Challenges of the Standard Model and the Nucleon Spin Puzzle Thomas Jefferson National Accelerator Facility (JLab) Recent Results from JLab Spin Program Summary and Outlook Xiaochao Zheng Univ. of Virginia October 17, 2009 Selected Results from the Nucleon Spin Program at Jefferson Lab

SU(2) L X U(1) Y SU(3) C Standard Model of Particle Physics

Success of the Standard Model in the strong interaction sector QCD tested in the high energy (perturbative, = “weak”) region Major Challenges within the Standard Model Understand and test QCD in extreme conditions (RHIC, LHC) Understand and test QCD in “strong” interaction region (non- perturbative) Understand the nucleon structure, how quarks and gluons form the nucleon's mass, momentum, and spin Standard Model of Particle Physics energy (GeV) (~1/distance) aSaS

Success of the Standard Model in the strong interaction sector QCD tested in the high energy (perturbative, = “weak”) region Major Challenges within the Standard Model Understand and test QCD in extreme conditions (RHIC, LHC) Understand and test QCD in “strong” interaction region (non- perturbative) Understand the nucleon structure, how quarks and gluons form the nucleon's mass, momentum, and spin Standard Model of Particle Physics

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) % the rest: quark orbital angular momentum and gluons Different decompositions: Jaffe, Ji, X. Chen et al. Bjorken Sum Rule verified to <10% level 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … :  ~ 30%;  G probably small, quark orbital angular momentum probably significant  Test of various Sum Rules  Transversity, Transverse-Momentum Dependent Distributions  Generalized Parton Distributions

Medium & High Energy Physics Facilities for Lepton Scattering High luminosity, and “continuous” polarized beam makes JLab an unique facility. ~ns: “continuous” >>ns: “pulsed”

Employment: ~650 User community: ~1200

Three Experimental Halls Hall A: pair of high resolution spectrometers (HRS), E' up to 4 GeV/c, DW = 7 msr luminosity up to cm -2 s -1 Hall C: High Momentum (HMS) and Short-Orbit Spectrometers (SOS) luminosity up to cm -2 s -1 Hall B: CEBAF Large Acceptance Spectrometer (CLAS) luminosity up to cm -2 s -1

Hall A polarized 3 He target longitudinal, transverse and vertical Luminosity=10 36 (cm -2 s -1 ) (highest polarized luminosity in the world) High in-beam polarization > 65% Effective polarized neutron target 13 completed experiments 6 approved with 12 GeV (A/C) 15 uA

Hall B/C Polarized proton/deuteron targets Polarized NH 3 /ND 3 targets Dynamical Nuclear Polarization In-beam average polarization 70-90% for p 30-40% for d Luminosity up to ~ cm -2 s -1 (Hall C) ~ cm -2 s -1 (Hall B)

JLab Spin Experiments Results: – Spin in the valence (high-x) region – Quark-Hadron duality – Moments: Spin Sum Rules and Polarizabilities – Higher twists: g 2 /d 2 Just completed: – GDH on the proton at very low Q 2 ; – Transversity (n) Planned at 6 GeV – g 2 p at low Q 2 Future: 12 GeV – Inclusive: A 1 /d 2, – Semi-Inclusive: Transversity, TMDs, Flavor- decomposition Review: Kuhn, Chen, Leader, arXiv: , PPNP 63 (2009) 1

Longitudinal Spin (I) Spin in Valence (high-x) Region (where we can test pQCD and models such as RCQM)

Valence (high-x) A 1 p and A 1 n results Hall B CLAS, Phys.Lett. B641, 11 (2006) Hall A E99-117, PRL 92, (2004) PRC 70, (2004) pQCD with HHC RCQM RCQM

Data for Dq/q Before JLabWith E99117 Data pQCD with HHC (HERMES data at large x not shown)

Inclusive Hall A and B and Semi-Inclusive Hermes BBS (pQCD w/ HHC) BBS+OAM PRL99, (2007) pQCD with Quark Orbital Angular Momentum

A 1 p at 11 GeV Projections for JLab at 11 GeV

Quark Hadron Duality in Spin Structure Function = ? Longitudinal Spin (II)

Duality in Spin-Structure: CLAS EG1b Results Phys.Rev.C75:035203,2007

A 1 3He (resonance vs DIS) Duality in Spin-Structure: Hall A E Results PRL 101, (2008)  1 resonance comparison with pdfs  integrated over resonances covered by the data, from the pion threshold to an x min corresponding to W=1.905 GeV

Parton Distributions (CTEQ6 and DSSV) DSSV, PRL101, (2008) CTEQ6, JHEP 0207, 012 (2002) Polarized PDFs Unpolarized PDFs

Moments of Spin Structure Functions  Sum Rules Global Property Spin Sum Rules for First Moments

