory non-exponentil form of the proton-pomeron vertex β (t) sorptive corrections, ssocite with eikonliztion, which le to ip in σ/t t t ~ 1 GeV, whose position moves to smller t s the collier energy increses () Pomeron exchnge contriution; (-e) re unitrity corrections to the pp elstic mplitue. (f) is two pion-loop insertion in the Pomeron trjectory (f) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

25 KMR moel GSP KMR vlues GSP consiering multiple chnnels MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

26 GLM - GSP (*) Gotsmn-Levin-Mor PLB (1998) Suppression ue to seconry interctions y itionl specttors hrons < S >= A( s, ) e A( s, ) Ω( s, ) Survivl proility s function of ν(s) = Ω (s, = 0) (Ω is the opcity or optic ensity of interction of incient hrons n, where is the rtio of the rius in soft n hr interctions) = R s / R h MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

27 GLM moel Eikonl moel originlly conceive so s to explin the exceptionlly mil energy epenence of soft iffrctive cross sections. Consiers tht the s-chnnel unitriztion enforce y the eikonl moel opertes on iffrctive mplitue in ifferent wy thn it oes on the elstic mplitue e consier the single-chnnel eikonl pproch Cse where the soft input is otine irectly from the mesure vlues of σ tot, σ el n hr rius R H < S > Tevtron LHC GLM MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

28 + n - Cross Sections + Tevtron Inclusive KMR iff inc GLM R η η = η σ iff + + σ iff iffrctive - η σ inc + + σ inc GSPs Rnges η e < < η e <.5 MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

29 +, - n Z 0 Rtios Pseuo-rpiity Dt (%) R(%) 1.8 TeV 14 TeV Totl Totl Totl η e < Z η < < e e Z e + + e.5 eν η e e < 1.1 (*) (*) 1.15 ± ± ± ± ± ± ± ± ± ± ± ± 1.41 CDF D0 LHC * η <1.1 Tevtron, without GSP 7. % Averge of KMR n GLM preictions MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

30 Other GSPs results Diffrctive prouction 1.8 TeV Pseuo-rpiity Moel R (%) η < 1.1 DGM ± e < 1.1 η e η e < 1.1 < 1.1 η e η e < 1.1 DGM 3.6 BH 0.8 KMR 15.0 GLM ± 1.1 ± 0.76 ± ± ch ch DGM Dynmicl Mss Gluon Lun (006) BH Block Hlzen moel (00) GLM Gotsmn Levin Mor (001) MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008

31 Conclusions Anlysis of n Z iffrctive hroprouction process n centrl rpiity istriutions of prouce leptons Using new Pomeron iffrctive prton istriutions (H1 Collortion DESY HERA) n theoreticl estimtes for gp survivl fctor Very goo greement with experiment (D0 n CDF, Tevtron) Improvement of t escription using gp survivl proility Importnt suject to verify future IP PDF s Estimtes to e compre t LHC MBGD 6th Interntionl Conference on Perspectives in Hronic Physics My 008