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**Transversity: Opportunities Now and Future**

Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory 3/27/2017

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**Transverse spin physics**

RHIC RHIC Bunce,Lambda E704,pp to Pi JLab COMPASS HERMES … BELLE 80 90 00 BHS Factorization unify (non)Universality Efremove-Teryav CSS Sivers Jaffe-Ji Collins Mulders et al. Ralston-Soper Collins-Soper Collins Qiu-Sterman BJY 3/27/2017 HALL A Meeting 2007

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**Outline Transversity and transverse spin physics**

Universality of the Collins Mechanism Non-universality of the Sivers effects Conclusion 3/27/2017

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**Parton distributions In DIS, Quark distribution matrix (P,k)**

Gauge links 3/27/2017

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**Leading order quark distribution**

expands at leading order, Although a leading-twist distribution, transversity is chiral-odd, and doesn’t contribute to the DIS structure function Unpolarized helicity transversity 3/27/2017

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**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 3/27/2017

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**Drell-Yan is an ideal place**

Combining two transversity distributions in Drell-Yan lepton pair production + - qT qT + - Double Transverse spin asymmetry 3/27/2017

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Opportunity at RHIC Vogelsang, et al, PRD, 1999 3/27/2017

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**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 (zk+pT) (k,sT) ~pTXsT 3/27/2017

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**What’s Single spin asymmetry?**

Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA)

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**SSAs in Modern era : RHIC, JLab, HERMES, …**

STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!!

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**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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**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

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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 kT ST . Sivers function ~ ST (PXkT) P

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Semi-Inclusive DIS Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target 3/27/2017

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**Universality of the Collins Fragmentation**

3/27/2017 HALL A Meeting 2007

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**Collins effects in e+e-**

Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06 3/27/2017

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**Collins asymmetry in pp collisions**

Collins Fragmentation function Quark transversity distribution FY, arXiv: [hep-ph] 3/27/2017

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**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!! 3/27/2017

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**One-gluon exchange (gauge link)?**

Metz 02, Collins-Metz 02: Universality of the Collins function!! 3/27/2017

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**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 3/27/2017

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**Extend to two-gluon exchange**

Universality preserved 3/27/2017 HALL A Meeting 2007

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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 3/27/2017 HALL A Meeting 2007

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**Collins from HERMES 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

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**Collins from COMPASS Smaller asymmetries than in proton case**

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

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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” 3/27/2017 HALL A Meeting 2007

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**DIS and Drell-Yan Initial state vs. final state interactions**

“Universality”: fundamental QCD prediction * * DIS Drell-Yan HERMES

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**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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**Experiment SIDIS vs Drell Yan**

HERMES Sivers Results RHIC II Drell Yan Projections Markus Diefenthaler DIS Workshop Munich, April 2007 x 3/27/2017

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**Non-universality: Dijet-correlation at RHIC**

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/ , hep-ph/ , hep-ph/ , hep-ph/ Qiu-Vogelsang-Yuan, arXiv: ; Collins-Qiu, arXiv: Voglesang-Yuan, arXiv: Collins, arXiv: Bomhof-Mulders, arXiv: Factorization? Universality?

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**qTDIS--- Sivers function from DIS qt--- imbalance of the dijet **

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

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**This simple picture does not hold for two-gluon exchanges**

Vogelang-Yuan, ; Qiu,Collins, ; Collins, Integrated over transverse momentum Similar calculations can be Shown for QCD 3/27/2017 DPN Meeting 2007

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**Failure or Opportunity?**

Collins,Qiu, 3/27/2017 HALL A Meeting 2007

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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 3/27/2017 HALL A Meeting 2007

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**Different PT Region ? ! 12GeV 12GeV 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 ? ! 12GeV 12GeV

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**Final PT Distribution PT dependence Which is valid for all Pt range**

SSA is suppressed by 1/Pt at large Pt Sivers function at low Pt Qiu-Sterman Twist-three

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**SIDIS cross sections at large Pt**

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**Transition from Perturbative region to Nonperturbative region?**

Compare different region of PT Nonperturbative TMD Perturbative 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 3/27/2017 HALL A Meeting 2007

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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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**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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**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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**Further factorization (q?<<Q)**

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

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**New challenge from STAR data (2006)**

Talks by Ogawa and Nogach in SPIN2006 3/27/2017 Users Meeting, BNL

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Some comments It’s 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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**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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**Twist-3 Fit to data RHIC STAR E704 BRAMHS**

Kouvaris,Qiu,Vogelsang,Yuan, 06

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**Compare to 2006 data from RHIC**

J.H. Lee, SPIN 2006

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**Two-hadron interference frag. fun.**

In DIS Collins,Heppelmann,Ladinsky, 94 Jaffe,Jin,Tang, 97 Bacchetta,Radici, 04,06 3/27/2017

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