1. H.Avakian, HEDT July 1 1 The Impact of Hermes on Other Experiments Harut Avakian (JLab) Hamburg, July 1

2. H.Avakian, HEDT July 1 2 Outline HERMES and the transverse structure of the nucleon 3D PDFs First measurements and interpretations Future measurements of SIDIS and DY DY at RHIC, JPARC,GSI SIDIS at JLAB12 and EIC GPDs with CLAS12 Summary

3. H.Avakian, HEDT July 1 3 PDFs f p u (x),… Form Factors F 1p u (t),F 2p u (t ).. TMD PDFs f p u (x,k T ), d2kTd2kT dx (FT) GPDs/IPDs W p u (x,r T ),… d2rd2r W p u (k,r T ) “Mother” Wigner distributions d2rd2r d2kTd2kT Measure momentum transfer to quark Direct info about momentum distributions No information about spatial location of partons Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k Structure of the Nucleon Measure momentum transfer to target Direct info about spatial distributions No direct information about underlying dynamics

4. H.Avakian, HEDT July 1 4 SIDIS kinematical plane and observables Trento Conventions Beam polarization Target polarization U unpolarized L long.polarized T trans.polarized sin  moment of the cross section for unpolarized beam and transverse target Phys.Rev. D70, 117504 (2004).

5. H.Avakian, HEDT July 1 5 Off diagonal PDFs related to interference between states with different orbital momentum Transverse momentum of quarks k T – required to describe azimuthal distributions of hadrons and in particular SSAs. k T - important for cross section description (also for exclusive production)  Universality of k T -dependent distribution and fragmentation functions. Sign flip for f 1T ┴, h 1 ┴ from DY to SIDIS predicted. (Collins,Metz 2003) Mulders & Tangerman (1995, the TMD “bible”) Transversity Sivers Boer-Mulders  Factorization proven for small k T. (Ji,Ma,Yuan 2005)  Gauge invariant definition of k T -dependent PDFs (Belitsky,Ji,Yuan 2003)  The role of final state interactions in SSA ( Brodsky et al,Collins 2002 ) Spin structure k T – leads to 3D description with 8PDFs

6. H.Avakian, HEDT July 1 6 Collins fragmentation: Longitudinally polarized target Study transversely polarized quarks in the longitudinally polarized proton Provides independent information on the Collins function. curves,  QSM from Efremov et al Kotzinian-Mulders Asymmetry (1996)

7. H.Avakian, HEDT July 1 7 HERMES effect # First measurement of significant SSA in electroproduction A UT ~ Collins Transverse with respect to  * ** e Kotzinian et al (1999) → HT (75%)

8. H.Avakian, HEDT July 1 8 Hard Processes Partonic scattering amplitude Fragmentation amplitude Distribution amplitude proton SIDIS/DER lepton pion electron positron pion e – e + to pions proton lepton antilepton Drell-Yan BNL JPARC FNAL

9. H.Avakian, HEDT July 1 9 Future results from BELLE Belle detector KEKB Asymmetric collider 8GeV e- + 3.5GeV e+

10. H.Avakian, HEDT July 1 10 l l+l+ RHIC-II DY-studies BNL DY di-lepton production at RHIC-II as a function of rapidity y Projected errors (red) compared to STAR and PHENIX (125 pb -1 ) and theory predictions. Factor 3-4 from continuous transverse data taking, 3-5 more lumi from new vertex focusing magnets. - - y y STAR HERMES coverage

11. H.Avakian, HEDT July 1 11 E906 @ 120 GeV requires shorter experiment. –E906 spect. is only 26m long (60m for E866) –New coils for M1 magnet (4.8 m was 14.5 m) 200820072010 Publications Expt. Funded 2009 Magnet DesignExperiment And constructionConstruction Proposed Jan. 2007 Experiment Runs x7 more data compared to E866 FNAL Main Injector 120 GeV Tevatron 800 GeV

