1. 1 Transversely polarized target for CLAS and CLAS12  Introduction  Structure of nucleon and 3D parton distributions  Semi-Inclusive processes and TMD distributions  Hard exclusive processes and GPDs  Projections  Summary Harut Avakian CLAS Collaboration Meeting March 1

2. 2 Describe the complex nucleon structure in terms of partonic degrees of freedom of QCD Physics Motivation QCD evolution tells us how parton distributions evolve, but not original distributions RHIC Spin & SIDIS Understanding of the orbital motion of quarks and spin-orbit correlations is crucial!!! EMC at CERN (85): J q

3. 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 Quantum Phase-Space Distributions of Quarks Measure momentum transfer to target Direct info about spatial distributions No information about underlying dynamics 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

4. 4 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

5. 5 h Single particle production in hard scattering Target fragmentation Current 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) x F <0 (target fragmentation) h

6. 6 Semi-Inclusive DIS 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 q f =f 1 u ( x ): probability to find a u-quark with a momentum fraction x Hard scattering Favored Fragmentation Unfavored

7. 7 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).

8. 8  s=20 GeV, p T =0.5-2.0 GeV/c   0 – E704, PLB261 (1991) 201.   +/- - E704, PLB264 (1991) 462. Single Spin Asymmetries in Recently, large transverse single-spin effects were observed also in p+p collisions (RHIC), at much higher CM energies. In collinear picture, the QCD predict small SSAs with transversely polarized protons colliding at high energies. Kane, Pumplin, Repko ‘78 FermiLab E-704 FNAL

9. 9 The Elephant and the village of the blind SSA Asymmetry comes from modulation of the initial distribution function (D.Sivers 1990) Asymmetry comes from the final state interactions in fragmentation (J.Collins 1993) Non-PQCD “surface effects (Ma,Boros et al) correlation between quark fields and the gluonic fields (“twist-3” Qiu&Sterman) Sivers effect forbidden by time reversal invariance (Collins 1993) k T – crucial for spin structure studies.

10. 10 Mechanisms for SSA L=1 Collins Fragmentation L/R SSA generated in fragmentation Unfavored SSA with opposite sign No effect in target fragmenation Orbital momentum generated in string breaking and pair creation produces left- right asymmetry from transversely polarized quark fragmentation (Artru-93) fragmentation of transversely polarized quarks into unpolarized hadrons ud d d u (favored)

11. 11 Mechanisms for SSA Sivers Distribution f 1T ┴ : unpolarized quarks in transversely polarized nucleon L/R SSA generated in distribution Hadrons from struck quark have the same sign SSA Opposite effect in target fragmentation T-odd f 1T ┴, requires final state interactions + interference between different helicity states (Brodsky et al., Collins, Ji et al. 2002)

12. 12 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) k T – leads to 3D description with 8PDFs  Transverse target provides access to spin-orbit correlations with all possible polarizations of quarks. Mulders & Tangerman (1995, the TMD “bible”) Transversity Off diagonal PDFs related to interference between states with different orbital momentum Sivers Boer-Mulders proton polarization quark polarization

13. 13 Sivers function: First measurement A UT ~ Sivers significantly positive    asymmetry  requires non-zero orbital angular momentum  first hint of naïve T-odd DF from DIS Phys.Rev.Lett.94:012002,2005. (100+ in hep SPIRES citation)

14. 14 Collins effect: First measurements significantly positive   and negative    asymmetries unexpected large    role of unfavoured (u →    fragmentation function? First extraction of transversity by Anselmino et al. (hep-ph/0701006) Soffer bound

15. 15 BELLE: Collins function measurements BELLE: Asymmetries in e + e - →h 1 h 2 X (H ┴ 1 H ┴ 1 ) _ Efremov et al. Phys.Rev.D. 73,094025 (2006) positivity limit 11 Belle detector KEKB Asymmetric collider 8GeV e- + 3.5GeV e+ First direct indication of non-0 Collins fragmentation !

16. 16 Different final states selects different combinations of GPDs N *L*L t N’   Q 2 >>, t<< H,E,H,E ~ Hunting for L q Hunting for L q in hard exclusive processes Generalised Parton Distributions - Műller (1994) - - Ji & Radyushkin (1996) - 10-30%(DIS) J q ( H + E) x dx = J q = 1/2  L z

17. 17 GPDs and spatial distributions Transverse position distributionTransverse position shift Shift in the transverse space of quarks in the transversely polarized proton first predicted in GPD framework, confirmed by Lattice (hep-ph/0612032) Transversely polarized proton Unpolarized quark

18. HU Feb 1518 → First (model dependent) constraints on J u and J d ! HERMES: DVCS with Transverse target and GPD E L = 64 pb -1  UT ~ sin(  S  cos(  Im{ H - E + … }+..

19. 19 CLAS Transversely Polarized Target  22.5 degree impact 22.5 o Measurements at different beam energies will allow study of Q 2 dependence for a fixed x in a wide range. CLAS12 CLAS6

20. 20 Collins Effect  UT ~ Collins Study the Collins fragmentation for all 3 pions with a transversely polarized target and measure the transversity distribution function.

21. 21 Sivers effect  UT ~ Sivers Requires: non-trivial phase from the FSI + interference between different helicity states

22. 22 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

23. HU Feb 1523 CLAS12 - Exclusive Target Asymmetries  Asymmetry for photons and rho highly sensitive to the GPD E and u- quark contributions to proton spin. Transversely polarized target e p ep   ~ GPD- E ~ J u E = 11 GeV ep  ep  CLAS12

24. 24 Summary Studies of exclusive and semi-inclusive hard processes with transverse target at CLAS6 and CLAS12 related to the spin, spin orbit correlations and orbital angular momentum (in particular Sivers function and GPD-E ) are crucial for understanding of the transverse structure of the nucleon Transverse target design in progress at OXFORD (field maps available) GSIM studies of scattering of high lumi beam with transverse target in progress. Few independent proposals for PAC32: Inclusive DIS Semi-Inclusive DIS Exclusive processes …………….. (proton & deuteron targets)

25. 25 Support slides…..

26. 26 PDFs and orbital momentum Transverse position shift using GPD-E Good agreement of HERMES (filled) and JLab (open) data with BBS curves for quarks aligned with proton spin, where the orbital motion is not as important. BBS (NP B441, 197 (1995) using helicity structure of perturbative QCD coupling at x→1 n=minimal number of spectator quarks =2

27. 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. 28 Nonperturbative TMDPerturbative region Boer-Mulders Asymmetry 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

29. 29  CLAS12 a 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.  Provide new insight into - quark orbital angular momentum contributions to the nucleon spin - 3D structure of the nucleon’s interior and correlations - quark flavor polarization  EIC will extend studies of 3D nucleon structure, to low x and high Q 2, important for all processes of interest: - deeply virtual exclusive processes (DVCS, DVMP) - semi-inclusive meson production with polarized beam and polarized targets Summary