Experimental Study of Nucleon Structure and QCD J. P. Chen, Jefferson Lab Workshop on Confinement Physics, March 12, 2012  Introduction  Selected JLab 6 GeV Experimental Results  Spin Distributions in the High-x (Valence Quark) Region and Quark-Hadron Duality  Moments of Spin Structure Functions: Spin Sum Rules and Polarizabilities  Transverse Spin, TMDs  Planned Experiments with JLab 12 GeV

QCD: still unsolved in non-perturbative region 2004 Nobel prize for ``asymptotic freedom’’ non-perturbative regime QCD ? Confinement: 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

Introduction Quarks/Gulons are confined in hadron To study/understand confinement: both static (spectroscopy) and dynamics Nucleon: an ideal laboratory to study strong interaction (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 Transverse dimension is crucial for understanding nucleon structure and QCD, help understanding confinement Elastic (Form Factors), Resonances, DIS, Spin, Transverse Spin, TMDs, GPDs

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 decomposition (X. Chen, et. Al, Wakamatsu, …) What observable directly corresponds to L z ~ b x X p y ? 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  Sum Rules at low Q 2, Higher-Twists  Transversity, Transverse-Momentum Dependent Distributions

JLab Spin Experiments Results: Spin in the valence (high-x) region Spin (g 1 /g 2 ) Moments: Spin Sum Rules, Spin Polarizabilities SSA in SIDIS: Transversity, TMDs On-going g 2 p at low Q 2 Future: 12 GeV Inclusive: A 1 /d 2, Semi-Inclusive: Transversity, TMDs, Flavor-decomposition Reviews: S. Kuhn, J. P. Chen, E. Leader, Prog. Part. Nucl. Phys. 63, 1 (2009)

Valence Quark Spin Structure A 1 at high x and flavor decomposition

Why Are PDFs at High x Important? Valence quark dominance: simpler picture -- direct comparison with nucleon structure models SU(6) symmetry, broken SU(6), diquark x  1 region amenable to pQCD analysis -- hadron helicity conservation? role of quark orbit angular momentum? Clean connection with QCD, via lattice moments (d 2 ) Input for search for new physics at high energy collider -- evolution: high x at low Q 2  low x at high Q 2 -- small uncertainties amplified -- example: HERA ‘anomaly’ (1998)

World data for A 1 Proton Neutron

JLab E Precision Measurement of A 1 n at Large x Spokespersons: J. P. Chen, Z. Meziani, P. Souder; PhD Student: X. Zheng First precision A 1 n data at high x Extracting valence quark spin distributions Test our fundamental understanding of valence quark picture SU(6) symmetry Valence quark models pQCD (with HHC) predictions Quark orbital angular momentum Crucial input for pQCD fit to PDF PRL 92, (2004) PRC 70, (2004)

Polarized Quark Distributions Combining A 1 n and A 1 p results Valence quark dominating at high x u quark spin as expected d quark spin stays negative! Disagree with pQCD model calculations assuming HHC (hadron helicity conservation) Quark orbital angular momentum Consistent with valence quark models and pQCD PDF fits without HHC constraint

Inclusive Hall A and B and Semi-Inclusive Hermes BBS BBS+OAM H. Avakian, S. Brodsky, A. Deur, and F. Yuan, PRL 99, (2007) pQCD with Quark Orbital Angular Momentum

Spin-Structure in Resonance Region: E Study Quark-Hadorn Duality Spokesperson: N. Liyanage, J. P. Chen, S. Choi; PhD Student: P. Solvignon PRL 101, (2008) A 1 3He (resonance vs DIS)  1 resonance vs. pdfs xQ2Q2 x

A 1 p at 11 GeV (CLAS12) Projections for JLab at 11 GeV A 1 n at 11 GeV (Hall C/A)

Moments of Spin Structure Functions Sum Rules, Polarizabilities

First Moment of g 1 p :  1 p EG1b, arXiv: EG1a, PRL 91, (2003) Spokespersons: V. Burkert, D. Crabb, G. Dodge, 1p1p Total Quark Contribution to Proton Spin (at high Q 2 ) Twist expansion at intermediate Q 2, LQCD, ChPT at low Q 2

First Moment of g 1 n :  1 n E94-010, PRL 92 (2004) E97-110, preliminary EG1a, from d-p 1n1n

 1 of p-n EG1b, PRD 78, (2008) E EG1a: PRL 93 (2004)

Effective Coupling Extracted from Bjorken Sum s/s/ A. Deur, V. Burkert, J. P. Chen and W. Korsch PLB 650, 244 (2007) and PLB 665, 349 (2008)

Second Spin Structure Function g 2 Burkhardt - Cottingham Sum Rule Spin Polarizabilities

Precision Measurement of g 2 n (x,Q 2 ): Search for Higher Twist Effects Measure higher twist  quark-gluon correlations. Hall A Collaboration, K. Kramer et al., PRL 95, (2005)

