Study Transverse Spin and TMDs with SIDIS Experiments J. P. Chen, Jefferson Lab Hall A Physics Workshop, December 14, 2011  Introduction  Transverse Spin and Transverse Momentum Dependent Distributions (TMDs)  Exploration: initial results from JLab 6 GeV experiment  Precision study in valence region: JLab12 GeV program  Precision study of the sea/gluons : Future EIC

QCD: still unsolved in non-perturbative region 2004 Nobel prize for ``asymptotic freedom’’ non-perturbative regime QCD ????? One of the top 10 challenges for physics! QCD: Important for discovering new physics beyond SM Nucleon structure is one of the most active areas

Nucleon Structure and QCD Colors are confined in hadronic system Nucleon: ideal lab to study QCD Nucleon = valence quarks (u u d or u d d) + sea + gluons Mass, charge, magnetic moment, spin, axial charge, tensor charge Decomposition of each of the fundamental quantities Mass: ~1 GeV, but u/d quark mass only a few MeV each! Momentum: quarks carry ~ 50% Spin: ½, quarks contribute ~30% Spin Sum Rule Orbital Angular Momentum Relations to TMDs and GPDs Tensor charge Lattice QCD Quarks and gluon field are in-separable Multi-parton correlations are important Beyond co-linear factorization Transverse dimension is crucial for understanding nucleon structure and QCD, help understanding confinement

Three Decades of Spin Structure Study 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small  = ( )% ! ‘spin crisis’ ( Ellis-Jaffe sum rule violated) 1990s: SLAC, SMC (CERN), HERMES (DESY)  = 20-30% the rest: gluon and quark orbital angular momentum A + =0 (light-cone) gauge (½)  + L q +  G + L g =1/2 (Jaffe) gauge invariant (½)  + Lq + J G =1/2 (Ji) (New decompositions: Chen et al., Wakamatsu, …) What observable directly corresponds to L z ~ b x X p y ? New progress, Ji/Yuan… Bjorken Sum Rule verified to <10% level 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … :  ~ 30%;  G probably small, orbital angular momentum probably significant  Valence Quark Spin Distributions, Higher-Twists  Transversity, Transverse-Momentum Dependent Distributions

Unpolarized and Polarized Structure functions

Parton Distributions (CTEQ6 and DSSV) DSSV, PRL101, (2008) Polarized PDFs Unpolarized PDFs JHEP 1001: 109 (2010)

Transverse Spin and Transverse Momentum Dependent Distributions Transversity and Tensor Charge TMDs: 3-D mapping in Momentum space Spin-orbital correlations, QCD dynamics

Transversity Three twist-2 quark distributions: Momentum distributions: q(x,Q 2 ) = q ↑ (x) + q ↓ (x) Longitudinal spin distributions: Δq(x,Q 2 ) = q ↑ (x) - q ↓ (x) Transversity distributions: δq(x,Q 2 ) = q ┴ (x) - q ┬ (x) It takes two chiral-odd objects to measure transversity Semi-inclusive DIS Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function) TMDs: (without integrating over P T ) Distribution functions depends on x, k ┴ and Q 2 : δq, f 1T ┴ (x, k ┴,Q 2 ), … Fragmentation functions depends on z, p ┴ and Q 2 : D, H 1 (x,p ┴,Q 2 ) Measured asymmetries depends on x, z, P ┴ and Q 2 : Collins, Sivers, … (k ┴, p ┴ and P ┴ are related)

Leading-Twist TMD PDFs f 1 = f 1T  = Sivers Helicity g 1 = h1 =h1 = Transversity h1 =h1 =Boer-Mulders h 1T  = Pretzelosity h 1L  = Worm Gear: Longi-transversity : Survive trans. Momentum integration Nucleon Spin Quark Spin g 1T = Worm Gear: Trans-helicity

Leading-Twist TMD PDFs f 1 = f 1T  = Sivers Helicity g 1 = h1 =h1 = Transversity h1 =h1 =Boer-Mulders h 1T  = Pretzelosity g 1T = Worm Gear: Trans-helicity h 1L  = Worm Gear: Longi-transversity : Probed with transversely pol target Nucleon Spin Quark Spin