Bjørken Sum Rule g A : axial vector coupling constant from neutron b-decay C NS : Q 2 -dependent QCD corrections (for flavor non-singlet) A fundamental relation relating an integration of spin structure functions to axial-vector coupling constant Based on Operator Product Expansion within QCD or Current Algebra, plus isospin invariance. Valid at large Q 2 (where higher-twist effects negligible) Data are consistent with the Bjørken Sum Rule at 5-10% level

Gerasimov-Drell-Hearn Sum Rule Circularly polarized photon on longitudinally polarized nucleon A fundamental relation between the nucleon spin structure and its anomalous magnetic moment Based on general physics principles Lorentz invariance, gauge invariance  low energy theorem unitarity  optical theorem causality  unsubtracted dispersion relation applied to forward Compton amplitude First measurement on proton up to 800 MeV (Mainz) and up to 3 GeV (Bonn) agree with GDH with assumptions for contributions from un- measured regions. New measurements from LEGS provided complimentary results on the proton, more precise results on the deuteron.

Generalized GDH Sum Rule Many approaches: Anselmino, Ioffe, Burkert, Drechsel, … Ji and Osborne (J. Phys. G27, 127, 2001): Forward Virtual-Virtual Compton Scattering Amplitudes: S 1 (Q 2,n), S 2 (Q 2,n) Same assumptions: no-subtraction dispersion relation optical theorem (low energy theorem)

Connecting GDH and Bjorken Sum Rules Q 2 -evolution of GDH Sum Rule provides a bridge linking strong QCD to pQCD Bjorken and GDH sum rules are two limiting cases High Q 2, Operator Product Expansion : S 1 (p-n) ~ g A  Bjorken Q 2 ~0, Low Energy Theorem: S 1 ~ k 2  GDH High Q 2 (> ~1 GeV 2 ): Operator Product Expansion Intermediate Q 2 region: Lattice QCD calculations Low Q 2 region (< ~0.1 GeV 2 ): Chiral Perturbation Theory Calculations: HB  PT: Ji, Kao, Osborne, Spitzenberg, Vanderhaeghen RB  PT :  Bernard, Hemmert, Meissner Reviews: Theory: Drechsel, Pasquini, Vanderhaeghen, Phys. Rep. 378,99 (2003) Experiments: Chen, Deur, Meziani, Mod. Phy. Lett. A 20, 2745 (2005)

JLab E (Hall A) Neutron spin structure moments and sum rules Q 2 evolution of neutron spin structure moments (sum rules) with pol. 3 He transition from quark- gluon to hadron Test  PT calculations Results published in several PRL/PLB’s GDH integral on neutron PRL 89 (2002) Q2Q2

EG1b, PLB672, 12 (2009) EG1a, PRL 91, (2003) 1p1p JLab CLAS Eg1a/Eg1b (Hall B) Proton spin structure moments and sum rules

E94-010, from 3 He, PRL 92, (2004) E97-110, from 3 He, preliminary EG1a, EG1b: from d-p very low Q 2 ! 1n1n Test fundamental understanding Test cPT at very low Q 2 GDH Sum and Spin Structure Function Moments at very low Q 2

JLab CLAS EG4 (Hall B) Proton and deuteron spin structure moments and sum rules at very Low Q 2 Expected statistical accuracy from EG4 Ran in 2006 Data being analyzed

 1 of p-n – Bjorken Sum EG1b, PRD 78, (2008) E EG1a: PRL 93 (2004) agree well with cPT pQCD w/o HT corrections agree with data surprisingly well down to Q 2 =1 GeV 2.

Effective Strong Coupling Constant A new attempt at low Q 2 Experimental Extraction of a S from Bjorken Sum

 s (Q) is well defined in pQCD at large Q 2. Can be extracted from data (e.g. Bjorken Sum Rule). Not well defined at low Q 2, diverges at L QCD The strong coupling constant from pQCD

Generalized Bjorken sum rule: Definition of effective QCD couplings PLB B95 70 (1980); PRD (1984); PRD (1989). Prescription: Define effective couplings from a perturbative series truncated to the first term in  s. Use to define an effective  s g1. Process dependent. But can be related through “Commensurate scale relations” S.J. Brodsky & H.J Lu, PRD (1995)‏ S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, H.J Lu, PLB (1996)‏ Extend it to low Q 2 down to 0: include all higher twists.

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) first attempt of effective a S extraction at low Q 2 no strong Q 2 dependence of strong force at large distances

“Comparison” with theory ↔ Fisher et al. Bloch et al. Maris-Tandy Bhagwat et al. Cornwall Godfrey-Isgur: Constituant Quark Model Furui & Nakajima: Lattice de Teramond et al: AdS/CFT (preliminary) Schwinger -Dyson the conformality (no Q 2 dependence) may imply that it's possible to use AdS/CFT correspondance to calculate strong interaction at low Q 2.

