1. H. Avakian, Argonne, April 8 1 Harut Avakian (JLab) Modification of transverse momentum distributions in nuclei Modification of transverse momentum distributions in nuclei Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider Argonne National Laboratory, April 7 - 9, 2010 TMDs and spin-orbit correlations k T -distributions Higher twists in SIDIS MC-simulations Projections for observables Conclusions

2. H. Avakian, Argonne, April 8 2 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

3. H. Avakian, Argonne, April 8 3 k T and FSI l l’ x,k T proton spectator system The difference is coming from final state interactions (different remnant) Tang,Wang & Zhou Phys.Rev.D77:125010,2008 lTlT l l’ x,k’ T l’ T spectator system nucleus total transverse momentum broadening squared BHS 2002 Collins 2002 Ji,Yuan 2002 soft gluon exchanges included in the distribution function (gauge link)

4. H. Avakian, Argonne, April 8 44 SIDIS: partonic cross sections kTkT P T = p ┴ +z k T p┴p┴ Ji,Ma,Yuan Phys.Rev.D71:034005,2005 Is the info on x-k T correlations accessible in k T integrated observables?

5. H. Avakian, Argonne, April 8 55 Quark distributions at large k T : models Effect of the orbital motion on the q- may be most significant JMR model q Dq M R, R=s,a  u/u (dipole formfactor), J.Ellis, D-S.Hwang, A.Kotzinian Higher probability to find a quark anti-aligned with proton spin at large k T (H.A.,S.Brodsky, A.Deur,F.Yuan 2007)

6. H. Avakian, Argonne, April 8 66 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 Understanding the transverse structure is crucial!

7. H. Avakian, Argonne, April 8 7 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 CLAS data would allow multidimensional binning to study k T -dependence for fixed x PTPT PTPT arXiv:1003.4549

8. H. Avakian, Argonne, April 8 8

9. 99 Quark distributions at large k T 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 bigger effect at large z

10. H. Avakian, Argonne, April 8 10 Jet limit: Higher Twist azimuthal asymmetries No leading twist, provide access to quark- gluon correlations T-odd H.A.,A.Efremov,P.Schweitzer,F.Yuan arXiv:1001.5467 “interaction dependent” Twist-2 Twist-3

11. H. Avakian, Argonne, April 8 11 Modification of Cahn effect Large cosn  moments observed at COMPASS Bag model arXiv:1001.3146 Gao, Liang & Wang Nuclear modification of Cahn may provide info on k T broadening and proton TMDs

12. H. Avakian, Argonne, April 8 12 ss x hh PTPT Fragmenting quark polarization CC CC y x SS hh PTPT  S =  +  h HT function related to force on the quark. M.Burkardt (2008) Collins mechanism for SSA fragmentation of transversely polarized quarks into unpolarized hadrons x PTPT hh  S =  y x PTPT hh S=S= y

13. H. Avakian, Argonne, April 8 13 Electroproduction kinematics: JLab12→EIC JLab  0.1<x B <0.7 JLab@12GeV Study of high x domain requires high luminosity, low x higher energies EIC JLab12 Q2Q2 EIC collider experiments H1, ZEUS 10 -4 <x B <0.02 EIC 10 -4 <x B <0.3 gluons (and quarks) fixed target experiments COMPASS  0.006<x B <0.3 HERMES  0.02<xB<0.3 gluons/valence and sea quarks valence quarks EIC (4x60):

14. H. Avakian, Argonne, April 8 14 LEPTO/PEPSI: quark distributions Need to model TMDs in LUND MC Implemented in PEPSI modification to LEPTO done by A. Kotzinian Add different widths for q+ and q- z>0.1 z>0.3 MC with Cahn Event Generator with polarized electron and nucleon: PEPSI,…. Acceptance check Design parameters Smearing/resolution routines Use GEANT as input Physics analysis using the “reconstructed” event sample

15. H. Avakian, Argonne, April 8 15  (p) = 0.05 + 0.06*p [GeV] % EIC 4x60 (Lumi 10 33,cm -2 sec -1, ~1 hour) K*s can be studied with EIC =0.1, =4

16. H. Avakian, Argonne, April 8 16 Nonperturbative TMD Perturbative region  sin  LU ~F LU ~ 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

17. H. Avakian, Argonne, April 8 17 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

18. H. Avakian, Argonne, April 8 18 Summary Studies of spin and azimuthal asymmetries in semi-inclusive processes at EIC : Measure nuclear modification of transverse momentum distributions and spin-orbit correlations of partons at small x, in a wide range of Q Study quark-gluon correlations (HT) in nucleon and nucleus Provide information on correlations of longitudinal and transverse degrees of freedom  EIC : Studies of nuclear modifications of spin orbit and quark-gluon correlations combined with JLab12 data will help construct a more complete picture about the structure of the nucleon and nuclei.

