Factorization Breaking in Diffractive Dijet Production. Gustav Kramer Universitaet Hamburg August 28, 2008

Transcription

1 Factorization Breaking in Diffractive Dijet Production Gustav Kramer Universitaet Hamburg

2 Publications With Michael Klasen PLB 58 (21) 259: γ p 2 jets+n EPJC 38 (24) 39: γ p 2 jets+p PRL 93 (24) 2322: γ p 2 jets+p JPG 31 (25) 1391: New fact. scheme arxiv: Review based on H1 and ZEUS data

3 Motivation Hard diffraction: Does factorization hold? Diffr. hadroproduction of dijets: Deep inelastic scattering: Yes Direct photoproduction Hadroproduction: No Resolved photoproduction Why next-to-leading order? σ tot = σ dir (x γ,m γ ) + σ res (x γ,m γ ) At LO x γ = 1, but at NLO x γ 1 log(m γ )-dependence cancels CDF Coll., PRL 84 (2) 543

4 Kinematics Diffractive processes at HERA: Inclusive DIS: Diffractive DIS: Experimental cuts: H1 Coll., EPS 23 and DIS 24

5 Diffractive Parton Distributions Double factorization: Hard QCD factorization: Regge factorization: Pomeron flux factor: Pomeron tracectory: G. Ingelman, P. Schlein, PLB 152 (1985) 256

6 Proof of Hard Factorization Diffractive deep inelastic scattering: Light cone coordinates: q µ = (q +,q,q T ) Leading regions: H: q µ O(Q) J: l µ (,Q/ 2, T ) A: k µ «O(Q) Soft gluon attachments: J.C. Collins, PRD 57 (1998) 351 Poles in k + -plane: Final state: Upper half-plane Initial state: Lower half-plane

7 Multipomeron Exchanges Direct photoproduction: X Resolved photoproduction: X Modify the Regge trajectory Factorization breaking

8 Diffractive Photoproduction of Dijets Cross section: Photon flux: Weizsäcker-Williams approximation

9 Diffractice parton distributions (DPDFs) DPDFS from diffractive DIS measurements of F_2^D: H1 Coll., A. Aktas et al., Eur. Phys. J C 48 (26) 715 H1 26 fit A and H1 26 fit B, both M_Y < 1.6 GeV H1 Coll., A. Aktas et a., JHEP 1 (27) 42 H1 27 fit jets ZEUS Coll., S. Chekanov et al., Eur. Phys. J. C38 (24) 43 ZEUS LPS fit, measurement for ep -->e'px, only proton, no additional proton dissociation in final state

10 Factorization Breakink at NLO W-depend.:photon flux 1 x P-depend.:Pomeron fl H NLO, R=1. dσ/dw [pb/gev] 6 4 dσ/dlog 1 (x IP ) [pb] 6 4 NLO, R=.42 2 H NLO, R=1. 2 NLO, R= W [GeV] log 1 (x IP )

11 Factorization Breaking at NLO W depend.: photon flux 1 8 x P depend.: pom. flux 1 8 NLO, R=1. NLO, R=.46 dσ/dw [pb/gev] 6 4 dσ/dlog 1 (x IP ) [pb] NLO, R=1. 2 NLO, R= W [GeV] log 1 (x IP )

12 Factorization Breaking at NLO 1 xgam-depend.,dir./resolv 1 z Pdepend.,gluoninpom. 8 8 [pb] 6 [pb] 6 dσ/dx γ 4 dσ/dz IP 4 2 NLO, R=1. NLO, R= x γ 2 NLO, R=1. NLO, R= z IP

13 Factorization Breaking in NLO [pb] dσ/dη _ jets eta^jets-dependence H1 prelim. NLO, R=1. NLO, R= η _ jets dσ/d η jets [pb] Delta eta^jets-depend. NLO, R=1. NLO, R= η jets

14 E T -Distribution Importance of large E T : Direct process dominates IS singularity less important Hadronization corrections small Experimentally directly accessible Less sensitive than xγ Result: Suppressed result fitted at Low E_T Unsuppressed 5% too low for low E_T Suppression less at high E_T dσ/de T jet1 [pb/gev] H NLO, R=1. NLO, R= E T jet1 [GeV]

