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Transverse Partonic Structure of the Proton Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 5/24/2017 1 5/24/2017 90 00 2 (non)Universality unify Factorization BJY Collins BHS Mulders et al. Collins 80 Qiu-Sterman Jaffe-Ji Sivers CSS Efremove-Teryav Collins-Soper Ralston-Soper RHIC RHIC JLab … BELLE COMPASS HERMES E704,pp to Pi Bunce,Lambda Transverse spin physics Transverse spin physics Goal Quark transversity distributions Orbital motion of quarks and gluons? Transverse partonic structure of proton Various transverse momentum dependent physics (additional information on nucleon structure) Sivers function (PDF) Collins function (FF) … 3 Transverse Momentum Dependent Parton Distributions Nucleon Structure, connection to GPDs, quantum phase space distribution Single spin asymmetry phenomena Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,… 4 Connection between TMD and GPD Wigner distributions Ji: PRL91,062001(2003) After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs 5 Quantum Phase-Space Distributions of Quarks Wp u(k,r) Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k “Mother” Wigner distributions FT TMD PDFs fpu(x,kT), TMD FFs Dup+(kT,z) Measure momentum transfer to quark Direct info about momentum distributions IPDs Wpu(x,rT),… PDFs fpu(x),… FFs Dup+(z) x=0 GPDs Hpu(x,x,t), GDAs Fudp+(x,x) Form Factors F1pu(t),F2pu(t ).. GPD Measure momentum transfer to target Direct info about spatial distributions Some PDFs same in exclusive and semi-inclusive analysis H.Avakian, Nov 19, 2004 6 TMD Distribution: the definition Gauge Invariance requires the Gauge Link Brodsky,Hwang,Schmidt 02’ Collins 02’ 7 Belitsky,Ji,Yuan 02’ Boer,Mulders,Pijlman, 03’ Polarized TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98) 8 Three classes in the view of a quark model S-wave Unpolarized, helicity, transversity S-P interference g_1T,h_1L f_1T^\perp, h_1^\perp P-P or S-D interference h_1T^\perp Miller 07, Burkardt 07, Avakian et al 08. 5/24/2017 EIC Meeting 2008 9 Lz≠0 Amplitude and Sivers Function All distributions can be calculated using the wave function. Sivers function: Lz=1 Lz=0 Similar expressions for others Ji, Ma, Yuan, Nucl. Phys. B (2003) 10 Where can we learn TMDs Semi-inclusive hadron production in deep inelastic scattering (SIDIS) Drell-Yan lepton pair production in pp scattering Relevant e+e- annihilation processes Many others… 5/24/2017 EIC Meeting 2008 11 Inclusive and Semi-inclusive DIS Inclusive DIS: Q Partonic Distribution depending on the longitudinal momentum fraction Semi-inclusive DIS: Q Probe additional information for parto transverse distribution in nucleon 12 Azimuthal Dependence in SIDIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations 13 5/24/2017 SIDIS Cross Section At leading power of 1/Q The structure functions depend on Q2, xB, z, PhT 14 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 15 Universality of the Collins Fragmentation 5/24/2017 16 Collins effects in e+e Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06 17 5/24/2017 Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, arXiv:0709.3272 [hep-ph] 18 5/24/2017 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!! 19 5/24/2017 One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!! 20 5/24/2017 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 21 5/24/2017 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 22 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” 5/24/2017 23 DIS and Drell-Yan Initial state vs. final state interactions * Drell-Yan * DIS HERMES “Universality”: fundamental QCD prediction 24 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/ Study QCD dynamics at different PT Region Integrate out PT (w/o weight) -- normal factorization, similar to inclusive DIS Large PT (>>QCD) -- hard gluon radiation, can be calculated from perturbative QCD Low PT (~QCD) -- nonperturbative information: TMD factorization formula 26 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 27 A difficulty at next-leadingpower (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 5/24/2017 28 Final PT Distribution PT dependence Sivers function at low Pt Qiu-Sterman Twist-three Which is valid for all Pt range SSA is suppressed by 1/Pt at large Pt 29 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 30 SIDIS cross sections at large Pt 1/Pt2 1/Pt4 1/Pt3 1/Pt5 31 Transition from Perturbative region to Nonperturbative region? Compare different region of PT Nonperturbative TMD Perturbative region 32 pp scattering experiments RHIC and RHIC II Collins effects, quark transversity Drell-Yan, quark Sivers Heavy flavor, gluon Sivers JPARC (pp collision at low energy) Drell-Yan, quark Sivers effects GSI-FAIR (ppbar collision) Drell-Yan, quark transversity Quark Sivers effects 5/24/2017 33 Summary We are in the early stages of a very exciting era of transverse spin physics studies, where the future JLAB, RHIC, 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 More work needs to be done 34 Quark distribution is deformed when nucleon is transversely polarized, because of the orbital motion y x This deformation will lead to a single transverse spin asymmetry (SSA), because of final state interactions y z Burkardt, 2003 35 Semi-Inclusive DIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 36 5/24/2017 What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA) 37 SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!! 38 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 39 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 40 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 41 Take Drell-Yan as an example (with non-zero transverse momentum q?) We need a loop to generate a phase + + + + - Kane et al., hard parton model + + - Twist-three Correlations Efremov-Teryaev, 82, 84 42 Qiu-Sterman, 91,98 Further factorization (q?<<Q) 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 43 Brodsky-Hwang-Schmidt,02 Ji-Qiu-Vogelsang-Yuan,06 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! Custom-made for high-energy processes In high-energy processes, one cannot measure k = (k0–kz) and therefore, one must integrate this out. The reduced Wigner distribution is a function of six variables [r,k=(k+ k)]. After integrating over r, one gets transversemomentum dependent parton distributions Alternatively, after integrating over k, one gets a spatial distribution of quarks with fixed Feynman momentum k+=(k0+kz)=xM. Collins from HERMES 46 Large, positive p+ asymmetries: no surprise from u-quark dominance Large, negative p asymmetries: first a surprise, now understood by large, negative disfavored Collins function Collins from COMPASS PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007 Smaller asymmetries than in proton case 47 First extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data By Anselmino et al., PRD 75 (07) Comparison with some models [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) Non-universality: Dijet-correlation at RHIC Proposed by Boer-Vogelsang Initial state and/or final state interactions? Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07 Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hepph/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? 50 The asymmetry could be related to that in DIS, only at the leading order (one-gluon exchange), qTDIS--- Sivers function from DIS qt--- imbalance of the dijet Hsivers depends on subprocess Qiu,Vogelsang,Yuan, 07 51 This simple picture does not hold for two-gluon exchanges Vogelang-Yuan, 0708.4398; Qiu,Collins, 0705.4121; Collins, 0708.4410 Similar calculations can be Shown for QCD 5/24/2017 Integrated over transverse momentum DPN Meeting 2007 52