Transverse Spin Physics: Recent Developments Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 4/25/2017

Transverse spin physics Goal Quark transversity distributions Orbital motion of quarks and gluons? Single transverse spin asymmetry Various transverse momentum dependent physics (additional information on nucleon structure) Sivers function (PDF) Collins function (FF) …

Outline Introduction: single transverse spin phenomena Universality of the Collins Mechanism Non-universality of the Sivers effects Conclusion 4/25/2017

What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA)

Single Spin Asymmetry Motivations: Its strong tied with the quark orbital angular momentum We have beautiful data Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…

SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!!

Why Does SSA Exist? Single Spin Asymmetry requires Helicity flip: one must have a reaction mechanism for the hadron to change its helicity (in a cut diagram) A phase difference: the phase difference is needed because the structure S ·(p × k) violate the naïve time-reversal invariance

Naïve parton model fails If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978), It is in general suppressed by αSmq/Q We have to go beyond this naïve picture

Two mechanisms in QCD Spin-dependent transverse momentum dependent (TMD) function Sivers 90 Brodsky,Hwang,Schmidt, 02 (FSI) Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03 Boer-Mulders-Pijlman,03 Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04 Twist-3 quark-gluon correlations (coll.) Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98 kT ST Sivers function ~ ST (PXkT) . P

Two major contributions Sivers effect in the distribution Collins effect in the fragmentation Other contributions… kT ST ST (PXkT) P (zk+pT) (k,sT) ~pTXsT 4/25/2017

Semi-Inclusive DIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 4/25/2017

Universality of the Collins Fragmentation 4/25/2017

Collins effects in e+e- Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06 4/25/2017

Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, arXiv:0709.3272 [hep-ph] 4/25/2017

Simple model a la Collins 93 Phase information in the vertex or the quark propagator Collins-93 e+e- annihilation Semi-inclusive DIS Hadron in a jet in pp Universality of the Collins Function!! 4/25/2017

One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!! 4/25/2017

Similar arguments for pp collisions By using the Ward Identity: same Collins fun. Conjecture: the Collins function will be the same as e^+e^- and SIDIS 4/25/2017

Extend to two-gluon exchange Universality preserved 4/25/2017

Extract the quark transversity from e+e- and SIDIS expreiments [1] Soffer et al. PRD 65 (02) [2] Korotkov et al. EPJC 18 (01) [3] Schweitzer et al., PRD 64 (01) [4] Wakamatsu, PLB 509 (01) [5] Pasquini et al., PRD 72 (05) [6] Anselmino et al., PRD 75 (07)

Key observations Final state interactions DO NOT provide a phase for a nonzero SSA Eikonal propagators DO NOT contribute to a pole Ward identity is applicable to warrant the universality arguments 4/25/2017

Predictions at RHIC Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98 Collins function: fit to the HERMES data, Vogelsang-Yuan, 05 4/25/2017

Collins contribution to SSA in inclusive hadron pp--> Pi X Add a soft contribution ~Pt Leading jet fragmentation contribution Lower cut for the jet (>1GeV), upper cut for the fragmentation (<1GeV) 4/25/2017

Recent STAR data May indicate the importance of the soft contribution 4/25/2017

Sivers effect is different It is the final state interaction providing the phase to a nonzero SSA Ward identity is not easy to apply Non-universality in general Only in special case, we have “Special Universality” 4/25/2017

DIS and Drell-Yan Initial state vs. final state interactions “Universality”: fundamental QCD prediction * * DIS Drell-Yan HERMES

A unified picture for SSA In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P At large P, SSA is dominated by twist-3 correlation effects At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

A difficulty at next-leading-power (1/Q) Mismatch at low and high transverse momentum SIDIS at 1/Q Bacchetta-Boer-Diehl-Mulders, 0803.0227 The factorization needs to be carefully examined at this order Earlier works indicates possible problems Afanasev-Carlson, PRD, 2006 Gamberg-Hwang-Metz-Schlegel, PLB, 2006 4/25/2017

Experiment SIDIS vs Drell Yan HERMES Sivers Results RHIC II Drell Yan Projections Markus Diefenthaler DIS Workshop Munich, April 2007 0.1 0.2 0.3 x http://spin.riken.bnl.gov/rsc/ 4/25/2017

Non-universality: Dijet-correlation at RHIC Proposed by Boer-Vogelsang Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07; Bacchetta, et al, photon-jet correlation, 07 Initial state and/or final state interactions? Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hep-ph/0505268, hep-ph/0601171, hep-ph/0609206 Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196 Collins-Qiu, arXiv:0705.2141  Voglesang-Yuan, arXiv:0708.4398 Collins, arXiv:0708.4410 Bomhof-Mulders, arXiv:0709.1390 Factorization? Universality?