W p u (x,k T,r ) Wigner distributions d2kTd2kT PDFs f 1 u (x),.. h 1 u (x)‏ GPDs d 2 k T dr z d3rd3r TMDs f 1 u (x,k T ),.. h 1 u (x,k T )‏ 3D imaging 6D Dist. Form Factors G E (Q 2 ), G M (Q 2 )‏ d2rTd2rT dx & Fourier Transformation 1D

Access TMDs through Hard Processes proton lepton pion proton lepton antilepton Drell-Yan BNL JPARC FNAL EIC SIDIS electron positron pion e – e + to pions  Gauge invariant definition (Belitsky,Ji,Yuan 2003)  Universality of k T -dependent PDFs (Collins,Metz 2003)  Factorization for small k T. (Ji,Ma,Yuan 2005)

Transverity2011 Franco Bradamante COMPASS Collins asymmetry 2010 data NEW nice confirmation of the 2007 results, with better statistics σ syst ~ 0.5 σ stat

Transverity2011 Franco Bradamante COMPASS Collins asymmetry 2010 data x > region - comparison with HERMES results good agreement 1/D NN NEW

Transverity2011 Franco Bradamante COMPASS Sivers asymmetry 2010 data x > region - comparison with HERMES results NEW

Status of Transverse Spin Study Large single spin asymmetry in pp->  X Collins Asymmetries - sizable for the proton (HERMES and COMPASS ) large at high x,  - and  has opposite sign  unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for the deuteron (COMPASS) Sivers Asymmetries - non-zero for  + from proton (HERMES), new COMPASS data - consistent with zero for  - from proton and for all channels from deuteron - large for K + ? Collins Fragmentation from Belle Global Fits/models: Anselmino, Prokudin et al., Vogelsang/Yuan et al., Pasquini et al., Ma et al., … Very active theoretical and experimental efforts RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, EIC, …

Initial Exploration at Hall A 6 GeV Transversity experiment E06-010

E06 ‑ 010 Experiment Spokespersons: Chen/Evaristo/Gao/Jiang/Peng First measurement on n ( 3 He) Polarized 3 He Target Polarized Electron Beam, 5.9 GeV – ~80% Polarization BigBite at 30º as Electron Arm – P e = 0.7 ~ 2.2 GeV/c – Upgraded detector package HRS L at 16º as Hadron Arm – P h = 2.35 GeV/c – Excellent PID for  /K/p 7 Excellent PhD Students K. Allada, C. Dutta, J. Huang, J. Katich, X. Qian, Y. Wang, Y. Zhang (all graduated) 3 Hard-working Postdocs: A. Camsonne, Y. Qiang, V. Sulkosky Strong Contributions/Supports from Hall A Collaboration, Hall A and JLab 18 Beam Polarimetry (Møller + Compton) Luminosity Monitor

JLab Polarized 3 He Target longitudinal, transverse and vertical Luminosity=10 36 (1/s) (highest in the world) High in-beam polarization ~ 60% Effective polarized neutron target 13 completed experiments 7 approved with 12 GeV (A/C) 15 uA

History of Figure of Merit of Polarized 3 He Target High luminosity: L(n) = cm -2 s -1 Polarization in all 3 directions (L, T, V) Record high in-beam ~ 60% polarization Fast spin flip (every 20 minutes) Performance of 3 He Target

Separation of Collins, Sivers and pretzelocity effects through angular dependence

3 He Target Single-Spin Asymmetry in SIDIS 3 He Sivers SSA: negative for π +, 3 He Collins SSA small Non-zero at highest x for  + Blue band: model (fitting) uncertainties Red band: other systematic uncertainties X. Qian et al., PRL 107: (2011)

Neutron Results with Polarized 3He from JLab Collins asymmetries are not large, except at x=0.34 Sivers negative Blue band: model (fitting) uncertainties Red band: other systematic uncertainties X. Qian at al., PRL 107:072003(2011)

Asymmetry A LT Result 3 He A LT : Positive for  - To leading twist: Preliminary J. Huang et al., arXiv: , accepted to PRL

–Corrected for proton dilution, f p –Predicted proton asymmetry contribution < 1.5% (π + ), 0.6% (π - ) –Dominated by L=0 (S) and L=1 (P) interference Consist w/ model in signs, suggest larger asymmetry Neutron A LT Extraction Preliminary Trans-helictiy

Precision TMD Study in the Valence Region SoLID SIDIS program with 12 GeV upgrade

