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2/11/20141 Transversity: Opportunities Now and Future Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

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Transverse spin physics 2/11/2014 HALL A Meeting 2007 2 80 90 00 Bunce, Lambda E704, pp to Pi HERMES RHIC COMPASS BELLE RHIC JLab Ralston-Soper Efremove-Teryav Sivers Jaffe-Ji Qiu-Sterman Collins BHS Collins BJY Factorization unify (non)Universality Mulders et al. Collins-Soper CSS …

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3 2/11/2014 Outline Transversity and transverse spin physics Universality of the Collins Mechanism Non-universality of the Sivers effects Conclusion

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In DIS, 4 2/11/2014 Parton distributions Quark distribution matrix P,k) Gauge links

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5 2/11/2014 Leading order quark distribution expands at leading order, Although a leading-twist distribution, transversity is chiral-odd, and doesnt contribute to the DIS structure function Unpolarized helicity transversity

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6 2/11/2014 Measuring transversity is difficult Have to multiply another chiral-odd object (distribution or fragmentation) Drell-Yan and other processes in hadronic collisions Two-hadron production in DIS Semi-inclusive single hadron production in DIS

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7 2/11/2014 Drell-Yan is an ideal place Combining two transversity distributions in Drell-Yan lepton pair production + - - + q T Double Transverse spin asymmetry

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8 2/11/2014 Opportunity at RHIC Vogelsang, et al, PRD, 1999

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9 2/11/2014 Semi-inclusive DIS Collins fragmentation function is chiral- odd Combining with the quark transversity leads to single transverse-spin asymmetry in SIDIS Opening a whole window of SSAs in SIDIS (k,s T ) (zk+p T ) ~pTXsT~pTXsT

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10 Whats Single spin asymmetry? Single Transverse Spin Asymmetry (SSA) Final state particle is Azimuthal symmetric Transverse plane

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

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12 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

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13 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 α S m q /Q We have to go beyond this naïve picture

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14 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 Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04 Twist-3 quark-gluon correlations (coll.) Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98 P kTkT STST Sivers function ~ S T (P X k T ).

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15 2/11/2014 Semi-Inclusive DIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

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Universality of the Collins Fragmentation 2/11/2014 HALL A Meeting 2007 16

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17 2/11/2014 Collins effects in e + e - Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06

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18 2/11/2014 Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, arXiv:0709.3272 [hep-ph]

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19 2/11/2014 Simple model a la Collins 93 e + e - annihilationSemi-inclusive DISHadron in a jet in pp Phase information in the vertex or the quark propagator Collins-93 Universality of the Collins Function!!

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20 2/11/2014 One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Universality of the Collins function!!

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21 2/11/2014 Similar arguments for pp collisions Conjecture: the Collins function will be the same as e^+e^- and SIDIS By using the Ward Identity: same Collins fun.

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Extend to two-gluon exchange 2/11/2014 HALL A Meeting 2007 22 Universality preserved

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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 2/11/2014 HALL A Meeting 2007 23

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24 Collins from HERMES Large, positive asymmetries: no surprise from u-quark dominance Large, negative asymmetries: first a surprise, now understood by large, negative disfavored Collins function

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25 Collins from COMPASS Smaller asymmetries than in proton case PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007

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First extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data By Anselmino et al., PRD 75 (07)

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Comparison with some models [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)

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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 2/11/2014 HALL A Meeting 2007 28

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

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30 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

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2/11/2014 0.1 0.2 0.3 x 0 0 Experiment SIDIS vs Drell Yan HERMES Sivers ResultsRHIC II Drell Yan Projections Markus Diefenthaler DIS Workshop Munich, April 2007 http://spin.riken.bnl.gov/rsc/

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32 Proposed by Boer-Vogelsang Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 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? Non-universality: Dijet-correlation at RHIC

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33 The asymmetry could be related to that in DIS, only at the leading order (one-gluon exchange), q T DIS --- Sivers function from DIS q t --- imbalance of the dijet H sivers depends on subprocess Qiu,Vogelsang,Yuan, 07

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This simple picture does not hold for two-gluon exchanges 2/11/201434 DPN Meeting 2007 Vogelang-Yuan, 0708.4398; Qiu,Collins, 0705.4121; Collins, 0708.4410 Integrated over transverse momentum Similar calculations can be Shown for QCD

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Failure or Opportunity? 2/11/2014 HALL A Meeting 2007 35 Collins,Qiu,0705.2141

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Future opportunities at JLab Transverse spin physics with proton and neutron targets Crucial to extract the quark transversity Detailed mapping of TMDs at 12 GeV upgrade 2/11/2014 HALL A Meeting 2007 36

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37 Different P T Region Integrate out P T (w/o weight) -- normal factorization, similar to inclusive DIS Large P T (>> QCD ) -- hard gluon radiation, can be calculated from perturbative QCD Low P T (~ QCD ) -- nonperturbative information: TMD factorization formula ? ! 12GeV 12GeV

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38 Final P T Distribution P T dependence Which is valid for all P t range SSA is suppressed by 1/P t at large P t Sivers function at low P t Qiu-Sterman Twist-three

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39 SIDIS cross sections at large P t 1/P t 2 1/P t 4 1/P t 3 1/P t 5

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40 Transition from Perturbative region to Nonperturbative region? Compare different region of P T Nonperturbative TMDPerturbative region

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Opportunities at other 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 2/11/2014 HALL A Meeting 2007 41

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42 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

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43 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

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44 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 + ++ - + ++ -

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45 Further factorization (q ? <
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46 2/11/2014 Users Meeting, BNL New challenge from STAR data (2006) Talks by Ogawa and Nogach in SPIN2006

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47 Some comments Its difficult to explain this pattern in the current theoretical approaches Fragmentation (Collins effect) contributions? One possible reason could be the partial cancellation between the favored and disfavored contribution to Pi^0 production Check with the charged pions?

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48 Recent theoretical developments (twist-three) Complete formalism for single inclusive hadron production in pp collision has been derived, including the derivative and non-derivative terms Qiu, Sterman, 91, 98 Kouvaris,Qiu,Vogelsang,Yuan, 06 See also Koike, et al., 06,07

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

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

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52 2/11/2014 Two-hadron interference frag. fun. In DIS Collins,Heppelmann,Ladinsky, 94 Jaffe,Jin,Tang, 97 Bacchetta,Radici, 04,06

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