Preliminary results on neutron from E Spokespersons: J. P. Chen, S. Choi, N. Liyanage, plots by P. Solvignon

Burkhardt - Cottingham Sum Rule P N 3 He BC = Meas+low_x+Elastic 0<X<1 :Total Integral very prelim “low-x”: refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour Elastic: From well know FFs (<5%) “Meas”: Measured x-range Brawn: SLAC E155x Red: Hall C RSS Black: Hall A E Green: Hall A E (preliminary) Blue: Hall A E (spokespersons: N. Liyanage, former student, JPC) (preliminary)

BC Sum Rule P N 3 He BC satisfied w/in errors for 3 He BC satisfied w/in errors for Neutron (But just barely in vicinity of Q 2 =1!) BC satisfied w/in errors for JLab Proton 2.8  violation seen in SLAC data very prelim

Neutron Spin Polarizabilities   LT insensitive to  resonance RB ChPT calculation with resonance for  0 agree with data at Q 2 =0.1 GeV 2 Significant disagreement between data and both ChPT calculations for  LT Good agreement with MAID model predictions  0  LT Q2 Q2 Q2 Q2 E94-010, PRL 93 (2004)

Spin Polarizabilities Preliminary E (and Published E94-010) Spokesperson: J. P. Chen, A. Deur, F. Garibaldi, plots by V. Sulkosky Significant disagreement between data and both ChPT calculations for  LT Good agreement with MAID model predictions  0  LT Q2 Q2 Q2 Q2

Axial Anomaly and the  LT Puzzle N. Kochelev and Y. Oh; arXiv: v1

E : Proton g 2 Structure Function Fundamental spin observable has never been measured at low or moderate Q 2 BC Sum Rule : violation suggested for proton at large Q 2, but found satisfied for the neutron & 3 He. Spin Polarizability : Major failure (>8  of  PT for neutron  LT. Need g 2 isospin separation to solve. Hydrogen HyperFine Splitting : Lack of knowledge of g 2 at low Q 2 is one of the leading uncertainties. Proton Charge Radius : also one of the leading uncertainties in extraction of from  H Lamb shift. BC Sum Rule Spokespersons: Camsonne, Chen, Crabb, Slifer(contact), 6 PhD students, 3 postdocs Running until 5/2012 Spin Polarizability  LT

Single Target-Spin Asymmetries in SIDIS Transversity/Tensor Charge

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-Tranversity) : Survive trans. Momentum integration Nucleon Spin Quark Spin g 1T = Worm Gear Worm GearTrans-Helicity

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

Separation of Collins, Sivers and pretzelocity effects through angular dependence

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, … First neutron measurement from Hall A 6 GeV (E06-010) Solenoid with polarized 3 He at JLab 12 GeV Unprecedented precision with high luminosity and large acceptance

E He Target Single-Spin Asymmetry in SIDIS Spokespersons: J. P. Chen, E. Cisbani, H. Gao, X. Jiang, J-C. Peng, 7 PhD students 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 (2011) 107: (2011)

Results on Neutron Collins asymmetries are not large, except at x=0.34 Sivers negative Blue band: model (fitting) uncertainties Red band: other systematic uncertainties

Asymmetry A LT Result 3 He A LT Positive for  - To leading twist: Preliminary

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

JLab 12 GeV Era: Precision Study of TMDs From exploration to precision study with 12 GeV JLab Transversity: fundamental PDFs, tensor charge TMDs: 3-d momentum structure of the nucleon  Quark orbital angular momentum Multi-dimensional mapping of TMDs 4-d (x,z,P ┴,Q 2 ) Multi-facilities, global effort Precision  high statistics high luminosity and large acceptance

GEMs (study done with CDF magnet, 1.5T) 41

12 GeV: Mapping of Collins/Siver Asymmetries with SoLID Both  + and  - For one z bin ( ) Will obtain many z bins ( ) Tensor charge E He(n), Spokespersons: J. P. Chen, H. Gao, X. Jiang, J-C. Peng, X. Qian E (p), Spokespersons: K. Allda, J. P. Chen, H. Gao, X. Li, Z-E. Mezinai

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

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

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 mapping of SSA Collins and Sivers  +,  - and K +, K - New proposal polarized proton with SoLID Study factorization with x and z-dependences Study P T dependence Combining with the world data extract transversity and fragmentation functions for both u and d quarks determine tensor charge study TMDs for both valence and sea quarks study quark orbital angular momentum study Q 2 evolution Global efforts (experimentalists and theorists), global analysis much better understanding of multi-d nucleon structure and QCD Longer-term future: EIC to map sea and gluon SSAs

Summary Nucleon (spin) Structure provides valuable inf on QCD dynamics A decade of experiments from JLab: exciting results valence spin structure, duality spin sum rules and polarizabilities precision measurements of g 2 : high-twist first neutron transverse spin results: Collins/Sivers/A LT Bright future 12 GeV Upgrade will greatly enhance our capability Precision determination of the valence quark spin structure flavor separation Precision extraction of transversity/tensor charge/ TMDs