1. YerPHI, June 3, 2009 11 Electron Ion Collider Harut Avakian Feb 9, 2010

2. YerPHI, June 3, 2009 2 Physics motivation –TMDs and spin-orbit correlations Accessing TMDs in semi-inclusive DIS Higher twists in SIDIS –GPDs and quark-gluon imaging Accessing GPDs in hard exclusive processes Higher twists in hard exclusive processes Projections for transverse SSAs at EIC and comparison with JLAB12 SummaryOutline

3. YerPHI, June 3, 2009 33 Hard Processes Partonic scattering amplitude Fragmentation amplitude Distribution amplitude proton lepton pion proton lepton antilepton Drell-Yan BNL JPARC FNAL EIC SIDIS/DER electron positron pion e – e + to pions Collins (2002)

4. YerPHI, June 3, 2009 4 Electroproduction kinematics: HERA→JLab→EIC collider experiments H1, ZEUS (EIC) 10 -4 <x B <0.02 (0.3): gluons (and quarks) in the proton fixed target experiments COMPASS, HERMES  0.006/0.02<x B <0.3 : gluons/valence and sea quarks JLab/JLab@12GeV  0.1<x B <0.7 : valence quarks 27 GeV compass hermes JLab ( upgraded ) JLab@6GeV Q2Q2 EIC HERA ENC JLab12 EIC ENC Q2Q2 Study of high x domain requires high luminosity, low x higher energies

5. YerPHI, June 3, 2009 5 Hadrons in QCD are relativistic many-body systems, with a fluctuating number of elementary quark/gluon constituents and a very rich structure of the wave function. With 12 GeV we study mostly the valence quark component, which can be described with methods of nuclear physics (fixed number of particles). With an (M)EIC we enter the region where the many-body nature of hadrons, coupling to vacuum excitations, etc., become manifest and the theoretical methods are those of quantum field theory. EIC@JLab High-Level Overview

6. YerPHI, June 3, 2009 66 Single hadron production in hard scattering Measurements in different kinematical regions provide complementary information on the complex nucleon structure. x F - momentum in the CM frame x F >0 (current fragmentation) x F <0 (target fragmentation) h h Target fragmentationCurrent fragmentation Fracture Functions xFxF M 0 1 h h PDF GPD k T -dependent PDFsGeneralized PDFs PDF h FF DA exclusivesemi-inclusive semi-exclusive

7. YerPHI, June 3, 2009 7 Structure of the Nucleon GPDs/IPDs d2kTd2kT d2kTd2kT TMD PDFs f 1 u (x,k T ),.. h 1 u (x,k T )  Gauge invariant definition (Belitsky,Ji,Yuan 2003)  Universality of k T -dependent PDFs (Collins,Metz 2003)  Factorization for small k T. (Ji,Ma,Yuan 2005) W p u (k,r T ) “Mother” Wigner distributions d2rTd2rT PDFs f 1 u (x),.. h 1 u (x) quark polarization

8. YerPHI, June 3, 2009 8 EIC medium energy Electron energy: 3-11 GeV Proton energy: 12-60 GeV – More symmetric kinematics provides better resolution and particle id Luminosity: few x 10 34 cm -2 s -1 – in range around s ~ 1000 GeV 2 Polarized electrons and light ions –longitudinal and transverse Limited R&D needs 3 interaction regions (detectors) Potential upgrade with high-energy ring Main Features Electron energy: 4-20 GeV Proton energy: 50-250 GeV – More symmetric kinematics provides better resolution and particle id Luminosity: ~ 10 33 cm -2 s -1 – in range around s ~ 1000-10000 GeV 2 Polarized electrons and light ions –longitudinal and transverse Limited R&D needs ? interaction regions (detectors) 90% of hardware can be reused EIC@JLab EIC@RHIC

9. YerPHI, June 3, 2009 9 Current Ideas for EIC Energiessluminosity (M)EIC@JLabUp to 11 x 60150-2650Few x 10 34 Staged MeRHIC@BNL Up to 4 x 250(400-)4000Close to 10 33 Future ELIC@JLab Up to 11 x 25011000Close to 10 35 eRHIC@BNLUp to 20 x 32526000Few x 10 33 Most of the slides are for a “generic” US version of an EIC (5x50 or 4x60): polarized beams (longitudinal and transverse, > 70%) luminosities of at least 10 33 ( ~ 10 34 for exclusive processes) energies up to 10 x 250, or s = 10000 Present focus of interest (in the US) are the (M)EIC and Staged MeRHIC versions, with s up to 2650 and 4000, resp.