12. H.Avakian, HEDT July 1 12 Sivers function at

13. H.Avakian, HEDT July 1 13 Studies of DY at JPARC Expected distributions from Drell-Yan 50 GeV - Jen-Chieh Peng et al

14. H.Avakian, HEDT July 1 14 FAIR @GSI experiment:  asymmetric collider: p = 15.0 GeV in HESR p = 3.5 GeV in CSR  internal polarised target with p = 22 GeV 1 yr of data taking Experiments at FAIR "Facility of Antiproton and Ion Research"

15. H.Avakian, HEDT July 1 15 CLAS12 Solenoid 5T CTOF SVT Central Detector DC R1, R2, R3 LTCC FTOF PCAL EC HTCC TORUS Forward Detector Forward carriage Track resolution:  p (GeV/c) 0.003p + 0.001p 2  (mr) < 1  (mr)< 3 Wide detector and physics acceptance (current/target fragmentation) High beam polarization 85% High target polarization 85% Lumi > 10 35 cm -1 s -1 (NH 3,ND 3 HD?)

16. H.Avakian, HEDT July 1 16 CLAS12: Kinematical coverage Large Q 2 accessible with CLAS12 are important for separation of HT contributions Q 2 >1GeV 2 W 2 >4 GeV 2 (10) y<0.85 M X >2GeV SIDIS kinematics eXeX

17. H.Avakian, HEDT July 1 17 D.S.Hwang (JLab-07) Flavor Decomposition Use double spin asymmetries for different targets and final state particles to extract the helicity distributions for different flavors Sum over quark flavors Extraction of k T -dependent distributions q+ (f 1 +g 1 ) and q- (f 1 -g 1 ) will require unfolding of spin independent and spin dependent contributions Jakob, Mulders, Rodrigues, Nucl. Phys. A 1997 A.Bacchetta (JLab-07)

18. H.Avakian, HEDT July 1 18 A LL -P T -dependence P T -dependence of double spin asymmetries provide access to difference in k T -distributions of quarks with spin orientations along and opposite to the proton spin. hep-ph/0608048  0 2 =0.25GeV 2  D 2 =0.2GeV 2 proton deuteron

19. H.Avakian, HEDT July 1 19 SIDIS (  *p →  X): LL x-section subleading moment Azimuthal asymmetry most sensitive to the difference of widths in polarized and unpolarized distributions. data from proton and deutron provides a complete set required for the flavor dependence studies proton deuteron

20. H.Avakian, HEDT July 1 20 Collins fragmentation: Longitudinally polarized target  UL ~ KM curves,  QSM from Efremov et al Kotzinian-Mulders Asymmetry KM sin2  moment, sensitive to spin-orbit correlations: the only leading twist azimuthal moment for longitudinally polarized target More info will be available from SIDIS (COMPASS,EIC) and DY (RHIC,GSI) Transversely polarized quarks in the long. polarized nucleon

21. H.Avakian, HEDT July 1 21 Collins Effect  UT ~ Collins Study the Collins fragmentation for all 3 pions with a transversely polarized target and measure the transversity distribution function.

22. H.Avakian, HEDT July 1 22 Collins Effect: from asymmetries to distributions Extraction of transverse spin distributions from CLAS12 assuming a simple model for Collins fragmentation for the favored case. need

23. H.Avakian, HEDT July 1 23 Sivers effect  UT ~ Sivers Requires: non-trivial phase from the FSI + interference between different helicity states Significant effect predicted in the target fragmentation region, in particular for baryons (target remnant also asymmetric)

24. H.Avakian, HEDT July 1 24  polarization in the target fragmentation Semi-inclusive and exclusive Lambda production in the target fragmentation region provide access to underlying PDFs with CLAS12 p e Λ 1 2 e’ Accessing polarized and strange PDFs with unpolarized target ! (no gluons) W.Melnitchouk and A.W.Thomas ‘96 J.Ellis, D.Kharzeev, A. Kotzinian ‘96  – unique tool for polarization study due to self-analyzing parity violating decay

