Transverse Spin and TMDs from SIDIS with Transversely

Transverse Spin and TMDs from SIDIS with Transversely Polarized Nucleon Jian-ping Chen, Jefferson Lab INT-10 -3, EIC Program, Nov. 12, 2010 § Introduction § Longitudinal and Transverse Spin: Inclusive Scattering Polarized Structure, OAM, g 2/d 2, Higher-twists § Transverse Spin with SIDIS at JLab Preliminary neutron (3 He) results from 6 Ge. V experiment 12 Ge. V plan: 3 -d mapping § EIC simulations: 4 -d (x, z, PT, Q 2) projections p/K (quark/sea TMDs) (done by Min Huang/Xin Qian) D and D_bar (gluon TMDs) (done by Xin Qian) § Orbital Angular Momentum

Introduction Why EIC? Why do we care about transverse (spin) structure?

Why EIC? Why Transverse? • EIC: the ultimate machine to study quark gluon structure of nucleon/nuclear and strong interaction (QCD)? • WHY EIC? to our non-physics or non-nuclear physics friends: Breakthrough in understanding strong interaction (in strong region)? Full understanding of nucleon structure ? • Nucleon, most of the visible matter Dark effects also present (magnified) in strong interaction • We do not really know where or if it will have a breakthrough We are familiar (comfortable) with e-p (e-ion) • Most major modern discoveries not done as major facilities initially designed/intended for. • Need justification(s) for EIC, guess best case for it • What question(s) to address/to ask? Confinement? • Spin has provided many surprises Transverse: new ingredient to possible more surprises

Strong Interaction and QCD • Strong interaction, running coupling ~ 1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works (to certain level) at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size) as confinement v • theoretical tools: p. QCD, OPE, Lattice QCD, …, models, … A major challenge in fundamental physics: Understand QCD in strong interaction region Study and understand nucleon structure E

Nucleon Structure and QCD • Colors are confined in hadronic system • Nucleon: ideal lab to study QCD • Nucleon = u u d + sea + gluons • Mass: ~1 Ge. V, but u/d quark mass only a few Me. V each! Spin: ½, quarks contribute ~30% Spin Sum Rule(s) Orbital Angular Momentum Relations to GPDs and TMDs? • Quarks and gluon field are in-separable • Spin-orbit correlations • Multi-parton correlations • Transverse dimension is crucial for a full understanding of nucleon structure and QCD, help understanding confinement • • Complexity vs. simplicity: beauty in physics Precision: key to possible new understanding Not JUST imaging as in tomography !

Nucleon Spin Structure Spin, Orbit Angular Momentum, Higher-Twists: quark-gluon correlations

Polarized Structure Functions and PDFs DSSV, PRL 101, 072001 (2008)

Spin Asymmetries in Valence (High-x) Region Hall B CLAS, Phys. Lett. B 641 (2006) 11 Hall A E 99 -117, PRL 92, 012004 (2004) PRC 70, 065207 (2004)

p. QCD with Quark Orbital Angular Momentum F. Yuan, H. Avakian, S. Brodsky, and A. Deur, ar. Xiv: 0705. 1553 Inclusive Hall A and B and Semi-Inclusive Hermes BBS+OAM

Transverse Spin in Inclusive Scattering: g 2 (Color Polarizability) or Lorentz Force: d 2 • B-C Sum Rule • 2 nd moment of g 2 -g 2 WW d 2: twist-3 matrix element

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, 142002 (2005)

BC Sum Rule 0<X<1 : Total Integral P Brawn: SLAC E 155 x Red: Hall C RSS Black: Hall A E 94 -010 Green: Hall A E 97 -110 (preliminary) Blue: Hall A E 01 -012 (very preliminary) N ary in prelim BC = Meas+low_x+Elastic “Meas”: Measured x-range 3 He “low-x”: refers to unmeasured low x part of the integral. Assume Leading Twist Behaviour Elastic: From well know FFs (<5%)

d 2(Q 2) E 08 -027 “g 2 p” projected SANE 6 Ge. V Experiments Sane: recently completed in Hall C “g 2 p” in Hall A, 2011 LQCD “d 2 n” recently completed in Hall A

