1. Studies of OAM at JLAB Introduction Exclusive processes Semi-Inclusive processes Summary Harut Avakian Jefferson Lab UNM/RBRC Workshop on Parton Angular Momentum, NM, Feb 2005 * In collaboration with V.Burkert and L.Elouadrhiri

2. Parton picture: Longitudinal and transverse variables “long before”

3.     J G =  1 1 )0,, q(q()0,, q(q( 2 1 2 1 xE xHxdxJ q X. Ji, Phy.Rev.Lett.78,610(1997) Quark Angular Momentum Sum Rule GPDs H u, H d, E u, E d provide access to total quark contribution to proton angular momentum. ½ = ½ (  u+  d+  s) + L q + J g J q Proton’s spin Large x contributions important.

4. PDFs f p u (x,k T ), g 1, h 1 FFs F 1p u (t),F 2p u (t).. d2kTd2kT  =0,t=0 dx Measure momentum transfer to quark Measure momentum transfer to target Analysis of SIDIS and DVMP are complementary TMD PDFs f p u (x,k T ), GPDs H p u (x, ,t).. 3D Parton Distributions

5. Form Factor Studies n 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 2006/2007

6. Form Factor Studies Use various parameterizations for GPDs to fit the existing form factor data A.Afanasev hep-ph/9910565 Diehl et al, Eur.Phys.J c39 (2005) M.Guidal et al PRD (2005) Different parameterizations yield different contributions for quarks to the OAM A)Large L d and small L u B)Sum of L u and L d small More observables needed for detailed studies of GPDs and the OAM (RCS,DVCS,DVMP) Issues: different realistic fits to FFs produce different values for Lq fits done at high t, need to be extrapolated to t→0

7. DVCS DVMP Hard Exclusive Processes and GPDs hard vertices hard gluon DVCS – for different polarizations of beam and target provide access to different combinations of GPDs H, H, E long. only DVMP for different mesons is sensitive to flavor contributions (     select H, E, for u/d flavors, , K select H, E) Study the asymptotic regime and guide theory in describing HT. ~

8. Deeply Virtual Compton Scattering ep->e’p’  Different 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 +.. } ~  = x B /(2-x B ),k = t/4M 2 Kinematically suppressed d4d4 dQ 2 dx B dtd  ~ | T DVCS + T BH | 2 DVCSBH T BH : given by elastic form factors T DVCS : determined by GPDs GPD  UT  ~ sin  Im{k 1 ( F 2 H -F 1 E ) +.. } Unpolarized beam, transverse target: Kinematically suppressed

9. Deeply Virtual Compton Scattering ep→e’p’  Interference responsible for SSA, contain the same lepton propagator P 1 (  ) as BH Way to access to GPDS GPD combinations accessible as azimuthal moments of the total cross section.

10.  -dependent amplitude Strong dependence on kinematics of prefactor  -dependence, at y=y col P 1 (  )=0 Fraction of pure DVCS increases with t and   =0  =45  =90 BH DVCS x=0.25 5.7 GeV

11. DVCS Experiments  sin  +  sin2  S. Stepanyan et al. Phys. Rev. Lett. 87 (2001) CLAS at 4.3 GeV HERMES 27 GeV A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

12. Define relation between A LU and s 2 I effect of other non-0 moments ~5-10% effect of finite bins ~10% Define background corrections pion contamination ~10% radiative background ADVCS <3% at CLAS GPDs from ep->e’p’  Requirements for precision (<15%) measurements of s 2 I and GPDs from DVCS SSA: More relevant when proton is not detected

13. DVCS event samples 3 event samples(after data quality cuts) 1)ep 0 photons (~2M events) tight cuts on PID,missing mass MX 2) ep  1 photon in Calorimeter (~150000 events) cut on the direction   X <0.015, 3) ep  2 photon(   ) in Calorimeter (~70000 events) cut on the direction   X <0.02, Kinematic coverage of 5.75 GeV(red) and 5.48(blue) CLAS data sets Angular cut most efficient in separating  0 ep  DVCS  ep   

14.  0 MC vs Data Exclusive pi0 production simulated using a realistic MC Kinematic distributions in x,Q 2,t tuned to describe the CLAS data

15.  0 beam SSA cross section Main unknown in corrections of photon SSA are the  0 contamination and its beam SSA. Contamination from  0 photons increasing at large t and x and also at large f. Significant SSA measured for exclusive  0s also should be accounted Use ep  to estimate the contribution of  0 in the ep and ep  samples 1.6<Q 2 <2.6, 0.22<x<0.32 CLAS 5.7 GeV PRELIMINARY

16. BH cos  moment BH cos  moment can generate ~3% sin2  in the A LU

17. DVCS SSA kinematic dependences at 5.7 GeV A LU for ep->ep[  ] sample with -t<0.5 GeV 2 Fine binning allows to observe the x and Q 2 dependence Preliminary data for fully exclusive ep  is consistent with the ep data and consistent with GPD base predictions PRELIMINARY