Transverse Spin (I): Inclusive g 2 Structure Function and Moments Burkhardt - Cottingham Sum Rule

g 2 : twist-3, q-g correlations Experiments: transversely polarized target SLAC E155x, (p/d) JLab Hall A (n), Hall C (p/d) g 2 leading twist related to g 1 by Wandzura-Wilczek relation g 2 -g 2 WW : a clean way to access twist-3 contribution, quantify q-g correlations.

Precision Measurement of g 2 n (x,Q 2 ): Search for Higher Twist Effects Measure higher twist, study quark-gluon correlations. PRL 95, (2005)

BC Sum Rule P N 3 He BC = Meas+low_x+Elastic 0<X<1 :Total Integral “low-x”: unmeasured low x part of the integral. Assume Leading Twist behaviour Elastic: From well known form factors (<5%) “Meas”: Measured x-range Brown: SLAC E155x Red: Hall C RSS Black: Hall A E Green: Hall A E (preliminary) Blue: Hall A E (preliminary) very preliminary

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

Spin Polarizabilities Higher Moments of Spin Structure Functions at Low Q 2

Higher Moments: Generalized Spin Polarizabilities (how nucleons respond to virtual photons) generalized forward spin polarizability  0 generalized longitudinal-transverse spin polarizability  LT

Neutron Spin Polarizabilities   LT insensitive to  resonance Significant disagreement between data and both cPT calculations for  LT Good agreement with MAID model predictions  0  LT Q2 Q2 Q2 Q2 E94-010, PRL 93 (2004)

Proton Spin Polarizability Only longitudinal data, model for transverse (g 2 )  0 sensitive to resonance Large discrepancies with cPT! 0p0p  0 p Q 6 PLB672, 12 (2009)

Summary of Comparison with  PT Results on GDH sum, G 1 p, G 1 n, G 1 p-n in general agree well with at least one of the cPT calculations;  LT puzzle:  LT not sensitive to , one of the best quantities to test  PT, data disagree with all calculations (HB  PT, RB  PT/D) by several hundred %! A challenge to  PT theorists. Very low Q 2 data g 1 /g 2 on n( 3 He) (E97-110), also g 1 on p and D available soon (EG4) Recently approved: g 2 on proton E08-027

Color Polarizabilities and Higher Twists Higher Moments of Spin Structure Functions at High Q 2

Color Polarizabilities and Higher Twists leading twist (twist 2) higher twists leading twist, can be obtained from moments of g 1 twist-3, can be obtained from moments of g2 twist-4

X. Zheng, October 17, 2009 BROWN : E155, PLB. 553 (2003) 18 BLACK : E94010, PRL. 92 (2004) RED : RSS. PRL 98(2007) Magenta: E99-117, PRC 70(2004) Existing World Data on d 2 : PROTON NEUTRON d 2 (Q 2 )

X. Zheng, October 17, 2009 MAID Model stat only NEUTRON Some preliminary data RED : RSS. (Hall C, NH 3,ND 3 ) arXiv: BLUE: E (Hall A, 3 He) preliminary GREEN: E (Hall A, 3 He) courtesy of V. Sulkosky very preliminary d 2 (Q 2 ) other ongoing analysis: Hall C “SANE” - for the proton Hall A “d2n”

50 Proton: nucl-ex/ Phys.Lett.B613: ,2005 Phys.Rev.Lett.93:212001,2004 fit Q 2 = GeV 2, Neutron Proton-Neutron Color Polarizabilities and Higher Twists fit Q 2 = GeV 2, For both proton and neutron, the value indicates the m 4 term roughly cancel with m 6 term, i.e. the total higher twist effect is small, down to Q 2 =1 GeV 2. EG1b result in preparation, higher precision data are expected.

CHL-2 Upgrade magnets and power supplies Enhance equipment in existing halls 6 GeV CEBAF Add new hall

Solenoid spectrometer for SIDIS at 11 GeV GEMs Proposed for PVDIS at 11 GeV

Polarized 3He Target Performance Courtesy of Chiranjib Dutta figure credit: C. Dutta

Several Target Groups: JLab, UVa, W&M, Temple, Kentucky, UNH,... Polarized 3He Target Performance

Summary Spin structure study full of surprises and puzzles A decade of experiments from JLab: exciting results valence spin structure, quark-hadron duality spin sum rules, polarizabilities, and extraction of effective a S test  PT calculations,  ‘  LT puzzle’ precision measurements of g 2 /d 2 : higher twists first quasi-elastic target SSA: 2-photon to probe GPDs JLab plays a major role in recent experimental efforts shed light on our understanding of strong + QCD Bright future complete a chapter in spin structure study with 6 GeV 12 GeV Upgrade will greatly enhance our capability Goal: a full understanding of nucleon structure and strong interaction