Twist-4 f 2 extraction and Color Polarizabilities • JLab + world n data, m 4 = (0. 019+-0. 024)M 2 • Twist-4 term m 4 = (a 2+4 d 2+4 f 2)M 2/9 • extracted from m 4 term f 2 = 0. 034+-0. 005+-0. 043 • Color polarizabilities/Lorentz force c. E = 0. 033+-0. 029 c. B = -0. 001+-0. 016 • Proton and p-n f 2= -0. 160+-0. 179 (p), -0. 136+-0. 109 (p-n) Review: Prog. Part. Nucl. Phys. 63, 1(2009) PLB 93 (2004) 212001

Transversity and TMDs What have we learned?

“Leading-Twist” TMD Quark Distributions Quark Nucleon Unpol. Long. Trans. Unpol. Long. Transversity Trans. Sivers worm-gear Pretzelocity

Pasquini, GPD 2010 GTMDs Wigner-Ds FT b FT TMDs GPDs spin densities FT PDs Form Factors charge densities

Separation of Collins, Sivers and pretzelocity effects through angular dependence in SIDIS

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

JLab 6 Ge. V Neutron Transversity Experiment: E 06 -010 Preliminary Results

E 06‑ 010 Experiment • First measurement on n (3 He) • Polarized 3 He Target • Polarized Electron Beam Luminosity Monitor – ~80% Polarization – Fast Flipping at 30 Hz – PPM Level Charge Asymmetry controlled by online feed back • Big. Bite at 30º as Electron Arm – Pe = 0. 7 ~ 2. 2 Ge. V/c • HRSL at 16º as Hadron Arm – Ph = 2. 35 Ge. V/c • 7 Ph. D Thesis Students (4 graduated this year) Beam Polarimetry (Møller + Compton) 21

JLab polarized 3 He target 15 u. A ülongitudinal, transverse and vertical üLuminosity=1036 (1/s) (highest in the world) üHigh in-beam polarization ~ 65% üEffective polarized neutron target ü 13 completed experiments 6 approved with 12 Ge. V (A/C)

Performance of 3 He Target • High luminosity: L(n) = 1036 cm-2 s-1 • Record high 65% polarization (preliminary) in beam with automatic spin flip / 20 min

Preliminary Asymmetry ALT Result To leading twist: • Preliminary 3 He ALT - Systematic uncertainty is still under work - Projected neutron ALT stat. uncertainty : 6~10%

Planned JLab 12 Ge. V Experiment: E 12 -10 -006 Precision 3 -d mapping in the valence region

Precision Study of Transversity and TMDs • From exploration to precision study • Transversity: fundamental PDFs, tensor charge • TMDs provide 3 -d structure information of the nucleon • Learn about quark orbital angular momentum • Multi-dimensional mapping of TMDs – 3 -d (x, z, P┴), limited Q 2 range. • Precision high statistics – high luminosity and large acceptance

Solenoid detector for SIDIS at 11 Ge. V Y[cm] Yoke Coil 3 He Target FGEMx 4 Aerogel LGEMx 4 LS Gas Chere nkov HG SH GEMx 2 PS Z[cm]

3 -d Mapping of Collins/Sivers Asymmetries 12 Ge. V With SOLID (L=1036) • Both p+ and p • For one z bin (0. 5 -0. 55) • Will obtain 8 z bins (0. 30. 7) • Upgraded PID for K+ and K-

Power of SOLID

EIC Simulation: p/K (Min Huang/Xin Qian) Precision 4 -d mapping in the sea quark region