15 E_T-distribution for preliminary data dσ/de T jet1 [pb/gev] Fit to low E_T bin NLO, R=1. Largest E_T-bin fitted better with R=1 (unsuppressed) resolved suppression only should fit better NLO, R= E T jet1 [GeV]

16 Factorization Scale Dependence Inclusive photoproduction: Diffractive photoproduction: MK, Rev. Mod. Phys. 74 (22) 1221 M. Klasen, G. K., EPJC 38 (24)39

17 Factorization Scale Dependence (1) Michael Klasen, G. K., JPG 31 (25) 1391

18 dσ/dw [pb/gev] Breaking in resolved/resoved/direct-is W-dependence:Photon fl NLO, R=.46 NLO, R=.35 (res) NLO, R=.32 (res+dir IS) dσ/dlog 1 (x IP ) [pb] x P-dependence:Pom. fl. 1 8 NLO, R=.46 NLO, R=.35 (res) 6 NLO, R=.32 (res+dir IS) W [GeV] log 1 (x IP )

19 Breaking in resolved or resolved/direct-is 1 xgam-depend.:direct/res. z P-depend.:gluon in P 1 8 NLO, R=.46 8 NLO, R=.35 (res) [pb] 6 NLO, R=.32 (res+dir IS) [pb] 6 dσ/dx γ 4 dσ/dz IP x γ 2 NLO, R=.46 NLO, R=.35 (res) NLO, R=.32 (res+dir IS) z IP

20 Breaking in resolved or resolved/direct_is [pb] dσ/dη _ jets 1 eta^{jets}-dependence 8 NLO, R=.46 NLO, R=.35 (res) 6 NLO, R=.32 (res+dir IS) 4 2 dσ/d η jets [pb] Delta eta^{jets}-depend NLO, R=.46 NLO, R=.35 (res) NLO, R=.32 (res+dir IS) η _ jets η jets

21 Breakind in resolved or resolved/direct-is dσ/de T jet1 [pb/gev] ET^{jet1}-dependence NLO, R=.46 NLO, R=.35 (res) NLO, R=.32 (res+dir IS) jet1 E T [GeV] ET-dependence perfectly described by resolved and resolved/direct-is Supression factors slightly different R=.35 (resolved) R=.32 (resolved/direct- IS)

22 dσ/dw [pb/gev] Factorization Breaking at NLO, high E_T W-depend.: photon flux NLO, R=1. NLO, R= W [GeV] dσ/dlog 1 (x IP ) [pb] X P depend.: pom. flux NLO, R=1. NLO, R= log 1 (x IP )

23 Factorization Breaking at NLO, high E_T 2 x_gamma-dependence z_ P-dependence NLO, R=1. 16 NLO, R=1. 14 NLO, R= NLO, R=.62 [pb] 12 [pb] 12 dσ/dx γ 1 8 dσ/dz IP x γ z IP

24 Factorization Breaking, high E_T eta^jets-dependence H1 prelim. NLO, R=1. NLO, R=.62 Delta eta^jets-depend [pb] dσ/dη _ jets dσ/d η jets [pb] η _ jets NLO, R=1. NLO, R= η jets

25 Factorization Breaking, high E_T dσ/de T jet1 [pb/gev] E_T distribution NLO, R=1. NLO, R= E T jet1 [GeV] Two lowest E_T bins agree Highest E_T bin agrees bettter with unsuppressed Resolved suppression only would account for this

26 Breaking in resolved or resolved/direct-is dσ/dw [pb/gev] W- depend.: photon flux x P-depend.: pomeron fl NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) dσ/dlog 1 (x IP ) [pb] NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) W [GeV] log 1 (x IP )

27 Breaking in resolved or resolve/direct-is [pb] dσ/dx γ x-gamma-dependence NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) x γ [pb] dσ/dz IP z_ P-dependence NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) z IP

28 Breaking in resolved or resolved/direct-is [pb] dσ/dη _ jets 1 eta^jets-dpendence NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) η _ jets dσ/d η jets [pb] Delta eta^jets-depend NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) η jets

29 Breaking in resolved or resolved/direct-is dσ/de T jet1 [pb/gev] E_T-dependence NLO, R=.62 NLO, R=.38 (res) NLO, R=.3 (res+dir IS) E T jet1 [GeV] All three E_T bins agree very well difference to global suppression not significant R=.62 global suppr. R=.38 resolved supp. R=.32 resolved/direct_is supp.

