1 Harut Avakian Studies on transverse spin effects at Jlab QCD Structure of the Nucleon June 12-16, 2006, Rome Physics motivation k T -effects from unpolarized data TMD-studies from polarized target data Summary

2 Physics Motivation Cross section is a function of scale variables x,y,z = E-E’ y = /E x = Q 2 /2M z = E h / z In 1D world (no orbital motion) quarks polarized if nucleon is polarized, 3PDFs. No azimuthal asymmetries in LO Transverse spin effects are observable as correlations of transverse spin and transverse momentum of quarks.  Describe the complex nucleon structure in terms of quark and gluon degrees of freedom using polarized SIDIS

3 Transverse momentum of quarks k T – crucial for orbital momentum and spin structure studies. k T – lead to 3 dimensional description k T – required to describe azimuthal distributions of hadrons and in particular SSAs. k T - important for cross section description (also for exclusive production) - P T distributions of hadrons in DIS - exclusive photon production (DVCS) - hard exclusive vector meson x-section  Factorization of k T -dependent PDFs proven at low P T of hadrons (Ji et al)  Universality of k T -dependent distribution and fragmentation functions proven (Collins,Mets…) Off diagonal PDFs related to interference between L=0 and L=1 light-cone wave functions. Mulders & Tangerman

4 SIDIS (  *p->  X) x-section at leading twist: The structure functions depend on Q 2, x B, z, P hT Unpolarized target Longitudinally pol. Transversely pol. Studies of PDFs require three experiments f1f1 h ┴ 1T g 1T f ┴ 1T h1h1 h┴1h┴1 g1g1 h ┴ 1L k T -evenk T -odd TMD PDFs T-odd

5 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’ ) x hh PTPT sTsT  S’ CC sin(2  h ) CC Combination of Collins asymmetry measurements with 3 different targets will provide info to separate the chiral-odd distribution functions and measure the Collins function SS STST y A UT ∞h 1 H 1 ┴ SS y x hh PTPT sTsT  S’ CC A UU ∞h 1 ┴ H 1 ┴ sin(  h  S’ )= h 1 ┴ H 1 ┴ cos(2  h ) sTsT PTPT hh CC S=hS=h y A UL ∞h 1L H 1 ┴ ┴ unpolarizedlongitudinally polarizedtransversely polarized Initial quark polarization Scattered quark polarization

6 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 Anselmino et al

7 Azimuthal Asymmetries in SIDIS Intrinsic transverse momentum of partons (Cahn 1978) Higher twists (Berger 1980, Brandenburg et al 1995) Gluon bremsstrahlung (Georgi & Politzer, Mendez 1978) at z→1 All known contributions to and are “flavor blind”

8 Unpolarized target azimuthal asymmetries preliminary Significant cos ,  cos2  observed at large P T at 5.7 GeV New proposal in preparation for JLab PAC to study azimuthal moments at 11 GeV (large Q 2 and P T ) CLAS 5.7 GeV M.Osipenko

9 Tests of partonic picture CTEQ5M PDFs + Binnewies FF X=0.3, Q 2 =2.5 GeV 2, W=2.5 GeV GRSV2000 JLab data consistent with partonic description ( ) E at JLAB

10 Missing mass of pions in ep->e’  X Large Delta(1232) contribution makes  - different (M x >1.5 GeV applied) -- 00 ++ n 00  ++

11 A LL : P T -dependence Expected flat in perturbative limit Difference between neutral and charged pions Data is needed in small bins in x,Q 2,P T,  to measure  0 and  D for polarized and unpolarized targets and probe their variations (Kotzinian et al)  0 u and  0 d  D fav and  D unfav

12 SSA: P T -dependence of sin  moment  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) A LU 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 GeV)A UT GeV PRELIMINARY TMDpQCD

13 Higher Twist SSAs Target sin  SSA (Bacchetta et al ) 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 The same unknown fragmentation function

14 Complete azimuthal coverage crucial for separation of sin  sin2  moments Target 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 No indication of Collins effect for  0 (x20 more data expected )

15 Kotzinian-Mulders asymmetry: new CLAS proposal 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 Prospects with polarized deuteron. H unf =-1.2H fav H unf =-5H fav H unf =0 curves,  QSM from Efremov et al 60 days of CLAS+IC (L= cm -2 s -1 )

16 For Collins fragmentation use fit to HERMES ( Efremov 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 expected for  - &  0 Exclusive 2 pion background may be important Distribution functions from  QSM from Efremov et al

17 Summary  Significant azimuthal moments in pion production in SIDIS were measured at CLAS providing information on transverse momentum distributions of quarks.  Measurement of Collins asymmetries at JLab with unpolarized and polarized targets will provide access to leading twist chirall-odd distribution functions (Boer,Mulders and transversity distributions)  SSA measurements in a wide range of Q 2, would allow studies of higher twist effects and probe T-odd distributions  SSA measurements in a wide range of P T will allow to study the transition from non-perturbative to perturbative description.

18 support slides…

19 Flavor decomposition of T-odd f┴ (g┴, f 1T ┴ ) 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

20 PT-dependence

21 PT-dependence

22 CLAS12: kinematic distributions CLAS12 allow wide kinematical coverage of SIDIS

23 SSA: P T -dependence of sin  moment  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) A LU 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 GeV)A UT GeV PRELIMINARY TMDpQCD

24 Azimuthal Asymmetries in semi-exclusive limit Higher twists (Berger 1980, Brandenburg et al 1995) z→1 dominant contribution u+e- →e-  + d Dominant contribution to meson wave function is the perturbative one gluon exchange and approach is valid at factor ~3 lower Q 2 than in case of hard exclusive scattering (Afanasev & Carlson 1997)

25 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 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

26 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

27 SIDIS (  *p→  X) cross section: Unpolarized target e Unpolarized target Study the transverse polarization of quarks in the unpolarized nucleon. cos  (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

28 SIDIS (  *p→  X) cross section: polarized target Study the transverse polarization of quarks in the longitudinally polarized nucleon. sin  (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 Target fragmentation (Lambda, azimuthal moments) at leading twist Longitudinally pol. target ep

29 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 e p

30 cos2  : predictions V.Barone Projections for CLAS12 in progress.. Significant asymmetry predicted for HERMES Asymmetry is LT! (not decreasing with 1/Q) The only mechanism with sign change from  + to  -

31 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!

32 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 )

33 Higher Twist SSAs Target sin  SSA (Bacchetta et al ) 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 The same unknown fragmentation function

34 CLAS12: kinematic distributions Large Q 2 accessible with CLAS12 are important for cos2  studies

35 Acceptance generated reconstructed Extract acceptance moments from MC

36 Collins Effect and Kotzinian-Mulders Asymmetry Study the Collins fragmentation with longitudinally polarized target. Measure the twist-2 Mulders TMD (real part of interference of L=0 and L=1 wave functions)  UL ~ KM longitudinally polarized target Non-zero asymmetry measured at 5.7 GeV, new proposal will improve erors by a factor ~3 Measurement at 11 GeV will allow extend the Q2 and x range and perform a flavor decomposition of u/d contributions.

37 CLAS12 : Mulders TMD projections Simultaneous measurement of, exclusive  with a longitudinally polarized target important to control the background.  UL ~ KM