1. 1 Harut Avakian Jefferson Lab Studies of transverse spin effects at JLab Transversity 2005, Como, September 7-10, 2005 * In collaboration with P.Bosted, V.Burkert and L.Elouadrhiri

2. 2 Outline  Physics motivation  SIDIS studies at 6 GeV  Factorization tests  Spin azimuthal asymmetries  Future plans  Summary

3. 3 h Single pion production in hard scattering Target fragmentationCurrent fragmentation Fracture Functions xFxF M 0 1 h h PDF GPD k T -dependent PDFsGeneralized PDFs Wide kinematic coverage of large acceptance detectors allows studies of hadronization both in the target and current fragmentation regions x F - momentum in the CM frame x F >0 (current fragmentation) PDF h x F <0 (target fragmentation) h

4. 4 Polarized Semi-Inclusive DIS Cross section is a function of scale variables x,y,z Parton-Hadron transition: by fragmentation function D  +(  ( z ): probability for a u-quark to produce a  + (  - ) with momentum fraction z Hadron-Parton transition: by distribution function f 1 u ( x ): probability to find a u-quark with a momentum fraction x 1u  = E-E’ y = /E x = Q 2 /2M z = E h / z

5. 5 Transverse momentum of quarks To study orbital motion of quarks in semi-inclusive DIS measurements in a wide range of x,z,P T,  are required. k T – led to introduction of k T dependent PDFs (TMDs) k T – crucial for orbital momentum and spin structure studies –led to SSA in hard scattering processes k T - important for cross section description - P T distributions of hadrons in DIS - exclusive photon production (DVCS) - hard exclusive vector meson cross section - pp →  0 X (E704,RHIC) cross sections Spin-Azimuthal Asymmetries: sensitive to k T

6. 6 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 Off diagonal PDFs related to interference between L=0 and L=1 light-cone wave functions. Boer-Mulders 1998 Kotzinian-Mulders 1996 Collins-1993 To observe the transverse polarization of quarks in SIDIS spin dependent fragmentation is required!

7. 7 Collins Effect: azimuthal modulation of the fragmentation function D(z,P T )=D 1 (z,P T )+H 1 ┴(z,P T ) sin(  h  S’ ) spin of quark flips wrt y-axis  S’ =  -  S sin(  h  S ) CC SS STST y x hh PTPT sTsT  S’ CC F UT ∞h 1 H 1 ┴  S’ =  -  S =  -  h SS y x hh PTPT sTsT  S’ CC s T (p×k T )↔ h 1 ┴ F UU ∞h 1 ┴ H 1 ┴  S =  +  h s T (q×P T )↔ H 1 ┴ sin(2  h )  S’ =  -  S =  -  h x CC sin(2  h ) sTsT PTPT hh CC S=hS=h y F UL ∞h 1L H 1 ┴ ┴ (s T k T )(pS L )↔ h 1L ┴ sin  C =sin(  h  S’ ) cos(2  h )

8. 8 Schafer-Teryaev sum rule Precise measurement of Collins asymmetries for different hadrons (  0,  + +  - ) would allow to test the Schafer-Teryaev sum rule

9. 9 High efficiency reconstruction of  0  +  opens a new avenue in SIDIS (HMP) 1)SIDIS  0 production is not contaminated by diffractive   0 SSA sensitive to the unfavored polarized fragmentation 3)HT effects and exclusive  0 suppressed 4)Simple PID by  0 -mass (no kaon contamination) 5)Provides information complementary to  +/- information on PDFs SIDIS with neutral pions

10. 10 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 HT effects and exclusive  0 suppressed

11. 11 Experimental Setup (CLAS+IC) Inner Calorimeter (424 PbWO 4 crystals) for the detection of high energy photons at forward lab angles (increases  0 acceptance ~3 times at z~0.5). Polarized target 13 o 50 o  solid NH 3 polarized target  proton polarization >75%  high lumi ~ 1.5  10 34 s -1 cm -2 IC

