1. Hard exclusive processes at EIC Andrzej Sandacz Sołtan Institute for Nuclear Studies, Warsaw  Introduction  DVCS – from Central Detector only  Exclusive Meson production  DVCS – including fast ‘recoil’ proton - experimental aspects -  Tagging spectator protons for deuteron beam  Conclusions workshop on ‘Hard Exclusive Process at JLab 12 GeV and a Future EIC’ University of Maryland College Park, October 29-30, 2006

2. Deeply Virtual Compton Scattering e p → e p  The same final state in DVCS and Bethe-Heitler interference I up to twist-3 BMK (2002) interference + structure of azimuthal distributions a powerful tool to disantangle leading- and higher-twist effects and extract DVCS amplitudes including their phases P 1 (Φ), P 2 (Φ) BH propagators harmonics with twist-2 DVCS amplitudes (related to GPDs) c 0 DVCS, c 1 I, s 1 I and c 0 I (the last one Q suppresed)

3. Towards extraction of full set of GPDs example: method proposed by Belitsky, Mueller, Kirchner (2002)  measure e p → e p γ cross sections both for e + and e - for unpolarized, longitudinally and transversely polarized protons  σ + (φ) – σ - (φ) I Λ (φ) σ + (φ) + σ - (φ) – 2 σ BH (φ) 2 σ DVCS,Λ (φ)  from φ-dependence of I Λ ’s extract 8 leading-twist harmonics c I 1,Λ s I 1,Λ Λ = {unp, LP, T n P, T s P}  from these determine all 4 DVCS amplitudes (including their phases) which depend on GPDs  another 8 leading-twist harmonics c DVCS 0,Λ and c I 0,Λ cross check in experiment asymmetries simpler than cross sections, but extraction of DVCS amplitudes more involved Aim for DVCS - go beyond measurements of unpolarized cross sections, access interference term and exploit azimuthal angle dependence

4. Available measurements of asymmetries for DVCS lepton charge or single spin asymetries at moderate and large x B HERMES and JLAB results  beam-charge asymmetry A C (φ)  beam-spin asymmetry A LU (φ)  longitudinal target-spin asymmetry A UL (φ)  transverse target-spin asymmetry A UT (φ,φ s ) F 1 and F 2 are Dirac and Pauli proton form factors

5. Unpolarized cross sections for DVCS cross section σ DVCS averaged over φ for unpolarised protons H1 and ZEUS DIS 2006 at small x B ( < 0.01) H sea, H g

6. A simulation of DVCS at eRHIC HE setup: e +/- (10 GeV) + p (250 GeV) L = 4.4 · 10 32 cm -2 s -1 38 pb -1 /day acceptance of Central Detector (improved ZDR) 2° < θ lab < 178° diam. of the pipe - 20 cm, space for Central Detector: ≈ +/- 280 cm from IP event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV -2 DVCS + BH + INT cross section due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen acceptance simulated by kinematical cuts kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS ( θ γ, φ γ ) + expected for LHC ( θ e’, φ e’ ) LE setup: e +/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 10 32 cm -2 s -1 13 pb -1 /day E e’ > E min GeV E γ > 0.5 GeV 2° < θ e’ < 178° 2° < θ γ < 178° E min = 2 GeV (HE) or 1 GeV (LE) 2.5 < W < 28 GeV 1 < Q 2 < 50 GeV 2 0.05 < |t| < 1.0 GeV 2 1 < Q 2 < 50 GeV 2 10 < W < 90 GeV 0.05 < |t| < 1.0 GeV 2 HE setup LE setup

7. Distributions of events within acceptance of Central Detector log 10 (x Bj ) HE setup LE setup log 10 (x Bj ) Q 2 [GeV 2 ] W [GeV] Number of event [arbitrary units] DVCS BH Complementarity of HE and LE setups for covered W and x Bj ranges good coverage for 3 < W < 90 GeV and 1.5 · 10 -4 < x Bj < 0.2

8. Precision of DVCS unpolarized cross sections at eRHIC (1) L int = 530 pb -1 Assume 2 weeks for each setup σ(ep→epγ) = 292 pb Events divided into 6x6 bins of Q 2 and W for each setup Q 2 [GeV 2 ] eRHIC HE setup = 37 GeV For one out of 6 W intervals: 30 < W < 45 GeV eRHIC LE setup Q 2 > 1 GeV 2 10 < W < 95 GeV 0.05 < |t| < 1.0 GeV 2 Q 2 > 1 GeV 2 0.05 < |t| < 1.0 GeV 2 2.5 < W < 28 GeV σ(ep→epγ) = 173 pb L int = 530 pb -1 L int = 180 pb -1 Δσ /σ Reconstructed: ≈ 133 000 events ≈ 28 000 events

9. Precision of DVCS unpolarized cross sections at eRHIC (2)  eRHIC measurements of cross section will provide significant constraints For one out of 6 W intervals (30 < W < 45 GeV) L int = 530 pb -1 (2 weeks) Q 2 [GeV 2 ] eRHIC HE setup = 37 GeV σ(γ*p → γ p) [nb]

10. Precision of DVCS unpolarized cross sections at eRHIC (3)  EIC measurements of cross section will provide significant constraints For one out of 6 Q 2 intervals (8 < Q 2 < 15 GeV 2 ) W [GeV] = 10.4 GeV 2 σ(γ*p → γ p) [nb] also significantly extend the range towards small W

11. An example: Lepton charge asymmetry precision at eRHIC L int = 530 pb -1 divided in half between e + and e - cross section in 6x6 bins of Q 2 and W Dependence on azimuthal angle φ for (DVCS+BH+INT) Determination of smearing and acceptance as a function of φ crucial for the Fourier analysis, asymmetry also for φ -integrated cross sections Nb of events [arb. units] (φ rec -φ gen ) [º] φ gen [º] Acceptance HE setup RMS = 15º

