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04/18/23 1
Transverse Spin Physics: Recent Developments
Feng Yuan Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
2
Transverse spin physics
Goal Quark transversity distributions Orbital motion of quarks and gluons?
Single transverse spin asymmetry Various transverse momentum dependent
physics (additional information on nucleon structure)
Sivers function (PDF) Collins function (FF) …
3 04/18/23
Outline
Introduction: single transverse spin phenomena
Universality of the Collins Mechanism Non-universality of the Sivers effects Conclusion
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What’s Single spin asymmetry?
Single Transverse SpinAsymmetry (SSA)
Final state particle isAzimuthal symmetric
Transverse plane
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Motivations: Its strong tied with the quark orbital
angular momentumWe have beautiful dataNontrivial QCD dynamics, and
fundamental test of the factorization, and the universality of PDFs, FFs,…
Single Spin Asymmetry
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SSAs in Modern era : RHIC, JLab, HERMES, …
Central rapidity!!
BRAHMS
STAR
Large SSA continues at DIS epLarge SSA continues at DIS epand collider pp experiments!!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 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
P
kTST
Sivers function ~ ST (PXkT).
Two major contributions
Sivers effect in the distribution
Collins effect in the fragmentation
Other contributions…
04/18/23 10
kTST
P
(zk+pT)~pTXsT
(k,sT)
ST (PXkT)
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Semi-Inclusive DIS Transverse Momentum Dependent (TMD)
Parton Distributions and Fragmentations Novel Single Spin Asymmetries
U: unpolarized beamT: transversely polarized target
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Collins effects in e+e-
Reliable place to extract the information on the Collins fragmentation function
Belle Col., PRL 06
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Collins asymmetry in pp collisions
Collins Fragmentation function
Quark transversity distribution
FY, arXiv:0709.3272 [hep-ph]
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Simple model a la Collins 93
e+e- annihilation Semi-inclusive DIS Hadron in a jet in pp
Phase information in the vertexor the quark propagatorCollins-93
Universality of the Collins Function!!
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One-gluon exchange (gauge link)?
Metz 02, Collins-Metz 02:Gamberg-Mukherjee-Mulders, 08Universality of the Collins function!!
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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.
Extract the quark transversity from e+e- and SIDIS expreiments
[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)
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
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21 04/18/23
Predictions at RHIC
Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98Collins function: fit to the HERMES data, Vogelsang-Yuan, 05
Collins contribution to SSA in inclusive hadron pp--> Pi X
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•Leading jet fragmentation contribution•Lower cut for the jet (>1GeV), upper cut for the fragmentation (<1GeV)
Add a soft contribution ~Pt
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”
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DIS and Drell-Yan
Initial state vs. final state interactions
“Universality”: fundamental QCD prediction
HERMES
* *
Drell-Yan DIS
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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
A difficulty at next-leading-power (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
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04/18/23 0.1 0.2 0.3 x
0
0
Experiment SIDIS vs Drell Yan
HERMES Sivers Results RHIC II Drell Yan Projections
Markus DiefenthalerDIS WorkshopMunich, April 2007
http://spin.riken.bnl.gov/rsc/
29
Proposed by Boer-Vogelsang Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07; Bacchetta, et al, photon-jet correlation, 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
The simple picture does not hold for two-gluon exchanges
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Qiu,Collins, 0705.4121;Vogelang-Yuan, 0708.4398;Collins, 0708.4410
Integrated over transverse momentumBecchetta-Bomhof-Mulders-Pijlman, 04-06
Another example:Heavy flavor production
Heavy quarkonium production (gg channel) ep scattering
No SSA in color-singlet model Final state interaction in color-octet model
pp scattering Only initial state interaction in color-singlet ISI and FSI cancel out in color-octet
Open charm or beauty Different SSAs for charm and anti-charm
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Color-singlet model
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Final state interactions with quark and anti-quark cancel out eachother, no SSA in color-singlet model
Color-octet model
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Final state interactions can be summarized into a gauge link to infinity, nonzero SSA
pp scattering
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•Color-singlet model: only initial state interaction, non-zero SSA•Color-octet model: initial and final state interactions cancel out, no SSA
J/Psi Production at lower energy (JPARC or FAIR) Quark-channel dominates
Color-singlet: only initial state interaction contributes, -1/2Nc relative to Drell-Yan
Color-octet: both initial and final state interactions contribute, -(Nc^2+1)/2Nc relative to DY
04/18/23 DPN Meeting 2007 36
JPARC prediction
Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05
04/18/23 DPN Meeting 2007 37
Final A_N depends on the weight of the quark-channel contribution
Heavy quark SSA
04/18/23 DPN Meeting 2007 38
ISI: contribute to quark and anti-quark
~1/4Nc
FSI: contribute to anti-quark
~2/4Nc
FSI: contribute to quark
~(Nc^2-2)/4Nc
A factor ~4 difference between charm and anticharm
04/18/23 DPN Meeting 2007 39
At JPARC, the quark channel contributes ~60% for charm cross sections
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Summary
We are in the early stages of a very exciting era of transverse spin physics studies, where the future RHIC, JLAB, JPARC, FAIR, 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
42
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, NPB03Brodsky-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 CorrelationsEfremov-Teryaev, 82, 84Qiu-Sterman, 91,98
Kane et al., hard parton model
+++
-+++
-
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Further factorization (q?
<<Q) The collinear gluons dominate
Twist-three CorrelationsEfremov-Teryaev, 82, 84Qiu-Sterman, 91,98
Transverse Momentum Dependent distributions
Sivers, 90, Collins, 93,02Brodsky-Hwang-Schmidt,02Ji-Qiu-Vogelsang-Yuan,06
q?<<Q
4504/18/23 Users Meeting, BNL
New challenge from STAR data (2006)Talks by Ogawa and Nogach in SPIN2006
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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
48
Transition from Perturbative region to Nonperturbative region? Compare different region of PT
Nonperturbative TMD Perturbative region