Transverse spin and 3 D Parton Structure of

Transverse spin and 3 -D Parton Structure of Nucleon Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 9/30/2020 1

Exploring nucleon is of fundamental in Science Fundamental question of our universe Mass, energy-momentum, Spin structure, … Search for New Physics Jlab, RHIC, Tevatron, LHC, … Nucleon Structure How nuclei formed from nucleons, etc. . FRIB (RIA), Jlab, … Study the strong interaction physics Partonic Structure 9/30/2020 QCD dynamics: confinement Factorization, universality, … 2

Feynman Parton Model n Hadronic reactions Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon Electron. Ion Collider 12 Ge. V JLab 9/30/2020 3

Extension to transverse direction… n Semi-inclusive measurements ¨ Transverse momentum dependent (TMD) parton distributions n Deeply Virtual Compton Scattering and Exclusive processes ¨ Generalized parton distributions (GPD) 9/30/2020 4

Quantum phase space distribution n Wigner distributions Ji: PRL 91, 062001(2003) After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs 5

3 D image of quarks at fixed-x n GPDs can be used to picture quarks in the proton (Belitsky-Ji-Yuan, PRD 04) Beam direction z fm fm y x fm low x 6 moderate x high x

Transverse momentum dependent parton distribution n Straightforward extension ¨ Spin average, helicity, and transversity distributions n Transverse momentum-spin correlations ¨ Nontrivial distributions, STXPT, ST. PT ¨ In quark model, depends on S- and P-wave interference 9/30/2020 7

Motivations… ¨Nucleon Structure, spin correlation, orbital motion of quarks and gluon q. Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs, … q. Single spin asymmetry (SSA) phenomena 8

Where can we learn TMDs Semi-inclusive hadron production in deep inelastic scattering (SIDIS) n Drell-Yan lepton pair production in pp scattering n Di-jet (photon+jet) correlation in pp scattering n Relevant e+e- annihilation processes n Many others… n 9/30/2020 9

Inclusive and Semi-inclusive DIS JLab & EIC Inclusive DIS: Q Partonic Distribution depending on the longitudinal momentum fraction Semi-inclusive DIS: Q Probe additional information for parto transverse distribution in nucleon 10

JLab & EIC n n Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 11 9/30/2020

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… 9/30/2020 12

Universality of the Collins Fragmentation ep--> e Pi X e+e--> Pi Pi X pp--> jet(->Pi) X Metz 02, Collins-Metz 02, Yuan 07, Gamberg-Mukherjee-Mulders 08 Meissner-Metz 0812. 3783 Yuan-Zhou, 0903. 4680 9/30/2020 13

Model calculations of the Collins Effects Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!! 14 9/30/2020

Similar arguments for pp collisions Yuan, 0709. 3272 By using the Ward Identity: same Collins fun. The Collins function is the same as e^+e^- and SIDIS 15 9/30/2020

Extend to two-gluon exchange Universality preserved 9/30/2020 16

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 9/30/2020 17

Sivers effect is different It is the final state interaction providing a phase to the 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 Brodsky, Hwang, Schmidt 02 Collins, 02; Ji, Yuan, 02; Belitsky, Ji, Yuan, 02

DIS and Drell-Yan n Initial state vs. final state interactions * * Drell-Yan DIS HERMES n “Universality”: QCD prediction 19

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 9/30/2020 http: //spin. riken. bnl. gov/rsc/

QCD Dynamics TRANSVERSE MOMENTUM DEPENDENCE

Transition from Perturbative region to Nonperturbative region n Compare different region of PT Nonperturbative TMD Perturbative region 22

Perturbative tail is calculable n Transverse momentum dependence Power counting, Brodsky-Farrar, 1973 Integrated Parton Distributions Twist-three functions 9/30/2020 23

A unified picture Transverse momentum dependent Collinear/ longitudinal QCD PT << 9/30/2020 PT << Q Ji-Qiu-Vogelsang-Yuan, 2006 Yuan-Zhou, 2009 24

NLO corrections to SSA Vogelsang-Yuan, ar. Xiv: 0904. 0410 n SSA in Drell-Yan as an example, n Collinear factorization Collinear functions, evolution: Kang-Qiu, 08; Zhou-Yuan-Liang 08 9/30/2020 25

Future perspective Current and planed experiments will have more and more data on various transverse spin observables n Recent developments have laid solid theoretical ground to apply QCD theory to study the relevant nucleon structure n ¨ Quark transversity ¨ Orbital motion of quarks and gluon 9/30/2020 26

Semi-Inclusive DIS n n Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 27 9/30/2020

What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA) 28

SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!! 29

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 30

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 31

Quantum Phase Space Distribution n Wigner operator n Wigner distribution: “density” for quarks having position r and 4 -momentum k (off-shell) a la Saches 7 -dimensional distribtuion No known experiment can measure this!

Polarized TMD Quark Distributions Nucleon Quark Unpol. Long. Trans. Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98) 33

Three classes in the view of a quark model n S-wave ¨ Unpolarized, n helicity, transversity S-P interference ¨ g 1 T, h 1 L ¨ f 1 T┴, h 1┴ n P-P or S-D interference ¨ h 1 T┴ n Miller 07, Burkardt 07, Avakian et al 08. 9/30/2020 34