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

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

GPDs properties, link to DIS and form factors for P1 = P2 recover usual parton densities no similar relations; these GPDs decouple for P1 = P2 needs orbital angular momentum between partons Dirac axial pseudoscalar Pauli Ji’s sum rule total angular momentum carried by quark flavour q (helicity and orbital part)

½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg > ‘Holy Grails’ or the 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 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 > t p q E

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

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

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

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 Unpolarized cross sections extracted twist-3 contribution small

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

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

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

Unpolarised DVCS cross sections from HERA σDVCS at small 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 - 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

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

Lessons from DVCS at H1/ZEUS Skewing parameter R=Im DIS / Im DVCS ~ 0.5 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% Low sensitivity to b(Q2) vs. b(const.) Interplay of Rs (sea) and Rg (gluons) Color dipole phenomenology (no GPDs) also a satisfacory description

Hard exclusive meson production 4 Generalised Parton Distributions (GPDs) for each quark flavour and for gluons GPDs depend on 3 variables: x, x, t 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 H E Vector mesons (ρ, ω, φ) H E Pseudoscalar mesons (π, η) ~ Flavour sensitivity of DVMP on the proton ρ0 2u+d, 9g/4 ω 2u-d, 3g/4 φ s, g ρ+ u-d J/ψ g conserve flip nucleon helicity quarks and gluons enter at the same order of αS wave function of meson (DA Φ) additional information/complication

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 Martin-Ryskin-Teubner (MRT) Phys.Rev. D62 (2000) 014022 sensitivity to different gluon density distibutions 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)

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

W-dependence for hard exclusive processes at small x ϕ J/ψ ϒ 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

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

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

Selected results on R = σL/σT for ρ0 production the same W- and t-dependence for σL and 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

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

Comparison to GPD model Goloskokov-Kroll ‘Hand-bag model’; GPDs from DD using CTEQ6 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 σT decreases 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

Transverse target spin asymmetry for exclusive ρ0 production Give access to GPD E related to the orbital angular momentum of quarks Ji’s sum rule q q So far GPD E poorly constrained by data; mostly by Pauli form factors The asymmetry defined as to disentangle contributions from γL and γT the distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta The asymmetry defined as to disentangle contributions from γL and γT the distribution of ρ0 decay polar angle needed in addition Diehl and Sapeta Eur. Phys. J.C 41, 515 (2005)

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

ρ0 transverse target spin asymmetry from HERMES Transversely polarised proton target, PT ≈ 75% 2002-2005 data, 171.6 pb-1 for the first time ρ0 TTSA extracted separately for γ*L and γ*T

ρ0 transverse target spin asymmetry from HERMES in a model dependent analysis data favours positive Ju in agreement with DVCS results from HERMES

ρ0 transverse target spin asymmetry from COMPASS obtained using Double Ratio Method Transversely polarised deuteron target (6LiD), PT ≈ 50% 2002-2004 data obtained using Double Ratio Method in bins of ϑ = φ – φS: u (d) are for upstream (downstream) cell of polarised target arrows indicate transverse polarisation of corresponding cells raw asymmetry ε from the fit to DR(η) dilution factor f ≈ 0.38

ρ0 transverse 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)

Exclusive π+ production from HERMES e p → e n π+ ~ ~ at leading twist σL sensitive to GPDs H and E at small |t’| E dominates as it contains t-channel pion-pole ~ L/T separation not possible at HERMES, σT expected to be supressed as 1/Q2 σL VGG LO σL VGG LO+power corrections σT + ε σL Regge 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

Beam spin asymmetry in exclusive π0 production from CLAS ~ at leading twist σL sensitive 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 a fit α sinφ Regge model (Laget) pole terms (ω, ρ, b1) + box diagrams (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

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

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

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

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 HE setup 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

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

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!

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

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, if e+ and e- available as well as longitudinaly and transversely polarized protons Sufficient luminosity to do tripple-differential measurements in xB, Q2, t

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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 Ee’ > Emin GeV Eγ > 0.5 GeV 2° < θe’ < 178° 2° < θγ < 178° Emin = 2 GeV (HE) or 1 GeV (LE) DVCS + BH + INT cross section kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’ , φe’ ) HE setup LE setup 1 < Q2 < 50 GeV2 10 < W < 90 GeV 0.05 < |t| < 1.0 GeV2 due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen 1 < Q2 < 50 GeV2 0.05 < |t| < 1.0 GeV2 2.5 < W < 28 GeV