25. H.Avakian, HEDT July 1 25 Higher Twist SSAs and Quark-Gluon Correlations Target sin  SSA Beam sin  SSA Discussed as main sources of SSA due to the Collins fragmentation In jet SIDIS only contributions ~ D 1 (Sivers type) survive With H 1 ┴ (  0 )≈0 (or measured) Target and Beam SSA can be a valuable source of info on HT T-odd distribution functions Transversely polarized quarks ( et al. 0405154)

26. H.Avakian, HEDT July 1 26 Non-perturbative TMD Perturbative region  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) In the perturbative limit 1/P T behavior expected Asymmetries from k T -odd (g ┴,h 1 ┴ ) and k T -even (g 1 ) distribution functions are expected to have a very different behavior. 2.0 Beam SSA: CLAS @ 12 GeV

27. H.Avakian, HEDT July 1 27 Hard Scattering Processes: Kinematics Coverage Study of high x B domain requires high luminosity 27 GeV compass hermes JLab ( upgraded ) JLab@6GeV Q2Q2 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 HERA

28. H.Avakian, HEDT July 1 28 Nonperturbative TMDPerturbative region Boer-Mulders Asymmetry with EIC CLAS12 and EIC studies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations. Transversely polarized quarks in the unpolarized nucleon - CLAS12 EIC ep 5-7 GeV50-150 GeV sin(  C ) =cos(2  h )

29. H.Avakian, HEDT July 1 29 GPDs and spatial distributions Transverse position distribution Transverse position shift Large x contributions important.      1 1 )0,, q(q()0,, q(q( 2 1 xE xHxdx J q X. Ji, Phy.Rev.Lett.78,610(1997) Both Lattice and GPD model calculations confirm large sideways shift due to spin-orbit correlations!

30. H.Avakian, HEDT July 1 30 Deeply Virtual Compton Scattering ep→e’p’  GPD combinations accessible as azimuthal moments of the total cross section. DVCS BH  LU  ~ sin  {F 1 H( , t) +  (F 1 +F 2 ) H +kF 2 E } ~ Polarized beam, unpolarized target: Unpolarized beam, longitudinal target:  UL  ~ sin  {F 1 H +  (F 1 +F 2 )( H +.. } ~ Unpolarized beam, transverse target:  UT  ~ sin  {k(F 2 H – F 1 E ) + ….  }  = x B /(2-x B ),k = t/4M2 Kinematically suppressed

31. H.Avakian, HEDT July 1 31 GPDs H from expected DVCS asymmetries Precision measurements of DVCS asymmetries with unpolarized and longitudinally polarized targets would allow to pin down spatial distributions of quarks FT Spatial distribution of quarks changes with momentum x CLAS12 (2000h) GPD-H

32. H.Avakian, HEDT July 1 32 CLAS12 - Exclusive Target Asymmetries  Asymmetry for photons and rho highly sensitive to the u-quark contributions to proton spin. Transversely polarized target e p ep   ~ GPD- E ~ J u E = 11 GeV ep  ep  CLAS12