19. H. Avakian, Argonne, April 8 19 Support slides….

20. H. Avakian, Argonne, April 8 20 High energy quarks at small angles Struck quark kinematics (EIC 4x60) qq

21. H. Avakian, Argonne, April 8 21 SIDIS (  *p->  X) x-section at leading twist Measure Boer-Mulders distribution functions and probe the polarized fragmentation function Measurements from different experiments consistent TMD PDFs

22. H. Avakian, Argonne, April 8 22 k T and FSI l l’ x,k T proton spectator system The difference is coming from final state interactions (different remnant) Tang,Wang & Zhou Phys.Rev.D77:125010,2008 lTlT l l’ x,k’ T l’ T spectator system nucleus total transverse momentum broadening squared BHS 2002 Collins 2002 Ji,Yuan 2002

23. H. Avakian, Argonne, April 8 23 Transverse force on the polarized quarks Interpreting HT (quark-gluon-quark correlations) as force on the quarks (Burkardt hep-ph:0810.3589) Quark polarized in the x-direction with k T in the y-direction Force on the active quark right after scattering (t=0)

24. H. Avakian, Argonne, April 8 24 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 x F >0 (CFR) x F <0 ( TFR) EIC-MC

25. H. Avakian, Argonne, April 8 25  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

26. H. Avakian, Argonne, April 8 26 EIC medium energy Electron energy: 3-11 GeV Proton energy: 20-60 GeV – More symmetric kinematics provides better resolution and particle id Luminosity: ~ 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 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

27. H. Avakian, Argonne, April 8 27 JETSET:Single particle production in hard scattering Lund-MC should be modified to allow checks of sensitivity of measurements to different effects related to the transverse structure - Before - After quarkTarget remnant LUND Fragmentation Functions

28. H. Avakian, Argonne, April 8 28 Cross section is a function of scale variables x,y,z z SIDIS kinematical plane and observables U unpolarized L long.polarized T trans.polarized Beam polarization Target polarization sin2  moment of the cross section for unpolarized beam and long. polarized target

29. H. Avakian, Argonne, April 8 29 Identification using the missing mass may be possible    detected CLAS12 EIC4x60 FAST-MC Kaon production in SIDIS  (p) = 0.05 + 0.06*p [GeV] %

30. H. Avakian, Argonne, April 8 30 JLab, Nov 25 30 Azimuthal moments with unpolarized target quark polarization

31. H. Avakian, Argonne, April 8 31 JLab, Nov 25 31 Azimuthal moments with unpolarized target quark polarization

32. H. Avakian, Argonne, April 8 32 JLab, Nov 25 32 SSA with unpolarized target quark polarization

33. H. Avakian, Argonne, April 8 33 JLab, Nov 25 33 SSA with unpolarized target quark polarization

34. H. Avakian, Argonne, April 8 34 SSA with long. polarized target quark polarization

35. H. Avakian, Argonne, April 8 35 SSA with long. polarized target quark polarization

36. H. Avakian, Argonne, April 8 36 SSA with unpolarized target quark polarization

37. H. Avakian, Argonne, April 8 37 SSA with unpolarized target quark polarization

38. H. Avakian, Argonne, April 8 38 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

39. H. Avakian, Argonne, April 8 39  production in the target fragmentation x F - momentum in the CM frame Wide kinematical coverage of EIC would allow studies of hadronization in the target fragmentation region (fracture functions)  polarization in TFR provides information on contribution of strange sea to proton spin Study polarized diquark fracture functions sensitive to the correlations between struck quark transverse momentum and the diquark spin. xF()xF() EICCLAS12 (ud)-diquark is a spin and isospin singlet s-quark carries whole spin of 

40. H. Avakian, Argonne, April 8 40 Collins effect Simple string fragmentation for pions (Artru model) leading pion out of page  production may produce an opposite sign A UT Leading  opposite to leading  (into page)  hep-ph/9606390 Fraction of  in e  X % left from e  X asm 20% 40% ~75% ~50% Fraction of direct kaons may be significantly higher than the fraction of direct pions. LUND-MC L z L z 

41. H. Avakian, Argonne, April 8 41 K/K* and  separations Detection of K+ crucial for separation of different final states ( ,K*)

42. H. Avakian, Argonne, April 8 42 Sivers effect in the target fragmentation A.Kotzinian High statistics of CLAS12 will allow studies of kinematic dependences of the Sivers effect in target fragmentation region

43. H. Avakian, Argonne, April 8 43 27 GeV compass hermes JLab ( upgraded ) JLab@6GeV Q2Q2 EIC HERA ENC Hard Scattering Processes: Kinematics Coverage Study of high x domain requires high luminosity, low x higher energies 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 JLab12 EIC(4x60) ENC(3x15) Q2Q2

44. H. Avakian, Argonne, April 8 44 Hard Scattering Processes: Kinematics Coverage Study of high x domain requires high luminosity, low x higher energies 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

45. H. Avakian, Argonne, April 8 45 hep:arXiv-09092238

46. H. Avakian, Argonne, April 8 46 TMDs: QCD based predictions Large-Nc limit (Pobilitsa) Brodsky & Yuan (2006) Burkardt (2007) Large-x limit Do not change sign (isoscalar) All others change sign u→d (isovector)