Transverse Spin Physics Recent Developments Feng Yuan Lawrence

Transverse Spin Physics: Recent Developments Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 9/16/2020 1

Transverse spin physics n Goal ¨ Quark transversity distributions ¨ Orbital motion of quarks and gluons? n Single transverse spin asymmetry ¨ Various transverse momentum dependent physics (additional information on nucleon structure) ¨ Sivers function (PDF) ¨ Collins function (FF) ¨… 2

Outline Introduction: single transverse spin phenomena n Universality of the Collins Mechanism n Non-universality of the Sivers effects n Conclusion n 3 9/16/2020

What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA) 4

Single Spin Asymmetry n 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, … 5

SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!! 6

Why Does SSA Exist? n 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 7

Naïve parton model fails n If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978), ¨ It n is in general suppressed by αSmq/Q We have to go beyond this naïve picture 8

Two mechanisms in QCD n Spin-dependent transverse momentum dependent (TMD) function S k T ¨ Sivers T Sivers function ~ ST (PXk. T) 90. P ¨ Brodsky, Hwang, Schmidt, 02 (FSI) ¨ Gauge Property: Collins 02; Belitsky-Ji-Yuan, NPB 03 Boer-Mulders-Pijlman, 03 ¨ Factorization: Ji-Ma-Yuan, PRD 04; Collins, Metz, 04 n Twist-3 quark-gluon correlations (coll. ) ¨ Efremov-Teryaev, 82, 84 ¨ Qiu-Sterman, 91, 98 9

Two major contributions n Sivers effect in the distribution ST k. T P n Collins effect in the fragmentation (zk+p. T) (k, s. T) n ST (PXk. T) ~p. TXs. T Other contributions… 9/16/2020 10

Semi-Inclusive DIS n n Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 11 9/16/2020

Universality of the Collins Fragmentation 9/16/2020 12

Collins effects in e+en Reliable place to extract the information on the Collins fragmentation function Belle Col. , PRL 06 13 9/16/2020

Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, ar. Xiv: 0709. 3272 [hep-ph] 14 9/16/2020

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!! 15 9/16/2020

One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!! 16 9/16/2020

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 17 9/16/2020

Extend to two-gluon exchange Universality preserved 9/16/2020 18

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

Key observations Final state interactions DO NOT provide a phase for a nonzero SSA n Eikonal propagators DO NOT contribute to a pole n Ward identity is applicable to warrant the universality arguments n 9/16/2020 20

Predictions at RHIC Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98 Collins function: fit to the HERMES data, Vogelsang-Yuan, 05 21 9/16/2020

Collins contribution to SSA in inclusive hadron pp--> Pi X Add a soft contribution ~Pt • Leading jet fragmentation contribution • Lower cut for the jet (>1 Ge. V), upper cut for the fragmentation (<1 Ge. V) 9/16/2020 22

Recent STAR data n May indicate the importance of the soft contribution 9/16/2020 23

Sivers effect is different It is the final state interaction providing the phase to a nonzero SSA n Ward identity is not easy to apply n Non-universality in general n Only in special case, we have “Special Universality” n 9/16/2020 24

DIS and Drell-Yan n Initial state vs. final state interactions * Drell-Yan * DIS HERMES n “Universality”: fundamental QCD prediction 25

A unified picture for SSA n 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 n The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan, Phys. Rev. Lett. 97: 082002, 2006 26

A difficulty at next-leadingpower (1/Q) n Mismatch at low and high transverse momentum SIDIS at 1/Q ¨ n Bacchetta-Boer-Diehl-Mulders, 0803. 0227 The factorization needs to be carefully examined at this order ¨ Earlier n n works indicates possible problems Afanasev-Carlson, PRD, 2006 Gamberg-Hwang-Metz-Schlegel, PLB, 2006 9/16/2020 27

Experiment SIDIS vs Drell Yan HERMES Sivers Results RHIC II Drell Yan Projections 0 0 Markus Diefenthaler DIS Workshop Munich, April 2007 0. 1 0. 2 0. 3 x 9/16/2020 http: //spin. riken. bnl. gov/rsc/