DIS (electron) ØElectron: 2. 5°< ϴe < 150°Pe > 1. 0 Ge. V/c ØFull azimuthal-angular coverage DIS cut: Q 2 > 1 Ge. V 2 W > 2. 3 Ge. V 0. 8 > y > 0. 05 Capability to detect high momentum electron Q 2 > 1 Ge. V 2 ϴe > 5° No need to cover extreme forward angle for electron

EIC phase space 12 Ge. V: from approved So. LID SIDIS experiment Lower y cut, more overlap with 12 Ge. V 0. 05 < y < 0. 8

Study both Proton and Neutron ion momentum PN z Z/A Not weighted by Cross section. Flavor separation, Combine the data the lowest achievable x limited by the effective neutron beam and the PT cut

Cross Section in MC • Low PT cross section: • A. Bacchetta hep-ph/0611265 JHEP 0702: 093 (2007) • High PT cross section: • M. Anselmino et al. Eur. Phys. K. A 31 373 (2007) 6 x 6 Jacobian calculation • • PDF: CTEQ 6 M FF: Binneweis et al PRD 52 4947 <pt 2> = 0. 2 Ge. V 2 <kt 2> = 0. 25 Ge. V 2 NLO calculation at large PT – <pt 2> = 0. 25 Ge. V 2 – <kt 2> = 0. 28 Ge. V 2

• 11 + 60 Ge. V Projections with Proton on π+ 36 days L = 3 x 1034 /cm 2/s • 11 + 100 Ge. V 36 days L = 1 x 1034/cm 2/s For both above 2 x 10 -3 , Q 2<10 Ge. V 2 4 x 10 -3 , Q 2>10 Ge. V 2 • 3 + 20 Ge. V 36 days L = 1 x 1034/cm 2/s 4 x 10 -3 , Q 2<10 Ge. V 2 5 x 10 -3 , Q 2>10 Ge. V 2 Polarization 70% Overall efficiency 50% z: 12 bins 0. 2 - 0. 8 PT: 5 bins 0 -1 Ge. V φh angular coverage considered Show the average of Collins/Sivers/Pretzlosity projections Also π-

Projections with deuteron (neutron) • 11 + 60 Ge. V 72 days • 3 + 20 Ge. V 72 days D: 88% effective polarization

Projections with 3 He (neutron) • 11 + 60 Ge. V 72 days • 11 + 100 Ge. V 72 days • 12 Ge. V So. Lid 3 He: 87% effective polarization Equal stat. for proton and neutron (combine 3 He and D) 11 + 60 Ge. V 11 + 100 Ge. V 3+20 Ge. V P 36 d (3 x 1034/cm 2/s) 36 d (1 x 1034/cm 2/s) D 72 d 3 He 72 d

Proton π+ (z = 0. 3 -0. 7)

Proton K+ (z = 0. 3 -0. 7)

PT dependence (High PT) on p of π+ 10 bins 1 -- 10 Ge. V in log(PT)

EIC Simulation: D/D_bar (Xin Qian) Study Tri-gluon Correlations (Gluon TMDs)? Need update to take into account the new study by Kazuhiro Tanaka/Yuji Koike

Simulation • Use HERMES Tuned Pythia (From H. Avagyan) – Thanks to E. Aschenauer for providing input file for Charm production (Mc = 1. 65 Ge. V) • First try 11+60 configuration. • Physics includes: – VMD – Direct – GVMD – DIS (intrinsic charm) This is what we want!!

Event Generator • • Q 2: 1. -1500. y: 0. 05 -0. 9 LUND Fragmentation. Major decay channel of D meson is Branching ratio: 3. 8+0. 07%

D meson from Different Processes Dominated contamination is from GVMD, and then DIS at PT > 1 Ge. V Q 2 > 1 0. 9 > y > 0. 05 z > 0. 15 At large Q 2, contamination become smaller.

Decay Products and D meson Distribution D Dbar Electron, D meson, Dbar meson Pion vs kaon, momentum and polar angle.

