Hard exclusive processes -

1. Hard exclusive processes - experimental results and simulations for EIC Andrzej Sandacz Sołtan Institute for Nuclear Studies, Warsaw • DVCS at fixed target experiments and HERA • Vector Meson production at HERA • Transverse target spin asymmetry for ρ0 production • Exclusive π+and π0 production • DVCS at EIC EIC Collaboration Meeting, Stony Brook University, December 8, 2007

2. Generalized Parton Distributions g* g Factorisation: Q2 large, -t<1 GeV2 hard x+x x-x soft GPDs P2 P1 t ~ ~ depending on 3 variables: x, x, t 4 Generalised Parton Distributions : H, E, H, E for each quark flavour and for gluons for DVCS gluons contribute only at higher orders in αs

3. forP1 = P2recover usual parton densities no similar relations; these GPDs decouple forP1 = P2 needs orbital angular momentum between partons Dirac axial Pauli pseudoscalar GPDs properties, link to DIS and form factors Ji’s sum rule total angular momentum carried by quark flavour q (helicity and orbital part)

4. q q p p t • Contribution to the nucleon spin puzzle • E related to the angular momentum • 2Jq =  x (Hq (x,ξ,0)+Eq (x,ξ,0)) dx • ½ = ½ ΔΣ+ ΔG + < Lzq > + < Lzg > ‘Holy Grails’ orthe main goals GPD= a 3-dimensional picture of the partonic nucleon structure or spatial parton distribution in the transverse plane H(x, =0,t)→H(x,, rx,y) probability interpretation Burkardt y x P r x z E

5. Observables and their relationship to GPDs T The imaginary part of amplitude T probes GPD at x = x The real part of amplitude T dependson the integral of GPD over x DGLAP DGLAP ERBL

6. ~ DsC~cosf∙Re{ H+ xH +… } ~ DsLU~sinf∙Im{H+ xH+ kE} ~ DsUL~sinf∙Im{H+ xH+ …} DVCS Asymmetries measured up to now  different charges: e+ e-(only @HERA!): H polarization observables: H ~ H DsUT~sin(f-s)cos∙Im{k(H- E) + … } H, E kinematically suppressed x = xB/(2-xB ),k = t/4M2

7. <-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2 CLAS: DVCS - BSA Accurate data in a large kinematical domain Integrated over t

8. Results from JLAB Hall A E00-100 Q2 = 2.3 GeV2 xB = 0.36 PRL97, 262002 (2006) Difference of polarized cross sections Twist-2 Twist-3 extracted twist-3 contribution small Unpolarized cross sections

9. s1int~ dominant term at small |t| GPD !!! No Q2 dependence: strong indication for scaling and handbag dominance

10. Hermes DVCS-TTSA: TowardsE and Ju, Jd Hall A nDVCS-BSA: • Neutron obtained combining • deuteron and proton • F1 small and u & d cancel in x=0.36 and Q2=1.9GeV2

11. Lattice hep-lat 07054295 With VGG Code Present status of the MODEL-DEPENDENT Ju-Jd extraction

12. Unpolarised DVCS cross sectionsfrom HERA - Wide range of Q2 - sensitivity to QCD evolution of GPDs - Difference between MRS/CTEQ due to different xG at low xB - Meaurements of b significantly constrain uncertainty of models σDVCSatsmall xB (< 0.01) mostly sensitive to Hg, Hsea Q² and W dependence: NLO predictions bands reflect experimental error on slope b: 5.26 < b < 6.40 GeV-2

13. t dependence of DVCS cross section New H1 results on slopes - DIS07 DIS06

14. Good agreement with NLO predictions GPDs ≡ PDFs at low scale; skewing generated by QCD evolution • Sensitivity to Hg ; 15% change of Hg=> 10% change of cross section • Real part of DVCS amplitude – small effect, few% • Skewing parameter R=Im DIS / Im DVCS ~ 0.5 Interplay of Rs (sea) and Rg (gluons) • Low sensitivity to b(Q2) vs. b(const.) • Color dipole phenomenology (no GPDs) also a satisfacory description Lessons from DVCS at H1/ZEUS

15. 4 Generalised Parton Distributions (GPDs) for each quark flavour and for gluons GPDs depend on 3 variables: x, x, t H E Vector mesons (ρ, ω, φ) ~ ~ H E Pseudoscalar mesons (π, η) Hard exclusive meson production • factorisation proven only for σL σT suppressed of by 1/Q2 necessary to extract longitudinal contribution to observables (σL , …) • allows separation and wrt quark flavours Flavour sensitivity of DVMP on the proton conserve flip nucleon helicity • quarks and gluons enter at the same order of αS • wave function of meson (DA Φ) additional information/complication