33. H.Avakian, HEDT July 1 33 We recommend the completion of the 12 GeV Upgrade at Jefferson Lab. The Upgrade will enable new insights into the structure of the nucleon, the transition between the hadronic and quark/gluon descriptions of nuclei, and the nature of confinement. We recommend the construction of the Facility for Rare Isotope Beams, FRIB, a world-leading facility for the study of nuclear structure, reactions and astrophysics. Experiments with the new isotopes produced at FRIB will lead to a comprehensive description of nuclei, elucidate the origin of the elements in the cosmos, provide an understanding of matter in the crust of neutron stars, and establish the scientific foundation for innovative applications of nuclear science to society. We recommend a targeted program of experiments to investigate neutrino properties and fundamental symmetries. These experiments aim to discover the nature of the neutrino, yet unseen violations of time-reversal symmetry, and other key ingredients of the new standard model of fundamental interactions. Construction of a Deep Underground Science and Engineering Laboratory is vital to US leadership in core aspects of this initiative. The experiments at the Relativistic Heavy Ion Collider have discovered a new state of matter at extreme temperature and density—a quark-gluon plasma that exhibits unexpected, almost perfect liquid dynamical behavior. We recommend implementation of the RHIC II luminosity upgrade, together with detector improvements, to determine the properties of this new state of matter. NSAC Long-Range Plan Recommendations We recommend the completion of the 12 GeV Upgrade at Jefferson Lab. The Upgrade will enable new insights into the structure of the nucleon, the transition between the hadronic and quark/gluon descriptions of nuclei, and the nature of confinement.  JLab12: Measurements related to the spin, spin orbit correlations and orbital angular momentum of the quarks combined with HERMES,COMPASS, RHIC,BELLE,JPARC,GSI data will help construct a more complete picture about the spin structure of the nucleon beyond the collinear approximation BNL JPARC Summary

34. H.Avakian, HEDT July 1 34 Support slides….

35. H.Avakian, HEDT July 1 35 JLab@12GeV: Inclusive DIS BBS/LSS no OAM PDF measurements at large x provide additional information on OAM BBS/LSS with OAM

36. H.Avakian, HEDT July 1 36 Form Factor Studies G E (t)=F 1 (t)+t/4M 2 *F 2 (t) G M (t)=F 1 (t)+F 2 (t) ~9 0% Sachs Form Factors More data expected in 2007 A.Afanasev hep-ph/9910565 Diehl et al, Eur.Phys.J c39 (2005) M.Guidal et al PRD (2005) Issues: different realistic fits to FFs produce different values for Lq fits done at high t, need to be extrapolated to t→0

37. H.Avakian, HEDT July 1 37 Non-perturbative TMDPerturbative region Collins asymmetry & Boer-Mulders Effect BM cos2  moment, sensitive to spin-orbit correlations: the only leading twist azimuthal moment for unpolarized target P T -dependence of BM asymmetry allows studies of transition from non-perturbative to perturbative description (Unified theory by Ji et al). SIDIS (HERMES,COMPASS,CLAS,ZEUS,EIC) and DY (RHIC,GSI,JPARC) In the perturbative limit 1/P T 2 behavior expected (F.Yuan) CLAS12 4<Q 2 <5 (2000h @ 11 GeV with 10 35 sec -1 cm -2 ) quark-scalar diquark model (L.Gamberg) - s T (p×k T )↔ h 1 ┴ sin(  C ) =cos(2  h ) Transversely polarized quarks in the unpolarized nucleon

38. H.Avakian, HEDT July 1 38 Spin-Azimuthal Asymmetries Significant progress made recently in studies of Single-Spin Azimuthal Asymmetries (SSA) with longitudinally and transversely polarized targets in in electroproduction (HERMES, SMC,COMPASS, and CLAS), pp scattering (RHIC), and e+e- (BELLE).  SSA are sensitive to the orbital momentum of quarks, enable measurements of GPDs and k T -dependend PDFs (TMDs)  provide a window to the physics of partonic final and initial state interactions  model calculations indicate that SSA are not affected significantly by a wide range of corrections.  Good agreement in SSAs measured in a wide energy range in electroproduction and pp scattering. Spin asymmetries + azimuthal dependence → new class of measurements Spin-Azimuthal Asymmetries:

39. H.Avakian, HEDT July 1 39 SIDIS (  *p →  X): LL x-section at leading twist  Factorization of k T -dependent PDFs proven at low P T of hadrons (Ji et al) Collins effect measurement with longitudinally pol. target provide access to the chiral- odd Mulders distribution functions and probes the polarized fragmentation function TMD PDFs Correlation between the transverse momentum and transverse spin of quarks in longitudinally polarized proton First discussed by Kotzinian & Mulders -

