1. 1 Hard scattering processes: Experiment N.C.R. Makins *) University of Illinois at Urbana-Champaign *) in collaboration with H. Avakian SIR Workshop – Jefferson Lab, May 17-20, 2005 Introduction Semi-inclusive spin and azimuthal asymmetries and TMD distributions Hard exclusive processes and GPDs Conclusions

2. 2 Physics Motivation Parton Distribution Functions generalized to contain information not only on longitudinal, but also on the transverse distribution of partons:  Generalized Parton Distributions (GPD) H, E...  Transverse-momentum dependent (TMD) parton distributions Orbital Angular Momentum (OAM) in the focus. Transverse momentum of quarks is a key to OAM. Complementary sets of non-perturbative functions sensitive to different aspects of transverse distributions

3. 3 PDFs f p u (x,k T ), g 1, h 1 FFs F 1p u (t),F 2p u (t).. TMD PDFs: f p u (x,k T ),g 1,f ┴ 1T, h 1,h ┴ 1L d2kTd2kT  =0,t=0 dx W p u (x,k,r) “Parent” Wigner distributions d3rd3r d2kTd2kT (FT) GPDs: H p u (x, ,t), E p u (x, ,t), H,E,… GPD Measure momentum transfer to quark k T distributions also important for exclusive studies Measure momentum transfer to target Exclusive meson data important in understanding of SIDIS measurements Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k Some PDFs same in exclusive and semi-inclusive analysis Analysis of SIDIS and DVMP are complementary TMD ~

4. 4 SIDIS kinematic plane and relevant variables

5. 5 Quark Polarization from Semi-Inclusive DIS (SIDIS) In SIDIS, a hadron h is detected in coincidence with the scattered lepton: Flavor Tagging: Flavor content of observed hadron h is related to flavor of struck quark q via the fragmentation functions D(z) Favored / disfavored fragmentation functions: scaling variable

6. 6 Final Δq Measurement from HERMES First 5-flavor fit to Δq(x) No evidence of anti-quark polarization, or flavor-asymmetry,  s≈0 using all polarized data taken from 1996 - 2000 more in talks by Zhu, Christova Sensitive to factorization

7. A 1 p -kinematic dependence for  +/-/0 CLAS 5.7 GeV A1pA1p No significant z-dependence of A 1 in the range 0.3<z<0.7 x dependence of CLAS A 1 p (A ┴ =0) consistent with HERMES data at 3 times higher Q 2 and with LUND-MC (lines). CLAS PRELIMINARY HERMES

8. 8 SIDIS: factorization studies A 1 inclusive, from      sum and   are consistent (in range 0.4<z<0.7 ) A 1 p dependence can serve an important check of HT effects and applicability of simple partonic description. There is an indication that  A 1 p of   +    is lower than inclusive at large z. GRVS A1+-A1+- more in talk by P.Bosted

9. 9  0 in Semi-inclusive DIS as a test? 1)SIDIS  0 production is not contaminated by diffractive  2)HT effects and exclusive  0 suppressed 3)Simple PID by  0 -mass (no Kaon contamination) 4)Provides complementary to  +/- information on PDFs advantages:

10. 10 Distribution FunctionsFragmentation Functions Mulders & Tangerman, NPB 461 (1996) 197 Functions surviving on integration over Transverse Momentum The others are sensitive to intrinsic k T in the nucleon & in the fragmentation process Sivers PDF require FSI, vanish if quarks only in s-state! One T-odd function required to produce single-spin asymmetries in SIDIS transversity Sivers Collins

11. 11 Asymmmetry shows similar rise with x F as observed at E704 Sivers effect only can explain the data Analyzing power for π 0 confirmed at STAR at much higher energies

12. 12 Evidence of non 0 Collins effect First info on P T distribution undefined  contribution Collins Effect A UT ~ Collins more details in talk by G. Schnell

13. 13 Sivers effect A UT ~ Sivers Evidence of non 0 Sivers effect For  + consistent with increase with x,z,P T undefined  contribution