16. Dipole models for exclusive VM production at small x • at small x sensitivity mostly to gluons • at very small x huge NLO corrections, large ln(1/x) terms (BFKL type logs) • pQCD models to describe colour dipole-nucleon cross sections and meson WF dipole transv. size W-dep. t-dep. large weak steep small strong shallow • Frankfurt-Koepf-Strikman (FKS) Phys.Rev. D57 (1998) 512 sensitivity to different gluon density distibutions • Martin-Ryskin-Teubner (MRT) Phys.Rev. D62 (2000) 014022 • Farshaw-Sandapen-Shaw (FSS) Phys.Rev. D69 (2004) 094013 • Kowalski-Motyka-Watt (KMW) Phys.Rev. D74 (2006) 074016 sensitivity to ρ0 wave function • Dosch-Fereira (DF) hep-ph/0610311 (2006)

17. Recent ZEUS results on exclusive ρ0 production 2 < Q2 < 160 GeV2 32 < W < 180 GeV 2∙10-4 < xBj < 10-2 | t | < 1 GeV2 significant increase of precision + extended Q2 range 96-00 data: 120 pb-1 arXiv:0708.1478[hep-ex] W-dependenceσ∞Wδ • steeper energy dependence with increasing Q2

18. W-dependence for hard exclusive processes at small x ϕ ϒ J/ψ • steep energy dependence for all vector mesons in presence of hard scale Q2 and/or M2 • ‘universality’ of energy dependence at small x? at Q2+M2≈ 10 GeV2 still significant difference between ρ and J/ψ

19. dσ / dt - ρ0 example (1 out of 6) ZEUS Fit • shallower t-dependence with increasing Q2

20. Q2 and/or M2 • b-slopes decrease with increasing scale approaching a limit ≈ 5 GeV-2 at large scales • approximate ‘universality’ of slopes as a function of (Q2+ M2) t-dependence for hard exclusive processes at small x recent data suggestive of possible ≈ 15% difference between ρ and J/ψ

21. Selected results onR = σL/σTforρ0 production the same W- and t-dependence for σLand σT δL ≈ δT bL ≈ bT the same size of the longitudinal and transverse γ*involved in hard ρ0 production i.e. contribution of large qqbar fluctuations of transverse γ* suppressed

22. Comparison to ‘dipole models’ extensive comparison of the models to recent ZEUS ρ0 data in arXiv:0708.1478[hep-ex] below just selected examples • considered models describe qualitatively all features of the data reasonably well • recent ZEUS data are a challenge; none of the models gives at the moment satisfactory quantitative description of all features of the data

23. Comparison to GPD model ‘Hand-bag model’; GPDs from DD using CTEQ6 • Goloskokov-Kroll power corrections due to kt of quarks included arXiv:0708,3569[hep-ph] both contributions of γ*L and γ*T calculated W=90 GeV ■ H1 □ZEUS W=90 GeV ZEUS (recent) σ/10 W=75 GeV complete calculation leading twist only (in collinear approx.) • leading twist prediction above full calculation, even at Q2= 100 GeV2 ≈ 20% • contribution of σTdecreases with Q2, but does not vanish even at Q2= 100 GeV2 ≈ 10% • sea quark contribution, including interference with gluons, non-negligible 25% at Q2 = 4 GeV2

24. The asymmetry defined as to disentangle contributions fromγLandγTthe distribution of ρ0decay polar angle needed in addition Diehl and Sapeta Transverse target spin asymmetry for exclusive ρ0production Give access to GPD E related to the orbital angular momentum of quarks Ji’s sum rule q q So far GPDE poorly constrained by data; mostly by Pauli form factors The asymmetry defined as to disentangle contributions fromγLandγTthe distribution of ρ0decay polar angle needed in addition Diehl and Sapeta Eur. Phys. J.C 41, 515 (2005)

25. Assuming SCHC Simultaneous fit of 12 parameters of azimuthal distributions Im (E*H) / |H|2 Method forL/T separationused by HERMES A. Rostomyan and J. Dreschler arXiv:0707.2486 Angular distribution W(cos θ, φ, φs) and Unbinned Maximum Likelihood fit a prerequisite for the method: determination of acceptance correction as a function ofcos θ, φandφs

26. ρ0transverse target spin asymmetry from HERMES Transversely polarised proton target, PT≈ 75% 2002-2005 data, 171.6 pb-1 • for the first time ρ0TTSA extracted separately for γ*Land γ*T

27. ρ0transverse target spin asymmetry from HERMES • in a model dependent analysis data favours positive Ju in agreement with DVCS results from HERMES

28. obtained using Double Ratio Method ρ0transverse target spin asymmetry from COMPASS Transversely polarised deuteron target (6LiD), PT≈ 50% 2002-2004 data obtained using Double Ratio Method in bins ofϑ = φ – φS: u (d) are for upstream (downstream) cell of polarised target arrows indicate transverse polarisation of corresponding cells raw asymmetry εfrom the fitto DR(η) dilution factor f≈ 0.38

29. ρ0transverse target spin asymmetry from COMPASS new • asymmetry for deuteron target consistent with zero ongoing work on: • longitudinal/transverse separation • separation of incoherent/coherent in 2007 data taken with transversely polarised proton target (NH3)