Precision Study of Transversity and TMDs From exploration to precision study Transversity: fundamental PDFs, tensor charge TMDs: 3-d structure in momentum space Spin-orbit correlations: quark orbital angular momentum Multi-parton correlations: QCD dynamics Multi-dimensional mapping of TMDs 4-d (x,z,P ┴, Q 2 ) Multi-facilities, global effort Precision  high statistics high luminosity and large acceptance

Precision TMDs with SoLID (JLab) PAC 38 results: E : Neutron (3He) SSA in SIDIS with SoLID awarded the highest rating “A” Precision 4-d (x, z, PT, Q2) mapping of Collins/Sivers in valence region E : Neutron (3He) DSA and Longitudinal SSA in SIDIS with SoLID, “A” Precision map of A_LT and A_UL, worm-gear functions E : proton SSA in SIDIS with SoLID, conditional approval (target) Several TMD proposals in CLAS12 and Hall A/C approved A comprehensive and coherent program on TMDs

GEMs (study done with CDF magnet, 1.5T) 29

E , Approved with “A” Rating Mapping of Collins(Sivers) Asymmetries with SoLID Spokespersons: Chen/Gao/Jiang/Peng/Qian Both  + and  - Precision Map in region x( ) z( ) Q 2 (1-8) P T (0-1.6) <10% d quark tensor charge with world data Collins Asymmetry

Sivers Function Correlation between nucleon spin with quark angular momentum Important test for factorization f 1T  =

Expected Improvement: Sivers Function Significant Improvement in the valence quark (high-x) region Illustrated in a model fit (from A. Prokudin) f 1T  =

Map Collins and Sivers asymmetries in 4-D (x, z, Q 2, P T )

E : Worm-gear functions (“A’ rating: ) Spokespersons: Chen/Huang/Qiang/Yan Dominated by real part of interference between L=0 (S) and L=1 (P) states No GPD correspondence Lattice QCD -> Dipole Shift in mom. space. Model Calculations -> h 1L  =? -g 1T. h 1L  = g 1T = Longi-transversity Trans-helicity Center of points:

Discussion Unprecedented precision 4-d (x,z,P T,Q 2 ) mapping of SSA Collins, Sivers, worm-gear, other TMDs  +,  - and K +, K - Study factorization with x and z-dependences Study P T dependence On both proton and neutron and combine with world data (e+e-) extract transversity and fragmentation functions for both u and d quarks determine tensor charge study TMDs for valence quark region study quark orbital motion and spin-orbital correlations Need world data from high energy facilities (EIC,…) study Q 2 evolution, sea quarks, gluons Global efforts (experimentalists and theorists), global analysis much better understanding of multi-d nucleon structure and QCD Lead to breakthroughs

Precision TMD study: Sea and Gluons A Future Electron Ion Collider: ELIC, JLab

Into the “Sea”: A Future Electron-Ion Collider 12 GeV With 12 GeV we study mostly the valence quark component. An EIC aims to study the sea quarks, gluons, and scale (Q 2 ) dependence. mEIC EIC

Electron Ion Colliders on the World Map RHIC  eRHIC LHC  LHeC CEBAF  MEIC/EIC FAIR  ENC HERA

Medium Energy Three compact rings: 3 to 11 GeV electron Up to 12 GeV/c proton (warm) Up to 60 GeV/c proton (cold)

ELIC at ELIC at L ~ cm -2 s GeV protons GeV/n ions 3-11 GeV electrons 3-11 GeV positrons Green-field design of ion complex directly aimed at full exploitation of science program.

EIC Phase Space Coverage

An EIC with good luminosity & high transverse polarization is the optimal tool to to study this! Only a small subset of the (x,Q 2 ) landscape has been mapped here. Gray band: present “knowledge” Red band: EIC (1  ) Image the Transverse Momentum of the Quarks Exact k T distribution presently essentially unknown! Prokudin, Qian, Huang Prokudin

Summary Transverse spin and TMDs crucial for full understanding of nucleon structure and QCD Initial explorations worldwide  increasing interests JLab 6 GeV: initial results, first neutron (3He) measurement JLab 12 GeV plan: precision 4-d mapping in the valence region tensor charge Lattice QCD quark orbital motion QCD dynamics Electron-Ion Collider: understand sea and gluons Exciting new opportunities  lead to breakthroughs? Acknowledgements: some slides provided by collaborators and colleagues