14. 14 No sizeable effect. Possible cancellations in isoscalar target (6LiD) undefined  contribution Collins and Sivers Effects at COMPASS A UT Collins more details in talk by A.Bressan A UT Sivers

15. 15 ‘SSA from HERMES/COMPASS‘  check for consistency ‘‘Sivers function‘‘: hep-ph/0501196 HERMES COMPASS consistent more in A. Kotzinian’s talk

16. 16 Collins Effect and Kotzinian-Mulders Asymmetry Independent study the Collins fragmentation with longitudinally polarized target. Measure the twist-2 Mulders TMD (transversely pol. quarks in a longitudinally pol. proton)  UL ~ KM Real part of interfe-rence of wave functions with L=0 and L=1 more in P.Bosted’s talk undefined  contribution Efremov,Schweitzer (  QSM )

17. 17 Beam SSA: A LU “Collins” effect by Schweitzer et al. using e(x) “Sivers ” effect Afanasev & Carlson, Metz & Schlegel  sin  LU ’ ~ 1/Q (Twist-3) “Sivers” effect by F.Yuan using h 1 ┴ more details in E.Avetisyan’s talk

18. 18      e-e- e+e+ Collins Function In SIDIS Collins function always coupled with some(unknown) distribution function In e+e- only the Collins FF appears! 2-h inclusive transverse momentum dependent Xsection:

19. 19 Collins Function First direct measurement of the non 0 Collins function Rising behaviour vs. z more details in talk by A.Ogawa

20. 20 Transversity in double pion production h1h1 h2h2 quark RTRT “Collinear” dihadron fragmentation described by two functions at leading twist: D 1 (z,cos  R,M  ),H 1 R (z,cos  R,M  ) No transverse momentum of the pair center of mass! The angular distribution of two hadrons is sensitive to the spin of the quark The relative transverse momentum of the two hadrons replaces the P T in single-pion production

21. 21 2  transvers spin SSA Positive asymmetry observed for all invariant mass bins for proton No evidence for a sign flip at the  -mass (Jaffe et al.) more details in talk by Kobayashi

22. 22 2  transvers spin SSA Asymmetry vs M inv, x, z consistent with 0. Runs using p-target (NH 3 )

23. 23 Is the Sivers function “friend” of transversity? In the polarized proton u quarks are shifted (~ 0.4 fm defined by anomalous magnetic moment of proton) down and d quark up, giving rise to left-right asymmetries transversely polarized target b - Impact parameter shift defined by anomalous magnetic moment of proton (M.Burkardt) quark flavor polarization lead to SSA Or the “relative” of GPD E T

24. 24 Sivers effect in the target fragmentation x F <0 (target fragmentation) x F >0 (current fragmentation) x F - momentum in the CM frame Wide kinematic coverage required for studies of hadronization in the target fragmentation region more details in A.Kotzinian’s talk

25. 25 Deeply Virtual Compton Scattering ep->e’p’  GPD combinations accessible as azimuthal moments of the total cross section. DVCS BH  LU  ~ sin  Im{F 1 H +  (F 1 +F 2 ) H +kF 2 E } ~ Polarized beam, unpolarized target: Unpolarized beam, longitudinal target:  UL  ~ sin  Im{F 1 H +  (F 1 +F 2 )( H +.. } ~ Unpolarized beam, transverse target:  UT  ~ sin  Im{k(F 2 H – F 1 E ) + ….  }  = x B /(2-x B ),k = t/4M2 Kinematically suppressed

26. 26 Pioneering DVCS Experiments  sin  +  sin2  CLAS at 4.3 GeVHERMES 27 GeV SSA flips the sign from e+ to e-

27. 27 DVCS SSA: CLAS 5.7 GeV  Higher energy increases kinematics range.  Higher statistics allows binning of A LU in Q 2, t, x B  More data available from ongoing experiments 0.15<x<0.4 1.50 <Q 2 < 4.5 GeV 2 -t<0.5 more details in talk by M.Garcon VGG