30. ~ • at small |t’| E dominates as it contains t-channel pion-pole σLVGG LO σLVGGLO+power corrections σT+εσLRegge model (Laget) • LO calculations strongly underestimate the data • data support magnitude of the power corrections(kt and soft overlap) • Regge calculations provides good description of the magnitude of σtot and of t’ and Q2 dependences Exclusive π+ production from HERMES e p → e n π+ ~ ~ • at leading twist σLsensitive to GPDs H and E • L/T separation not possible at HERMES, σTexpected to be supressed as 1/Q2

31. Beam spin asymmetry in exclusive π0 production from CLAS a fit α sinφ Regge model (Laget) pole terms (ω, ρ, b1)+ boxdiagrams (cuts) • first measurement of BSA for exclusive π0 production above resonance region • sizeable BSA (0.04 – 0.11) indicate that both T and L amplitudes contribute • necessity for L/T separation and measurements at higher Q2 ~ • at leading twist σLsensitive to GPD H e p → e p π0 • no t-channel pion-pole (in contrast to exclusive π+ production) • any non-zero BSA would indicate L-T interference, i.e. contribution not described in terms of GPD’s preliminary

32. Cross sections for exclusive π0 production from JLAB HALL A DVCS Collab. E00-110 h = ±1 is the beam helicity from P. Bertin, Baryon-07 t-slope close to 0, maybe even small negative

33. dashed – prediction for σL from VGG model using GPDs Vanderhaeghen, Guichon, Guidal

34. Summary for existing measurements • New precise data on cross sections result in significantly more stringent constraints on the models for GPDs • Results on DVCS promissing; indication of scaling and handbag dominance in valence region good agreement with NLO for HERA data • To describe present data on DVMP, both at large and small x, including power corrections (or higher order pQCD terms) is essential • First experimental efforts to constrain GPD E and quark orbital momentum

35. Precision of DVCS unpolarized cross sections at eRHIC (1) HE setup: e+/-(10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day For one out of 6 W intervals (30 < W < 45 GeV) eRHIC HEsetup σ(γ*p →γ p) [nb] Lint = 530 pb-1 (2 weeks) <W> = 37 GeV Q2[GeV2] • eRHIC measurements of cross section will provide significant constraints

36. Precision of DVCS unpolarized cross sections at eRHIC (2) HE setup: e+/-(10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day LE setup: e+/-( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day For one out of 6 Q2 intervals (8 < Q2 < 15 GeV2) eRHIC Lint = 530 pb-1 Lint = 180 pb-1 σ(γ*p →γ p) [nb] <Q2> = 10.4 GeV2 W[GeV] • EIC measurements of cross section will provide significant constraints also significantly extend the range towards small W

37. Towards 3D mapping of parton structure of the nucleon at EIC (assumed for illustration) α’ = 0.125 GeV-2 Lint = 4.2 fb-1 simultaneous data in several (6) Q2 bins Sufficient luminosity to do triple-differential measurements in x, Q2, t at EIC!

38. W= 75 GeV , -t = 0.1 GeV2 Q2 =4.5 GeV2 , -t = 0.1 GeV2 Q2 [GeV2] W[GeV] Lepton charge asymmetry at eRHIC model ofBelitsky, Mueller, Kirchner(2002) forGPDs at small xB parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001)) except magnetic momentκsea(-3 < κsea< 2),whichenters Ji’s sum rule for Jq BMK use ‘improved’ charge asymmetries ACcosφ and ACsinφ HEsetup, Lint = 530 pb-1 divided equally betweene+ande- κsea= 2 κsea= -3 κsea= -3 κsea= 2 • measurements of asymmetries at EIC sensitive tool to validate models of GPDs

39. Summary for DVCS at eRHIC • Wide kinematical range, overlap with HERA and COMPASS 1.5 ·10-4 < xB < 0.2- sensitivity to quarks and gluons 1 < Q2 < 50 GeV2 - sensitivity to QCD evolution • DVCS cross sections - significant improvement of precision wrt HERA • Intereference with BH - pioneering measurements for a collider powerfull tool to study DVCS amplitudes full exploratory potential, ife+and e-available as well as longitudinaly and transversely polarized protons • Sufficient luminosity to do tripple-differential measurements in xB, Q2, t

40. Backup slide

41. 2° <θe’< 178° 2° < θγ < 178° Ee’ > Emin GeVEγ > 0.5 GeV Emin = 2 GeV (HE) or 1 GeV (LE) 1 < Q2 < 50 GeV2 1 < Q2 < 50 GeV2 10 < W < 90 GeV 0.05 < |t| < 1.0 GeV2 0.05 < |t| < 1.0 GeV2 A simulation of DVCS at eRHIC HE setup: e+/-(10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day LE setup: e+/-( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day diam. of the pipe - 20 cm, space for Central Detector: ≈ +/- 280 cm from IP acceptance of Central Detector(improved ZDR)2° <θlab< 178° acceptance simulated by kinematical cuts event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV-2 DVCS + BH + INT cross section kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’, φe’) LEsetup HEsetup due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen 2.5 < W < 28 GeV