40. H.Avakian, HEDT July 1 40 SIDIS (  *p →  X): UU x-section at leading twist  Factorization of k T -dependent PDFs proven at low P T of hadrons (Ji et al) Collins effect measurement with unpolarized target provide access to the chiral-odd Boer-Mulders distribution functions and probes the polarized fragmentation function TMD PDFs - Correlation between the transverse momentum and transverse spin of quarks First introduced in 1998 by Boer & Mulders Collins effect

41. H.Avakian, HEDT July 1 41 Λ production p ee’ Λ π 1 2 (ud)-diquark is a spin and isospin singlet s-quark carries whole spin of  K,K * 6 K+K+ K* + CLAS 5.7 GeV  – unique tool for polarization study due to self-analyzing parity violating decay Wide kinematic coverage of CLAS12 allows studies of hadronization in the target fragmentation region

42. H.Avakian, HEDT July 1 42 GPDs and spatial distributions Transverse position distribution Transverse position shift Shift in the transverse space of quarks in the transversely polarized proton first predicted in GPD framework, confirmed by Lattice Large x contributions important.      1 1 )0,, q(q()0,, q(q( 2 1 xE xHxdx J q X. Ji, Phy.Rev.Lett.78,610(1997) Spin of the quark ( Diehl,Haegler 2005 )

43. H.Avakian, HEDT July 1 43 Sivers effect in the target fragmentation Significant effect predicted in the target fragmentation region, in particular for baryons (target remnant also asymmetric) A.Kotzinian CLAS12 will allow studies of kinematic dependences of the Sivers effect in the target fragmentation region x F - momentum in the CM frame

44. H.Avakian, HEDT July 1 44 The DIS data from EMC (1987) and Fermilab (1993) are most consistent with intrinsic parton transverse momentum squared, of ~ 0.25 GeV 2 Azimuthal Asymmetries in SIDIS Higher twists (Berger 1980, Brandenburg & Muller 1995) Dominating at small P T Dominates in perturbative limit Positive contribution, significant at large z Gluon bremsstrahlung (Georgi & Politzer, Mendez 1978) at z→1 Intrinsic transverse momentum of partons (Cahn 1978)

45. H.Avakian, HEDT July 1 45 Both Lattice and GPD model calculations confirm large sideways shift due to spin-orbit correlations! Shifts in transverse space distributions for different quark and nucleon polarizations may be responsible for observed SSAs (M.Burkardt 2000) Quark distributions in the transverse space Unpolarized quarks in unpolarized nucleon ( Diehl,Haegler 2005 ) Spin of the proton Spin of the quark Unpolarized quarks in the transversely polarized nucleon Transversely polarized quarks in the unpolarized nucleon

46. H.Avakian, HEDT July 1 46 Drell-Yan @GSI DY with fixed target Study the p T dependence of the DY  -BW width of quark virtuality (  → only intrinsic k T ) M=4GeV

47. H.Avakian, HEDT July 1 47 Drell Yan @GSI spin-transfer from polarized electrons of the target to antiprotons GSI: M 2 ~10 GeV 2, s~30-50 GeV 2,  =x 1 x 2 =M 2 /s~0.2-0.3  exploration of valence quarks (h 1 q (x,Q 2 ) large) RHIC:  =x 1 x 2 =M 2 /s~10 -3  exploration of the sea quark A TT very small (~ 1 %) T=22 GeV (  s=6.7 GeV) T=15 GeV (  s=5.7 GeV) Anselmino et al. PLB 594,97 (2004) x F =x 1 -x 2

48. H.Avakian, HEDT July 1 48 SIDIS (  *p→  X) cross section at leading twist (Ji et al.) structure functions = pdf × fragm × hard × soft (all universal) e Unpolarized target Longitudinally pol. target Transversely pol. target e e p p Boer-Mulders 1998 Kotzinian-Mulders 1996 Collins-1993 To observe the transverse polarization of quarks in SIDIS spin dependent fragmentation is required! Do we understand well the helicity distributions?