D meson Reconstruction • Momentum res. : 0. 8 % * p /10 (Ge. V) • Polar angle res. : 0. 3 mr • Azimuthal angle res. : 1 mr – Thanks to R. Ent for providing these information. • 1. 8 Me. V invariant mass resolution. A better resolution would be desirable to reduce S/B. Background from random coincidence of pion and kaon in the final state. Naively,

144 Days @ L = 3 x 1034 on Proton 10 Ge. V > Momentum > 0. 6 Ge. V Polar angle > 10 degree 0. 9 > y > 0. 05; Q 2>1 Ge. V 2, PT > 1 Ge. V; z > 0. 15 Include decay of kaon and pion Additional 60% efficiency 80% polarization Sqrt(2) for angular separation. Dilution factor due to other processes and accidental pion and kaons. 2 x 2 bins in x and Q 2. D Dbar Calculations from Z. B. Kang D Dbar

Summary • • • Spin: from longitudinal to transverse Why transverse spin and transverse structure? What have we learned about TMDs? A beginning, surprises Preliminary results from 6 Ge. V neutron transversity experiment Planned 12 Ge. V • Precision 4 -d (x, z, PT, Q 2)mapping of TMDs in Valence quark region • Precision determination of tensor charge (LQCD) • EIC simulation/projections • • Ultimate coverage in kinematics, complete 4 -d (x, z, PT, Q 2) mapping for p/K Initial study on D/D_bar SIDIS Study sea and gluon TMDs Understudy QCD dynamics, spin-orbit correlations, multi-parton correlations • Orbital Angular Momentum • Lead to breakthroughs in a better understanding of nucleon structure and QCD

Quark Orbital Angular Momentum Definitions, Indirect Evidences, Experimental Observables, Models

Orbital Angular Momentum `Spin Crisis’ -> ~ 30%; G small so far Orbital angular momentum important from indirect experimental evidences Proton Form Factors A 1 ( d/d ) at high-x N-D transition … Definitions: A+=0 (light-cone) gauge (½)DS + Lq+ DG + Lg=1/2 (Jaffe) Gauge invariant (½)DS + Lq + JG =1/2 (Ji) § Ji’s sum rule -> GPDs (DVCS measurements), LQCD calculation § TMDs, Pretzelocity, Worm-gears, Sivers/Boer-Mulders. Model calculations What observable (more directly) corresponds to Lz~ bx X py Model independent relations?

Orbital Angular Momentum Pasquini, GPD 2010 1/2=(½)DS +Lqz+ JG not unique decomposition gauge invariant, but contains interactions through the gauge covariant derivative [ X. Ji, PRL 78, (1997) ] Ji’s sum rule quark orbital angular momentum: Lq = Jq - q not gauge invariant, but diagonal in the LCWFs basis [ R. L. Jaffe, NPB 337, (1990) ] in the light-cone gauge A+=0, model independent relations of Lqz with GPDs and TMDs

Distribution in x of Orbital Angular Momentum Pasquini, GPD 2010 Definition of Jaffe and Manohar: contribution from different partial waves TOT up down Lz=0 Lz=-1 Lz=+2 Comparison between the results with the Jaffe-Manohar definition and the results with the Ji definition (total results for the sum of up and down quark contribution) Jaffe-Manohar Ji

Orbital Angular Momentum v Definition of Jaffe and Manohar: contribution from different partial waves = 0 ¢ 0. 62 + (-1) ¢ 0. 14 + (+1) ¢ 0. 23 + (+2) ¢ 0. 018 = 0. 126 v Definition of Ji: [BP, F. Yuan, in preparation] [scalar diquark model: M. Burkardt, PRD 79, 071501 (2009)] Pasquini/Yuan

Pasquini, GPD 2010 GTMDs GPDs and TMDs probe the same overlap of quark LCWFs in different kinematics nucleon quark at » =0 UU UT LL TU TT TT LT 0 TL 0