10. YerPHI, June 3, 2009 10 (M)EIC@JLab: Basic Considerations Optimize for nucleon/nuclear structure in QCD - access to sea quarks/gluons (x > 0.01 or so) - deep exclusive scattering at Q 2 > 10 - any QCD machine needs range in Q 2  s = 1000 or so to reach decade in Q 2  high luminosity, >10 34 and approaching 10 35, essential  lower, more symmetric energies for resolution & PID Not driven by gluon saturation (small-x physics) … “Sweet spot” for - electron energies from 3 to 5 GeV (minimize synchrotron) - proton energies ranging from 30 to 60 GeV - but larger range of s accessible (E e = 11 GeV, E p = 12 GeV) Decrease R&D needs, while maintaining high luminosities - Potential future upgrade to high-energy collider, but no compromising of nucleon structure capabilities

11. YerPHI, June 3, 2009 11 The Detector Wide kinematic coverage and large acceptance would allow studies of hadronization both in the target and current fragmentation regions

12. YerPHI, June 3, 2009 12 SIDIS kinematical plane and observables Beam polarizationTarget polarization U unpolarized L long.polarized T trans.polarized sin(  S  moment of the cross section for unpolarized beam and transverse target PTPT

13. YerPHI, June 3, 2009 13 SIDIS: partonic cross sections kTkT P T = p ┴ +z k T p┴p┴

14. YerPHI, June 3, 2009 14 Double spin asymmetries and flavor decomposition Anti-parallel electron & quark spins Parallel electron & quark spins u-quarks are mainly aligned with proton spin (  u>0) HERMES

15. YerPHI, June 3, 2009 15 Quark distributions at large k T : models Effect of the orbital motion on the q- may be significant (H.A.,S.Brodsky, A.Deur,F.Yuan 2007) JMR model q Dq M R, R=s,a Higher probability to find a quark anti-aligned with proton spin at large k T u + <u -

16. YerPHI, June 3, 2009 16 Quark distributions at large k T : lattice Higher probability to find a d-quark at large k T Higher probability to find a quark anti-aligned with proton spin at large k T B.Musch arXiv:0907.2381

17. YerPHI, June 3, 2009 17 Extracting widths from A 1 Assuming the widths of f 1 /g 1 x,z and flavor independent Anselmino et al Collins et al Fits to unpolarized data EMC

18. YerPHI, June 3, 2009 18 A 1 A 1 P T -dependence CLAS data suggests that width of g 1 is less than the width of f 1 Anselmino Collins Lattice New eg1dvcs data allow multidimensional binning to study k T -dependence for fixed x

19. YerPHI, June 3, 2009 19 k T -distributions in nuclei Higher probability to find a hadron at large P T in nuclei k T -distributions may be wider in nuclei? P T = p ┴ +z k T CLAS Hall-C bigger effect at large z

20. YerPHI, June 3, 2009 20 A 1 P T -dependence in SIDIS M.Anselmino et al hep-ph/0608048 A LL  ) sensitive to difference in k T distributions for f 1 and g 1 Wide range in P T allows studies of transition from TMD to perturbative approach  0 2 =0.25GeV 2  D 2 =0.2GeV 2 Perturbative limit calculations available for : J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238

21. YerPHI, June 3, 2009 21 Flavor Decomposition @ EIC  quark polarization  q(x)  first 5-flavor separation

22. YerPHI, June 3, 2009 22 Precisely image the sea quarks Spin-Flavor Decomposition of the Light Quark Sea Flavor decomposition will be performed using binning in P T

23. YerPHI, June 3, 2009 23 Bruell,Ent The Gluon Contribution to the Proton Spin RHIC-Spin Projected data on  g/g with an EIC, via  + p  D 0 + X K - +  + assuming vertex separation of 100  m. Uncertainties in x  g smaller than 0.01 Measure 90% of  G (@ Q 2 = 10 GeV 2 )

24. YerPHI, June 3, 2009 24 Within the FFNS (no heavy quarks), the leading mechanism contributing to F 2, F L and F A. At high Q 2 with heavy quarks (VFNS), there is additional contribution to F 2, but not to F L and F A ! Measuring the charm content of the proton ln(Q 2 / m 2 Q 2 The heavy-quark content of the proton is due to resummation of the mass logarithms of the type α s ln(Q 2 / m 2 ) and thus, closely related to behavior of asymptotic perturbative series for high Q 2. N.Ya.Ivanov, Nucl. Phys. B 814 (2009), 142