Non-universality: Dijet-correlation at RHIC n Proposed by Boer-Vogelsang ¨ n Initial state and/or final state interactions? ¨ ¨ ¨ n Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07; Bacchetta, et al, photon-jet correlation, 07 Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hepph/0505268, hep-ph/0601171, hep-ph/0609206 Qiu-Vogelsang-Yuan, ar. Xiv: 0704. 1153; 0706. 1196 Collins-Qiu, ar. Xiv: 0705. 2141 Voglesang-Yuan, ar. Xiv: 0708. 4398 Collins, ar. Xiv: 0708. 4410 Bomhof-Mulders, ar. Xiv: 0709. 1390 Factorization? Universality? 29

The simple picture does not hold for two-gluon exchanges Qiu, Collins, 0705. 4121; Vogelang-Yuan, 0708. 4398; Collins, 0708. 4410 Becchetta-Bomhof-Mulders-Pijlman, 04 -06 9/16/2020 Integrated over transverse momentum 30

Another example: Heavy flavor production n Heavy quarkonium production (gg channel) ¨ ep scattering No SSA in color-singlet model n Final state interaction in color-octet model n ¨ pp scattering Only initial state interaction in color-singlet n ISI and FSI cancel out in color-octet n n Open charm or beauty ¨ Different SSAs for charm and anti-charm 9/16/2020 31

Color-singlet model Final state interactions with quark and anti-quark cancel out each other, no SSA in color-singlet model 9/16/2020 32

Color-octet model Final state interactions can be summarized into a gauge link to infinity, nonzero SSA 9/16/2020 33

pp scattering • Color-singlet model: only initial state interaction, non-zero SSA • Color-octet model: initial and final state interactions cancel out, no SSA 9/16/2020 34

J/Psi Production at lower energy (JPARC or FAIR) n Quark-channel dominates ¨ Color-singlet: only initial state interaction contributes, -1/2 Nc relative to Drell-Yan ¨ Color-octet: both initial and final state interactions contribute, -(Nc^2+1)/2 Nc relative to DY 9/16/2020 DPN Meeting 2007 36

JPARC prediction Final A_N depends on the weight of the quark-channel contribution n Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05 9/16/2020 DPN Meeting 2007 37

Heavy quark SSA ISI: contribute to quark and anti-quark ~1/4 Nc FSI: contribute to quark ~(Nc^2 -2)/4 Nc FSI: contribute to anti-quark ~2/4 Nc 9/16/2020 DPN Meeting 2007 38

A factor ~4 difference between charm and anticharm At JPARC, the quark channel contributes ~60% for charm cross sections 9/16/2020 DPN Meeting 2007 39

FAIR at GSI 9/16/2020 DPN Meeting 2007 40

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 n We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion n 41

What can we learn from SSA n 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, NPB 03 Brodsky-Yuan, PRD 06 42

Take Drell-Yan as an example (with non-zero transverse momentum q? ) n We need a loop to generate a phase + + + - Kane et al. , hard parton model + + + - Twist-three Correlations Efremov-Teryaev, 82, 84 43 Qiu-Sterman, 91, 98

Further factorization (q? <<Q) n The collinear gluons dominate q? <<Q Twist-three Correlations Efremov-Teryaev, 82, 84 Qiu-Sterman, 91, 98 Transverse Momentum Dependent distributions Sivers, 90, Collins, 93, 02 44 Brodsky-Hwang-Schmidt, 02 Ji-Qiu-Vogelsang-Yuan, 06

New challenge from STAR data (2006) Talks by Ogawa and Nogach in SPIN 2006 9/16/2020 Users Meeting, BNL 45

Extend to all other TMDs: large Pt power counting kt-even distributions have the same dependence on kt-odd distributions are suppressed at large kt n Power Counting Rule n kt-even: 1/kt 2 kt-odd: 1/kt 4 46

SIDIS cross sections at large Pt 1/Pt 2 1/Pt 4 1/Pt 3 1/Pt 5 47

Transition from Perturbative region to Nonperturbative region? n Compare different region of PT Nonperturbative TMD Perturbative region 48

Twist-3 Fit to data RHIC STAR E 704 BRAMHS Kouvaris, Qiu, Vogelsang, Yuan, 06 49

Compare to 2006 data from RHIC J. H. Lee, SPIN 502006

51