28. 28 DVCS measurements at HERMES Beam Charge Asymmetry Longitudinal Target Spin Asymmetry  C ~ cos  Re H With increased statistic asymmetries may constrain GPD models  ~sin  Im{F 1 H +  (F 1 +F 2 ) H... } ~ More in talk by F. Ellinghause

29. 29 Exclusive meson production Asymmetry depends linearly on the GPD E, which enters Ji’s sum rule. K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 Provide access to different combinations of GPD E and orbital momentum contributions J u,J d   -> 2E u + E d    -> E u - E d Different final state mesons filter out different combinations of unpolarized (H,E) and polarized (H,E) GPDs.   production on transverse target Studies needed to define on how far is the asymptotic regime and guide theory in describing HT. ~ GPD

30. Measurement of 3D PDFs require global analysis of SSAs for exclusive and semi-inclusive final states measured in a wide range of kinematics at different facilities. h1 The new data are just the first trickle of a great wealth of upcoming information on 3D PDFs Conclusions

31. 31 Questions to address in SIDIS How do we test the factorization and quantify its breakdown Do we need the global analysis of exclusive and semi- inclusive processes? How small the HT should be, to be interesting to measure? What is the contribution to pion SIDIS observables from exclusive vector mesons What we learn from P T -dependence of observables What we learn from target fragmentation (x F <0) studies

32. 32 pion SSA from           + SSA at large z may also have a significant (~20%) contribution from    PYTHIA at 5.7 GeV (CLAS @5.7GeV) Larger fraction of  + from  at low x and large z Exclusive   higher twist for SIDIS ) crucial for  X and  X studies

33. 33 Transversity Simple string fragmentation (Artru model) Sub-leading pion opposite to leading (into page) L=1  production may produce an opposite sign A UT Leading  opposite to leading  (into page) Better understanding of 2 pion asymmetries will help to understand transvers spin SSA mesurements 

34. 34 Nonperturbative TMD Perturbative region P T -dependence of beam SSA  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) In the perturbative limit 1/P T behavior expected Asymmetries from k T -odd and k T -even (g 1 ) distribution functions are expected to have a very different behavior (flat A 1 p (P T ) observed at 5.7 GeV).

35. 35 SSA: P T -dependence of sin  moment  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) CLAS @4.3 GeV Beam and target SSA for  + (not sensitive to MX-cut) are consistent with increase with P T CLAS @5.7 GeV

36. 36 SIDIS: target and current fragmentation x F <0 (target fragmentation, TFR) x F >0 (current fragmentation) x F - momentum in the CM frame Wide kinematic coverage of CLAS allows studies of hadronization in the target fragmentation region – probability of finding a parton q with momentum fraction x and a hadron h with energy fraction z in the proton (Trentadue & Veneziano).

37. 37 Beam SSA A LU at 6GeV W 2 >4GeV 2, Q 2 >1.5GeV 2 CLAS PRELIMINARY Beam SSA and Longitudinally pol. Target SSA provide information on HT ( 0 at leading order) - Target SSA at 27.5 GeV HERMES SSA in exclusive pion production

38. 38 Exclusive  measurements CLAS at 4.3 GeV W>1.75GeV HERMES at 27.5 GeV W>2GeV Decent description in pQCD framework already at moderate Q 2 GPDs(VGG) Regge

39. 39 Exclusive  + production Exclusive  +n separated by invariant and missing masses. n ++ e - p  e - n  + π+π0π+π0 Provide access to different combinations of orbital momentum contributions J u,J d   -> 2J u + J d    -> J u - J d  2J u - J d Significant transverse target SSA predicted for exclusive     ( Goeke et al hep-ph/0106012 ) CLAS 5.7 GeV

40. 40 Measuring the Q 2 dependence of SSA  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) Wide kinematic coverage allows to check the higher twist nature of beam and longitudinal target SSAs For fixed x, 1/Q behavior expected