25. YerPHI, June 3, 2009 25 Resummation for A= 2xF A / F 2 L.N. Ananikyan, N.Ya. Ivanov,. Nucl.Phys.B762:256-283,2007. N.Ya.Ivanov, Nucl. Phys. B 814 (2009), 142L.N. AnanikyanN.Ya. Ivanov The mass logarithms resummation (or heavy-quark densities) should reduce the pQCD predictions for R= F L / F T and A=2xF A / F 2. cos2  moment in charm meson production provides access to charm densities CTEQ PDFs used for estimates N.Ya.Ivanov, Nucl. Phys. B 814 (2009), 142

26. YerPHI, June 3, 2009 26 EIC: Kinematics Coverage Major part of current particles at large angles in Lab frame (PID at large angles crucial). ep 5 GeV50 GeV e’  + X all x F >0 z>0.3 EIC-MC (PYTHIA based) x F >0 (CFR) x F <0 ( TFR) EIC-MC

27. YerPHI, June 3, 2009 27 ss x hh PTPT Fragmenting quark polarization CC CC y x SS hh PTPT  S =  +  h x PTPT hh S=S= y HT function related to force on the quark. M.Burkardt (2008) Collins mechanism for SSA fragmentation of transversely polarized quarks into unpolarized hadrons

28. YerPHI, June 3, 2009 28 Sivers mechanisms for SSA - Correlation between quark transverse momentum and the proton spin SS x  kT PTPT Proton polarization SS SIDIS Drell-Yan M.Burkardt (2000) HT asymmetries (T-odd) No leading twist, provide access to quark-gluon correlations

29. YerPHI, June 3, 2009 29 Nonperturbative TMD Perturbative region  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) In the perturbative limit 1/P T behavior expected Study for SSA transition from non-perturbative to perturbative regime. EIC will significantly increase the P T range. P T -dependence of beam SSA 4x60 100 days, L=10 33 cm -2 s -1

30. YerPHI, June 3, 2009 30  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) 1/Q behavior expected (fixed x bin) Study for Q 2 dependence of beam SSA allows to check the higher twist nature and access quark-gluon correlations. Q 2 -dependence of beam SSA

31. YerPHI, June 3, 2009 31 Boer-Mulders Asymmetry with CLAS12 & EIC CLAS12 and EIC studies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations and test unified theory (Ji et al) Nonperturbative TMD Perturbative region Transversely polarized quarks in the unpolarized nucleon - CLAS12 EIC ep 5-GeV50 GeV sin(  C ) =cos(2  h ) Perturbative limit calculations available for : J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238

32. YerPHI, June 3, 2009 32 Sivers effect: pion electroproduction EIC measurements at small x will pin down sea contributions to Sivers function S. ArnoldS. Arnold et al arXiv:0805.2137 M. AnselminoM. Anselmino et al arXiv:0805.2677 GRV98, Kretzer FF (4par) GRV98, DSS FF (8par)

33. YerPHI, June 3, 2009 33 Sivers effect: Kaon electroproduction At small x of EIC Kaon relative rates higher, making it ideal place to study the Sivers asymmetry in Kaon production (in particular K-). Combination with CLAS12 data will provide almost complete x-range. EIC CLAS12

34. YerPHI, June 3, 2009 34 Sivers effect: sea contributions Negative Kaons most sensitive to sea contributions. Biggest uncertainty in experimental measurements (K- suppressed at large x). GRV98, DSS FF S. ArnoldS. Arnold et al arXiv:0805.2137 M. AnselminoM. Anselmino et al arXiv:0805.2677 GRV98, Kretzer FF

35. YerPHI, June 3, 2009 35 Pretzelosity @ EIC EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements 5x50 e  X positivity bound -- ++

36. YerPHI, June 3, 2009 36 DVMP DVMP Hard Exclusive Processes and GPDs hard vertices DVCS – for different polarizations of beam and target provide access to different combinations of GPDs H,H, E,E long. only DVMP for different mesons is sensitive to flavor contributions (     /K* select H, E, for u/d flavors, , K select H, E) DVCS

37. YerPHI, June 3, 2009 37 Gluon Imaging with exclusive processes Goal: Transverse gluon imaging of nucleon over wide range of x: 0.001 < x < 0.1 Two-gluon exchange dominant for J/ , ,  production at large energies  sensitive to gluon distribution squared! LO factorization ~ color dipole picture  access to gluon spatial distribution in nuclei Fit with d  /dt = e -Bt Measurements at DESY of diffractive channels ( J/ , , ,  ) confirmed the applicability of QCD factorization: t-slopes universal at high Q 2 flavor relations  :  Hard exclusive processes provide access to transverse gluon imaging at EIC! A.Levy(hep:0907.2178)