49. H.Avakian, HEDT July 1 49 JLab at 12 GeV High luminosity polarised beam Complementarity of high luminosity and wide geometric acceptance halls Wide physics acceptance (exclusive, semi- inclusive current and target fragmentation)  JLab12: Measurements related to the spin, spin orbit correlations and orbital angular momentum of the quarks combined with COMPASS, RHIC,BELLE data will help construct a more complete picture about the spin structure of the nucleon beyond the collinear approximation

50. H.Avakian, HEDT July 1 50 Quark helicity distributions: simple model Quarks have spin, which can be aligned or anti aligned with proton spin On- On-shell quarks with longitudinal momentum 1-x Leading-order diagram contributing to parton distribution at large x

51. H.Avakian, HEDT July 1 51 Perturbative limit On- On-shell quark with longitudinal momentum 1-x As As x->1, the virtuality of these lines goes to infinity Leading-order diagram contributing to parton distribution at large x Farrar & Jackson All propagators are far off-shell: / k ? 2 /(1-x) À  QCD 2 X X X X Spectator power counting (more partons, more suppression)

52. H.Avakian, HEDT July 1 52 The Large-x (x →1) Behavior of the PDFs Brodsky & Yuan, hep-ph/0610236. Large-x behavior of PDFs used in phenomenology k ┴ -odd Survive k ┴ integration T-even T-odd X X X X X X X X Eight propagators (1-x) 8, (1-x) -4 from the scattering, (1-x) -1 from the phase space integral ~(1-x) 3

53. H.Avakian, HEDT July 1 53 The Large-x (x →1) Behavior of the PDFs Brodsky & Yuan, hep-ph/0610236. Large-x behavior of PDFs used in phenomenology k ┴ -odd Survive k ┴ integration T-even T-odd X X X X X X X X Eight propagators (1-x) 8, (1-x) -4 from the scattering, (1-x) -1 from the phase space integral ~(1-x) 3

54. H.Avakian, HEDT July 1 54 The Large-Nc Behavior of the PDFs Use the large Nc limit of QCD to study TMD PDFs qg interaction constant In color singlet Feynman diagrams every vertex loop Introduced by ‘t Hooft in1974 isospin Nc-power P.Pobylitsa hep-ph/0301236

55. H.Avakian, HEDT July 1 55 The Large-Nc limit of QCD to study TMD PDFs  3 – isospin Pauli matrice t 1,t 2 – isospin projection of quark fields (  3 ) uu =1, (  3 ) dd =-1 Change sign from + (SIDIS) to – (DY) Nucleon mass M=O(Nc) Large-Nc approach predicts signs and relative Nc power of TMDs, used in phenomenology.  3 – nucleon isospin P.Pobylitsa hep-ph/0301236 Do not change sign (isoscalar) All others change sign u→d (isovector) Introduced by ‘t Hooft in1974 qg interaction constant In color singlet Feynman diagrams every vertex loop

56. H.Avakian, HEDT July 1 56 SIDIS (  *p→  X) cross section: Unpolarized target e Unpolarized target Study the transverse polarization of quarks in the unpolarized nucleon. cos2  (Boer-Mulders function h 1 ┴ ) and sin  g┴) azimuthal moments of the x- section as a function of x, Q 2, P T, z cos  cos2  azimuthal moments and Cahn and Berger effects Transition from non-perturbative to perturbative description at large P T Target fragmentation (Lambda, azimuthal moments) at leading twist

57. H.Avakian, HEDT July 1 57 SIDIS (  *p→  X) cross section: polarized target Study spin orbit correlations in the longitudinally polarized nucleon. sin2  (Mulders function h 1L ┴ ) and sin   f L ┴) azimuthal moments of the x-section as a function of x, Q 2, P T, z A 1 and flavor decomposition (g 1 ), P T -dependence of A 1 and k T -helicity dependences Target fragmentation (Lambda, azimuthal moments) at leading twist Longitudinally pol. target ep