12. 12 Factorization studies with pions Double spin asymmetries consistent with simple partonic picture A 1 p inclusive and   (~30 times more data expected) an serve as an important check of HT effects and applicability of the simple partonic description. LUND-MC CLAS PRELIMINARY A1A1 60 days of CLAS+IC (L=1.5.10 34 cm -2 s -1 )

13. 13  Unpolarized Semi-inclusive electroproduction of  + measured.  Complete 5-dimensional cross sections were extracted.  Direct separation of different structure functions. x=0.28-0.32 z=0.16-0.19 p T =0.41-0.53 GeV Q 2 =2.23-2.66 GeV 2 CLAS Azimuthal asymmetries at CLAS M.Osipenko

14. 14 Significant SSA measured for pions with longitudinally polarized target Complete azimuthal coverage crucial for separation of sin  sin2  moments SSA measurements at CLAS p 1 sin  +p 2 sin2  0.12<x<0.48 Q 2 >1.1 GeV 2 P T <1 GeV ep→e’  X W 2 >4 GeV 2 0.4<z<0.7 M X >1.4 GeV y<0.85 CLAS PRELIMINARY p 1 = 0.059±0.010 p 2 =-0.041±0.010 p 1 =-0.042±0.015 p 2 =-0.052±0.016 p 1 =0.082±0.018 p 2 =0.012±0.019

15. 15 Flavor decomposition of T-odd f┴ With SSA measurements for      and   on neutron and proton (     ) assuming H fav = H u→  + ≈ -H u→  - =- H unfav In jet SIDIS with massless quarks contributions from H 1 ┴ vanish gauge link contribution L With H 1 ┴ (  0 )≈0 (or measured) target and beam HT SSAs can be a valuable source of info on HT T-odd distribution functions

16. 16 Longitudinally polarized target SSA using CLAS+IC Provide measurement of SSA for all 3 pions, extract the Mulders TMD and study Collins fragmentation with longitudinally polarized target Allows also measurements of 2-pion asymmetries H unf =-1.2H fav H unf =-5H fav H unf =0 curves,  QSM from Efremov et al 60 days of CLAS+IC (L=1.5.10 34 cm -2 s -1 )

17. 17 CLAS12 High luminosity polarized (~80%) CW beam Wide physics acceptance (exclusive, semi-inclusive current and target fragmentation) Wide geometric acceptance 12GeV significantly increase the kinematic acceptance (x10 lumi)

18. 18 Collins Effect  UT ~ Collins Study the Collins fragmentation for all 3 pions with a transversely polarized target and measure the transversity distribution function. JLAB12 cover the valence region. SSA in fragmentation Subleading SSA has oppositesign No effect in TFR

19. 19 Sivers effect  UT ~ Sivers Asymmetry in distribution Subleading SSA has same sign Opposite sign effect in TFR Measure the Sivers effect for all 3 pions with a transversely polarized target in a wide kinematic range (TFR & CFR).

20. 20 Sivers function extraction from A UT (  0 ) does not require information on fragmentation function. It is free of HT and diffractive contributions. F 1T =∑ q e q 2 f 1T ┴q A UT (  0 ) on proton and neutron will allow flavor decomposition w/o info on FF. In large Nc limit: f 1T u = -f 1T d Efremov et al (large x B behavior of f 1T from GPD E) CLAS12 projected CLAS12 projected CLAS12: Sivers effect projections

21. 21 Summary  Current data are consistent with a partonic picture, and can be described by a variety of theoretical models.  Significantly higher statistics of JLab, in a wide kinematical range will provide a full set of data needed to constrain relevant distribution (transversity,Sivers,Collins,…) functions.  Experimental investigation of properties of 3D PDFs at JLab, complementary to planed studies at HERMES, COMPASS, RHIC, BELLE, GSI, would serve as an important check of our understanding of nucleon structure in terms of quark and gluon properties.

