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Transverse spin and 3-D Parton Structure of Nucleon Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 5/24/2017 1 Exploring nucleon is of fundamental in Science Search for New Physics Fundamental question of our universe Mass, energy-momentum, Spin structure, … Jlab, RHIC, Tevatron, LHC,… Nucleon Structure How nuclei formed from nucleons, etc.. FRIB (RIA), Jlab, … Study the strong interaction physics Partonic Structure 5/24/2017 QCD dynamics: confinement Factorization, universality,… 2 Feynman Parton Model Hadronic reactions Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon ElectronIon Collider 12 GeV JLab 5/24/2017 3 Extension to transverse direction… Semi-inclusive measurements Transverse momentum dependent (TMD) parton distributions Deeply Virtual Compton Scattering and Exclusive processes Generalized parton distributions (GPD) 5/24/2017 4 Quantum phase space distribution Wigner distributions Ji: PRL91,062001(2003) After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs 5 3D image of quarks at fixed-x 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 Straightforward extension Spin average, helicity, and transversity distributions Transverse momentum-spin correlations Nontrivial distributions, STXPT, ST.PT In quark model, depends on S- and P-wave interference 5/24/2017 7 Motivations… Nucleon Structure, spin correlation, orbital motion of quarks and gluon Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,… Single spin asymmetry (SSA) phenomena 8 Where can we learn TMDs Semi-inclusive hadron production in deep inelastic scattering (SIDIS) Drell-Yan lepton pair production in pp scattering Di-jet (photon+jet) correlation in pp scattering Relevant e+e- annihilation processes Many others… 5/24/2017 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 Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 11 5/24/2017 Two major contributions Sivers effect in the distribution ST kT P Collins effect in the fragmentation (zk+pT) (k,sT) ST (PXkT) ~pTXsT Other contributions… 5/24/2017 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 5/24/2017 13 Model calculations of the Collins Effects Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!! 14 5/24/2017 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 5/24/2017 Extend to two-gluon exchange Universality preserved 5/24/2017 16 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 5/24/2017 17 Sivers effect is different It is the final state interaction providing a phase to the nonzero SSA Ward identity is not easy to apply Non-universality in general Only in special case, we have “Special Universality” Brodsky,Hwang,Schmidt 02 Collins, 02; Ji,Yuan,02; Belitsky,Ji,Yuan,02 DIS and Drell-Yan Initial state vs. final state interactions * * Drell-Yan DIS HERMES “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 5/24/2017 http://spin.riken.bnl.gov/rsc/ QCD Dynamics TRANSVERSE MOMENTUM DEPENDENCE Transition from Perturbative region to Nonperturbative region Compare different region of PT Nonperturbative TMD Perturbative region 22 Perturbative tail is calculable Transverse momentum dependence Power counting, Brodsky-Farrar, 1973 Integrated Parton Distributions Twist-three functions 5/24/2017 23 A unified picture Transverse momentum dependent Collinear/ longitudinal QCD PT << 5/24/2017 PT << Q Ji-Qiu-Vogelsang-Yuan,2006 Yuan-Zhou, 2009 24 NLO corrections to SSA Vogelsang-Yuan, arXiv:0904.0410 SSA in Drell-Yan as an example, Collinear factorization Collinear functions, evolution: Kang-Qiu, 08; Zhou-Yuan-Liang 08 5/24/2017 25 Future perspective Current and planed experiments will have more and more data on various transverse spin observables Recent developments have laid solid theoretical ground to apply QCD theory to study the relevant nucleon structure Quark transversity Orbital motion of quarks and gluon 5/24/2017 26 Semi-Inclusive DIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 27 5/24/2017 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 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 30 Two mechanisms in QCD Spin-dependent transverse momentum dependent (TMD) function S k T Sivers T Sivers function ~ ST (PXkT) 90 . P 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 31 Quantum Phase Space Distribution Wigner operator 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 Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman 33 (96&98) Three classes in the view of a quark model S-wave Unpolarized, helicity, transversity S-P interference g1T, h1L f1T┴, h1┴ P-P or S-D interference h1T┴ Miller 07, Burkardt 07, Avakian et al 08. 5/24/2017 34