12. Lepton charge asymmetry precision at eRHIC BMK use ‘improved’ charge asymmetries CoA unp c(1) and CoA unp s(1) model of Belitsky, Mueller, Kirchner (2002) for GPDs at small x B parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001)) except magnetic moment κ sea (-3 < κ sea < 2), which enters Ji’s sum rule for J q κ sea = 2 κ sea = -3  measurements of asymmetries at EIC sensitive tool to validate models of GPDs Q 2 [GeV 2 ] W = 75 GeV, -t = 0.1 GeV 2 W [GeV] Q 2 =4.5 GeV 2, -t = 0.1 GeV 2

13. Detection of scattered fast protons (‘recoils’) Aim: clean subsample of exclusive events => control of effects of DD in main sample Since scattering angles of fast protons are small they stay within the beam pipe and follow trajectories determined by magnetic fileds of accelarator Note different θ rec scales for HE and LE setups θ r [rad ] p r [GeV ] θ r [rad ] p r [GeV ] HE LE Nb of events [arb. units]

14. A method for detection of recoil protons (or horizontally) = Beam transport matrix at the detectorat the IP 10 cm σ x ≈ σ y ≈ 30 μm Elements of TM depend on distance L from IP and on δ = (p r –p b )/p b Requirements  Distance from the nominal beam orbit > 12 σ beam envelope  High sensitivity to the angles at the IP  No strong dependence of TM elements on δ

15. Beams characteristics and transport protons ε * = 9.5 nm β* x/y = 0.26 m σ 0 x/y = 50 μm σ 0 θx/y = 191 μrad Considered option: linac-ring for 10 GeV e + 250 GeV p transport program written by Christoph Montag (CAD-BNL) electrons ε * = 2.5 nm β* x/y = 1 m σ 0 x/y = 50 μm σ 0 θx/y = 50 μrad 12 σ beam envelope Distance from beam orbit [m] L [m] RP 1 @ 23.3 mRP 2 @ 57.4 m

16. Transverse coordinates of recoil protons at positions of RP’s L = 23.3 mL = 57.4 m x D [m] y D [m] all in acceptance of RP

17. Full acceptance including Roman Pots RP 1 @ L = 23.3 mRP 2 @ L = 57.4 m Nb of events [arb. units] Acceptance generated accepted (CD + RP) For RP 2 range of t with reasonable acceptance wider, but … -t [GeV 2 ] ‘reasonable’ acceptance |t| > 0.35 GeV 2 for RP 1 |t| > 0.15 GeV 2 for RP 2 average acceptance for 0.05 < |t| < 1.0 GeV 2 12% for RP 1 25% for RP 2

18. Determination of recoil angles θ and φ at the IP p r [GeV] a 11 or a 33 L eff [m] TM elements relevant for determination of θ * x and θ * y  Effect of transverse smearing of IP ( ≈ 70 μm) small at RP’s because of small a 11 and a 33 θ * x ≈ x D / L x eff θ * y ≈ y D / L y eff θ * and φ of recoil at IP  With RP1 significantly higher sensitivity to angle at IP because of larger L eff

19. Resolution for reconstructed recoil and tagging of exclusive events Nb of events [arb. units] (θ r rec -θ r gen ) [ rad ] (t r rec – t gen ) [GeV 2 ] 21 μrad RMS 124 μrad 0.046 RMS RP 2 RP 1 t r rec ≈ - (p beam · θ r rec ) 2 No measurement of p r Nb of events [arb. units] RP 1 RMS 5.7 º2.8 º6.4 º (φ eγ rec -φ eγ gen ) [ º ](φ r rec -φ r gen ) [ º ](φ eγ rec -φ r rec ) [ º ] Full simulation incl. smearing of CD and RP, size of IP and angular beam divergence

20. Conclusions for resolution and tagging recoil protons  Detection of fast recoil protons possible at moderate |t| (above ≈ 0.3 GeV 2 )  Good precision of reconstructed angles at IP for recoils  Accuracy of t derived from recoil limited by beam angular divergence and unmeasured recoil momentum  A possible method to tag exclusive process by correlation of azimuthal angles  Extension of |t| range (down to ≈ 0.12 GeV 2 ) with detected recoil possible but with poor precision of recoil angles

21. Exclusive production of mesons at eRHIC Results of previous simultations of ρ 0 and J/ψ exclusive production at eRHIC shown at ‘Current and Future Directions at RHIC’ - 2002 Main ingredients of those simulations e (10 GeV) + p (250 GeV) Detector angular acceptance between ZDR (± 1m) and ‘updated ZDR’ (± 3m) Ranges of W and xbj for hard production similar as shown for DVCS Nb of accepted events ≈ 650 000 ρ 0 production at large Q 2 L int = 330 pb -1

22. Exclusive production of mesons at eRHIC (2) J/ψ production at large Q 2 J/ψ photo-production Nb of accepted events ≈ 5200 Nb of accepted events ≈ 67 000

23. Tagging spectator protons from deteron beam spectator protons traced down to RP1 or RP2 in deuteron rest frame each component with Gaussian distribution σ = 35 MeV Assumed settings of magnets for 250 GeV deuteron beam Nb of events Results below – for RP1 x D [m] y D [m] all in acceptance of RP efficiency ≈ 0.96 Nb of events  Tagging of proton spectators feasible, with high efficiency

24. Summary for DVCS at eRHIC  Wide kinematical range, overlap with HERA and COMPASS 1.5 ·10 -4 < x B < 0.2 - sensitivity to quarks (mostly u+ubar) and gluons 1 < Q 2 < 50 GeV 2 - 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  Feasibility of using RP detectors at range of moderate to large t for selection of exclusive events