30 Factorization Breaking at NLO dσ/dy [pb] y-dependence:photon fl. 5 ZEUS NLO, R=1. NLO, R= y dσ/x IP [pb] x P-depend.:Pomeron fl ZEUS NLO, R=1. NLO, R= x IP

31 Factorization Breaking at NLO, ZEUS 6 xgam-depend.:dir./resol. ZEUS z P-depend.:gluon in po. 3 5 NLO, R=1. NLO, R= [pb] [pb] dσ/dx γ 3 2 dσ/dz IP x γ 5 ZEUS NLO, R=1. NLO, R= z IP

32 Factorization Breaking at NLO, ZEUS MX-dependence 1 eta^{jet1}-dependence dσ/dm X [pb/gev] ZEUS NLO, R=1. NLO, R=.71 dσ/dη jet1 [pb] ZEUS NLO, R=1. NLO, R= M X [GeV] η jet1

33 Factorization Breaking at NLO, ZEUS dσ/de T jet1 [pb/gev] ET^{jet1}-dependence ZEUS NLO, R=1. Two highest ET-bins better described with R=1 NLO, R= E T jet1 [GeV]

34 Breaking in resolved or resolved/direct-is dσ/dy [pb] y-depend.:photon flux ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) y dσ/x IP [pb] x P-depend.:Pomeron fl ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) x IP

35 Breaking in resolved or resolved/direct-is xgam-depend.:direct/res. ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) z P-depend.:gluon in po ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) [pb] [pb] dσ/dx γ 3 2 dσ/dz IP x γ z IP

36 Breaking in resolved or resolved/direct_is dσ/dm X [pb/gev] MX-dependence ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) dσ/dη jet1 [pb] eta^{et1}-dependence ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) M X [GeV] η jet1

37 Breaking in resolved or resolved/direct-is dσ/de T jet1 [pb/gev] ET_dependence ZEUS NLO, R=.71 NLO, R=.53 (res) NLO, R=.45 (res+dir IS) E T jet1 [GeV] Resolved or resolved/direct-is slightly better than global suppression R=.71 global supp. R=.53 resolved supp. R=.45 resolved/direct- IS suppression

38 Ratio data/theory, low-e_t and high E_T H1 low E T jetprelim. / Theory E_T depend. H1 low_e_t 1 NLO QCD R =.35 (res) R =.32 (res+dir IS) H1 high E T jet prelim. / Theory E_T depend. H1 high E_T NLO QCD R =.38 (res) R =.3 (res+dir IS) E T jet1 [GeV] E T jet1 [GeV]

39 ZEUS / Theory Ratio data/theory :ZEUS different norm E_T-depend norm paper Norm reduced by 15% 1 NLO QCD R =.53 (res) R =.45 (res+dir IS) ZEUS 99 / Theory NLO QCD R =.38 (res) E T jet1 [GeV] E T jet1 [GeV]

40 Conclusions Hard diffraction: Factorizable or not? Deep inelastic scattering: Yes Diffractive parton densities Hadronic scattering: No Multipomeron exchanges Diffractive photoproduction of dijets: Yes global suppression of order.5 definitely established, suppression E_T dependent Initial state singularity at NLO Reolved suppression only or resolved/direct-is suppression describes data almost equally well, suppression factor~1/3, little E_T dependence Agrees with two-channel eikonal model of Kaidalov et al.: Generalized vector meson dominance: γ ρ, ω, Rapidity gap survival probability: R =.34