22. 22 support slides…

23. 23 Higher Twist SSAs Target sin  SSA (Bacchetta et al. 0405154) Beam sin  SSA In jet SIDIS only contributions ~ D 1 survive Discussed as main sources of SSA due to the Collins fragmentation With H 1 ┴ (  0 )≈0 (or measured) Target and Beam SSA can be a valuable source of info on HT T-odd distribution functions

24. 24 SIDIS: factorization studies JLab data at 6GeV are consistent with factorization and partonic description for variety of ratio observables P.Bosted

25. 25 Collinear Fragmentation  quark The only fragmentation function at leading twist for pions in eN→e’  X is D 1 (z) E e =5.7 GeV No significant variation observed in z distributions of  + for different x ranges (0.4 1.5) and for A1p as a function of P T

26. 26 CLAS12: Transversity projections A UT ~ Collins Simultaneous measurement of, exclusive  with a transversely polarized target 10 - 3

27. 27 Study the Collins fragmentation mechanism with long. polarized target For  - and  0 SSA is sensitive to unfavored fragmentation SSA: x-dependence HT–SSA significant for  + and  0 (non-Collins?) A UL (  0 ) ~ H 1 favore +H 1 unfavored PRELIMINARY 5.7 GeV

28. 28 Indicate a negative sin2  moment measured for  +. Some indication of negative   SSA (more data required for  - and  0 ) More data required to correct for exclusive 2  contribution. SSA: kinematical dependence

29. 29 Non-perturbative 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 (F.Yuan SIR-2005) 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). 2.0

30. 30 Exclusive production background from PYTHIA Pions from string (direct) present the lower limit for current fragmentation events Filled (open) symbols represent pions from exclusive (all) vector mesons. electron  0 sample “clean” at large z (non-string pions are mainly from semi-inclusive  +,  )

31. 31 For Collins fragmentation use chirally invariant Manohar-Georgi model (Bacchetta et al) Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H 1 d→  /H 1 u→  ), band correspond to -2.5<R<0  - and  0 SSA will also give access to h 1L d CLAS-5.7GeV First glimpse of Twist-2 TMD h 1L ┴ PRELIMINARY More data required with  - &  0 Exclusive 2 pion background may be important Distribution functions from  QSM from Efremov et al

32. 32 CLAS+Inner Calorimeter (IC) CLAS CLAS+IC Reconstruction efficiency of high energy  0 with IC increases ~ 3 times at large z due to small angle coverage (target in ~60cm from IC) IC  E /E=0.0034/E+0.038/√E+0.022 00

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) Understanding of 2 pion asymmetries will help to understand transversity measurements ++ 00  SIDIS @11 GeV: 2 pions

34. 34 SIDIS: factorization studies A 1 inclusive, from      sum and   are consistent (in range 0.4<z<0.7 ) GRVS HERMES There is an indication that  A 1 p of   +    is lower than inclusive at large z. More data required for 2 pion (  ) final state studies

35. 35 GEANT simulation Angular acceptance for charged tracks for eg1+IC configuration (polarized target at -67 cm from IC) Maximum angle ~50 o Minimum angle ~14 o 13 o 50 o

36. 36 exclusive production background Pions from string present the lower limit for current fragmentation events Fraction of pions from non-diffractive vector mesons adds up to SIDIS sample Fraction of pions from exclusive rho-0(black squares) should have a special treatment

37. 37 exclusive production background Fraction of charged pions from rho-0 especially high for neutron target

38. 38 production background from exclusive events Non string pions are mainly from semi-inclusive rho+

39. 39 SSA: P T -dependence of sin  moment  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) A LU CLAS @4.3 GeV Beam and target SSA for  + are consistent with increase with P T In the perturbative limit is expected to behave as 1/P T A UL (CLAS @5.7 GeV)A UT HERMES @27.5 GeV PRELIMINARY TMDpQCD