38. YerPHI, June 3, 2009 38 CLAS12 EIC4x60 M(e’  +X) ++ --    - Quark Imaging with exclusive processes Horn,Bruell,Weiss Simulation for charged  + production, assuming 100 days at a luminosity of 10 34, with 5 on 50 GeV (s = 1000) More demanding in luminosity - Physics closely related to JLab 6/12 GeV - quark spin/flavor separations - nucleon/meson structure V. Guzey, Ch. Weiss: Regge model T. Horn: π + empirical parameterization

39. YerPHI, June 3, 2009 39 SSAs in exclusive pion production HT SSAs are expected to be very significant EIC can measure Q 2 dependence of HT SSAs significantly extending the range of CLAS12 P.Kroll & S. Goloskokov arXiv:0906.0460 Transverse photon matters HERMES CLAS Dubna-2003

40. YerPHI, June 3, 2009 40 GPDs from cross section ratios Study ratio observables: K/K*/  +,polarization transfer Different final state mesons filter out different combinations of unpolarized (H,E) and polarized (H,E) GPDs. M.Diehl et al. hep-ph/0506171 K *+ K+K+

41. YerPHI, June 3, 2009 41 Quark Imaging with exclusive processes Horn,Cooper Using an empirical fit to kaon electroproduction data from DESY and JLab assuming 100 days at a luminosity of 10 34, with 5 on 50 GeV (s = 1000) Rate estimate for KΛ Need good resolution to identify exclusive events    detected CLAS12 EIC4x60

42. YerPHI, June 3, 2009 42 Chiral-odd GPDs with exclusive  + GPD Large momentum transfer, large rapidity gap Virtual photon replaced with 2 gluons hard Ivanov et al. Phys.Part.Nucl.35:S67-S70,2004 Enberg et al. Eur.Phys.J.C47:87-94,2006 Smaller rapidity gap  + selects quark antiquark exchange with the nucleon Ratio of  0 L   T n/  0 L   L n directly related to ratio of GPDs H T /H Long distance part described by GPD H T pTpT

43. YerPHI, June 3, 2009 43 Summary  EIC : Measurements related to the spin, spin orbit and quark-gluon correlations (HT) combined with JLab12 HERMES,COMPASS, RHIC,BELLE,BABAR,Fermilab,J-PARC,GSI data will help construct a more complete picture about the spin structure of the nucleon beyond the collinear approximation. Studies of semi-inclusive and exclusive processes at EIC Provide detailed info on gluon and sea quark spatial imaging of the nucleon Measure transverse momentum distributions of partons at small x Define quark-gluon correlations using the wide range of Q 2 Investigate hadronization in target fragmentation

44. YerPHI, June 3, 2009 44 “An Electron-Ion Collider (EIC) with polarized beams has been embraced by the U.S. nuclear science community as embodying the vision for reaching the next QCD frontier. EIC would provide unique capabilities for the study of QCD well beyond those available at existing facilities worldwide and complementary to those planned for the next generation of accelerators in Europe and Asia. In support of this new direction: We recommend the allocation of resources to develop accelerator and detector technology necessary to lay the foundation for a polarized Electron Ion Collider. The EIC would explore the new QCD frontier of strong color fields in nuclei and precisely image the gluons in the proton.” Recent Progress toward a High-Luminosity EIC at JLab NSAC 2007 Long-Range Plan:

45. YerPHI, June 3, 2009 45 JLab, Nov 25 45 Support slides….

46. YerPHI, June 3, 2009 46

47. YerPHI, June 3, 2009 47 Interaction Region at ELIC Legend: MEIC =EIC@JLab 1 low-energy IR (s ~ 200) 3 medium-energy IRs (s < 2600) ELIC =high-energy EIC@JLab (s = 10000) (limited by JLab site) Use CEBAF “as-is” after 12-GeV Upgrade Rolf Ent (JLab) Common ENC/EIC Workshop GSI Darmstadt, May 30 2009

48. YerPHI, June 3, 2009 48 Miller/”pretzelosity” Spin densities from Lattice ( Spin densities from Lattice (QCDSF and UKQCD Collaborations) Proton spin quark spin GPD-E GPD-E T PasquiniPasquini, Cazzaniga & S. Boffi (2008)CazzanigaS. Boffi

49. YerPHI, June 3, 2009 49 JLab, Nov 25 49 Collins effect Simple string fragmentation (Artru model) Sub-leading pion opposite to leading (into page) Fraction of direct production different for different hadrons hep-ph/9606390 Fraction of  in e  X% left from e  X asm 40% 60% ~50% ~20% 75%0 L=1  production may produce an opposite sign A UT Leading  opposite to leading  (into page) 