18. JLab/CLAS Calorimeter and superconducting magnet within CLAS torus e e’ p γ → Dedicated detection of 3 particles e, p and γ in final state → Firmly establish scaling laws (up to Q 2 ~ 5 GeV 2 ), if observed, or deviations thereof understood, first significant measurement of GPDs. → Large kinematical coverage in x B and t JLab/Hall A 424 PbWO4 crystals HRS + PbF 2 + Plastic scintillator H(e,e’  p) D(e,e’  N)N Dedicated DVCS experiments dedicated calorimeters

19. Extraction of GPD H from A LU moment Red[blue] points correspond to projected A LU [un]corrected for  0 (bin by bin) H stands for the ratio of the A LU and prefactor calculated for all events in a bin (averaged over  Curves are for a simple model for CFF H (blue) and H+…(red)  (F 1 +F 2 ) H +kF 2 E ~20% ~ ep  2<Q 2 <2.4 GeV c LU A LU /c LU

20. Target Spin Asymmetry: t- Dependence Measurements with polarized target will constrain the polarized GPD and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.  UL  ~ sin  Im{F 1 H +  (F 1 +F 2 )( H +.. }  LL  ~ cos  Re{F 1 H +  (F 1 +F 2 )( H +.. } ~ Unpolarized beam, longitudinal target: Kinematically suppressed ~ First data available(5 CLAS days), more(60 days) to come at 6 GeV

21. CLAS (4.2 GeV) Regge (JML) C. Hadjidakis et al., PLB 605 GPD formalism (beyond leading order) describes approximately data for x B 1.5 GeV 2 GPD (MG-MVdh) CLAS (5.75 GeV) Analysis in progress Two-pion invariant mass spectra Decent description in pQCD framework already at moderate Q 2 Exclusive ρ meson production: ep → epρ 0

22. Exclusive     and     e p e p  π + π - e - p  e - n  + π+π0π+π0 ++ n 00 Provide access to different combinations of orbital momentum contributions J u,J d   -> 2J u + J d   -> J u - J d

23. Exclusive   production on transverse target A ~ 2H u + H d B ~ 2E u + E d 00 K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 E u, E d needed for angular momentum sum rule. 00 A ~ H u - H d B ~ E u - E d ++ Asymmetry is a more appropriate observable for GPD studies at JLab energies as possible corrections to the cross section are expected to cancel 2  ┴ (Im(AB*))/           t/4m 2 ) - Re      UT 

24. TMD measurements in SIDIS (  *p→  X) TMD PDFs related to interference between L=0 and L=1 light-cone wave functions. f 1T ┴ ep → e  X D 1 sin(  h  S  h 1 ┴ ep → e  X H 1 ┴ sin(  h  S’  h 1L ┴ ep → e  X H 1 ┴ sin(  h  S’  f L ┴ ep → e  X D 1 sin  h g ┴ ep → e  X D 1 sin  h h L ep → e  X H 1 ┴ sin  h Significant beam and target SSA were observed in all listed channels, more data under way Process Moment TMDFF Survive in jet limit S T (q×P T )  S’=  -  h  S’=  -  h

25. E06-010 and E06-011 Sivers Effect studies with Transversely polarized target Proposal approved, to study the Sivers function at JLab (Hall-A)

26. Sivers SSA at CLAS @5.7GeV Expected precision of the A UT with transversely polarized target A UT ~ Sivers Measurement of  0 A UT at CLAS would allow model independent extraction of the Sivers function Simultaneous measurement of SIDIS, exclusive  and DVCS asymmetries with a transversely polarized target. ++

27. Polarized target SSA using CLAS at 6 GeV 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 )

28. Significant SSA measured for pions with longitudinally polarized target 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

29. A LU x-dependence: CLAS @ 5.7 GeV  +,0.5<z<0.8 Parton distribution g┴(x) is calculated within the same dynamical model of Afanasev, Carlson Assume k T is small Assume NLO corrections small Beam SSA for  0 may provide a FF independent access to g┴

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

31. 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 and accessible luminosity Provides new insight into - quark orbital angular momentum contributions - to the nucleon spin - 3D structure of the nucleon’s interior and correlations - quark flavor polarization

32. Summary  Current JLab data are consistent with a partonic picture, and can be described by a variety of theoretical models.  High luminosity, polarized CW beam, wide kinematic and geometric acceptance allow studies of exclusive and semi-inclusive processes, providing data needed to constrain relevant 3D distribution functions (TMDs,GPDs)  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.  CLAS12 Full acceptance, general purpose detector for high luminosity electron scattering experiments, is essential for high precision measurements of GPDs and TMDs in the valence region.