58. H.Avakian, HEDT July 1 58 SIDIS (  *p→  X) cross section: polarized target Study the transverse polarization of quarks in the Transversely polarized nucleon. sin  S (Sivers, f 1T ┴), sin  S (transversity, h 1 ) and cos  S  g 1T ) azimuthal moments of the x-section as a function of x,Q 2,P T,z 2 pion SSA (h 1 ) Target fragmentation (Lambda, azimuthal moments) at leading twist Transversely pol. target p

59. H.Avakian, HEDT July 1 59 Comparing Boer-Mulders Functions from Models (a)MIT bag model: F. Yuan, Phys. Lett. B575,45(2003). (b)Spectator model with axial-vector diquark: Bacchetta, Schaefer & Yang, Phys. Lett. B578,109(2004). (c)Large-N C limit, P.V. Pobylitsa, hep-ph/0301236 Knowledge of the Boer-Mulders functions is very poor.

60. H.Avakian, HEDT July 1 60 GSIM12 Events for exclusive  + production on proton (ep→e’  +n) Typical event

61. H.Avakian, HEDT July 1 61 p ┴ = P T – z k ┴ + O(k ┴ 2 /Q 2 ) k T -dependent SIDIS data fit on Cahn effect → =0.25GeV 2 EMC (1987) and Fermilab (1993) data (assuming  0 u =  0 d ) Anselmino et al Negative cos  moment from internal k T effects Not trivial flavor dependence (  0 u and  0 d ) of transverse momentum distributions of quarks

62. H.Avakian, HEDT July 1 62 SIDIS (  *p→  X) cross section at leading twist (Ji et al.) structure functions = pdf × fragm × hard × soft (all universal) e Unpolarized target Longitudinally pol. target Transversely pol. target e e p p Boer-Mulders 1998 Kotzinian-Mulders 1996 Collins-1993 To observe the transverse polarization of quarks in SIDIS spin dependent fragmentation is required! Do we understand well the helicity distributions?

63. H.Avakian, HEDT July 1 63 Contributions to  in Double Polarized SIDIS TMDs Mulders et al A 1 ~ A UL ~ A UT ~ Sivers Collins KM

64. H.Avakian, HEDT July 1 64 Power counting at large-x Eight propagators (1-x) 8, (1-x) -4 from the scattering, (1-x) -1 from the phase space integral –(1-x) 3 Spectator two quarks with spin-1 configuration will be suppressed by (1-x) 2 relative to spin-0 –q - » (1-x) 2 q + q+»q+» q-»q-» Spin-0Spin-1

65. H.Avakian, HEDT July 1 65 Quark helicity distributions: simple model Quarks have spin, which can be aligned or anti aligned with proton spin

66. H.Avakian, HEDT July 1 66 Power counting at large-x (1-x) -1 from the phase space +

67. H.Avakian, HEDT July 1 67 Azimuthal Asymmetries in SIDIS Due to color coherence the configuration with gluon inside the quark cone is more probable Why < 0 ? Chay,Ellis,Stirling-1991   x  =180  =0

68. H.Avakian, HEDT July 1 68 HT and Semi-Exclusive Pion Production E. Berger, S. Brodsky 1979 (DY), E.Berger 1980, A.Brandenburg, V. Khoze, D. Muller 1995 A.Afanasev, C.Carlson, C. Wahlquist Phys.Lett.B398:393-399,1997 ++ Fragmentation  + 00 Azimuthal asymmetries with opposite sign from HT effects Effect may be suppressed for semi-exclusive  0 compared to  +/-

69. H.Avakian, HEDT July 1 69 HT and Semi-Exclusive Pion Production E. Berger, S. Brodsky 1979 (DY), E.Berger 1980, A.Brandenburg, V. Khoze, D. Muller 1995 A.Afanasev, C.Carlson, C. Wahlquist Phys.Lett.B398:393-399,1997 ++ Fragmentation  + 00 Azimuthal asymmetries with opposite sign from HT effects Effect may be suppressed for semi-exclusive  0 compared to  +/-