The simple picture does not hold for two-gluon exchanges Qiu,Collins, 0705.4121; Vogelang-Yuan, 0708.4398; Collins, 0708.4410 Integrated over transverse momentum Becchetta-Bomhof-Mulders-Pijlman, 04-06 4/25/2017

Another example: Heavy flavor production Heavy quarkonium production (gg channel) ep scattering No SSA in color-singlet model Final state interaction in color-octet model pp scattering Only initial state interaction in color-singlet ISI and FSI cancel out in color-octet Open charm or beauty Different SSAs for charm and anti-charm 4/25/2017

Color-singlet model Final state interactions with quark and anti-quark cancel out each other, no SSA in color-singlet model 4/25/2017

Color-octet model Final state interactions can be summarized into a gauge link to infinity, nonzero SSA 4/25/2017

pp scattering Color-singlet model: only initial state interaction, non-zero SSA Color-octet model: initial and final state interactions cancel out, no SSA 4/25/2017

J/Psi Production at lower energy (JPARC or FAIR) Quark-channel dominates Color-singlet: only initial state interaction contributes, -1/2Nc relative to Drell-Yan Color-octet: both initial and final state interactions contribute, -(Nc^2+1)/2Nc relative to DY 4/25/2017 DPN Meeting 2007

JPARC prediction Final A_N depends on the weight of the quark-channel contribution Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05 4/25/2017 DPN Meeting 2007

Heavy quark SSA ~1/4Nc ~(Nc^2-2)/4Nc ~2/4Nc ISI: contribute to quark and anti-quark ~1/4Nc FSI: contribute to quark ~(Nc^2-2)/4Nc FSI: contribute to anti-quark ~2/4Nc 4/25/2017 DPN Meeting 2007

A factor ~4 difference between charm and anticharm At JPARC, the quark channel contributes ~60% for charm cross sections 4/25/2017 DPN Meeting 2007

FAIR at GSI 4/25/2017 DPN Meeting 2007

Summary We are in the early stages of a very exciting era of transverse spin physics studies, where the future RHIC, JLAB, JPARC, FAIR, and EIC experiments will certainly play very important roles We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion

What can we learn from SSA Quark Orbital Angular Momentum e.g, Sivers function ~ the wave function amplitude with nonzero orbital angular momentum! Vanishes if quarks only in s-state! Ji-Ma-Yuan, NPB03 Brodsky-Yuan, PRD06

Take Drell-Yan as an example (with non-zero transverse momentum q?) We need a loop to generate a phase + + + + - - + + Twist-three Correlations Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98 Kane et al., hard parton model

Further factorization (q?<<Q) The collinear gluons dominate q?<<Q Transverse Momentum Dependent distributions Sivers, 90, Collins, 93,02 Brodsky-Hwang-Schmidt,02 Ji-Qiu-Vogelsang-Yuan,06 Twist-three Correlations Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98

New challenge from STAR data (2006) Talks by Ogawa and Nogach in SPIN2006 4/25/2017 Users Meeting, BNL

Extend to all other TMDs: large Pt power counting kt-even distributions have the same dependence on kt kt-odd distributions are suppressed at large kt Power Counting Rule kt-even: 1/kt2 kt-odd: 1/kt4

SIDIS cross sections at large Pt

Transition from Perturbative region to Nonperturbative region? Compare different region of PT Nonperturbative TMD Perturbative region

Twist-3 Fit to data RHIC STAR E704 BRAMHS Kouvaris,Qiu,Vogelsang,Yuan, 06

Compare to 2006 data from RHIC J.H. Lee, SPIN 2006