1. Transverse Spin Physics: Recent Developments
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
4/25/2017

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. Outline Introduction: single transverse spin phenomena
Universality of the Collins Mechanism
Non-universality of the Sivers effects
Conclusion
4/25/2017

4. What’s Single spin asymmetry?
Transverse plane
Final state particle is
Azimuthal symmetric
Single Transverse Spin
Asymmetry (SSA)

5. Single Spin Asymmetry Motivations:
Its strong tied with the quark orbital angular momentum
We have beautiful data
Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…

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

7. 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

8. 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

9. 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 kT ST
Sivers function ~ ST (PXkT) . P

10. Two major contributions
Sivers effect in the distribution
Collins effect in the fragmentation
Other contributions… kT ST
ST (PXkT) P
(zk+pT)
(k,sT)
~pTXsT
4/25/2017

11. Semi-Inclusive DIS
Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations
Novel Single Spin Asymmetries
U: unpolarized beam
T: transversely polarized target
4/25/2017

12. Universality of the Collins Fragmentation
4/25/2017

13. Collins effects in e+e-
Reliable place to extract the information on the Collins fragmentation function
Belle Col.,
PRL 06
4/25/2017

14. Collins asymmetry in pp collisions
Collins Fragmentation function
Quark transversity distribution
FY, arXiv:  [hep-ph]
4/25/2017

15. 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!!
4/25/2017

16. One-gluon exchange (gauge link)?
Metz 02, Collins-Metz 02:
Gamberg-Mukherjee-Mulders, 08
Universality of the Collins function!!
4/25/2017

17. 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
4/25/2017

18. Extend to two-gluon exchange
Universality preserved
4/25/2017

19. 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)

20. 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
4/25/2017

21. Predictions at RHIC
Quark transversity: Martin-Schafer-Stratmann-Vogelsang, 98
Collins function: fit to the HERMES data, Vogelsang-Yuan, 05
4/25/2017

22. Collins contribution to SSA in inclusive hadron pp--> Pi X
Add a soft contribution ~Pt
Leading jet fragmentation contribution
Lower cut for the jet (>1GeV), upper cut for the fragmentation (<1GeV)
4/25/2017

23. Recent STAR data May indicate the importance of the soft contribution
4/25/2017

24. 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”
4/25/2017

25. DIS and Drell-Yan Initial state vs. final state interactions
“Universality”: fundamental QCD prediction * *
DIS
Drell-Yan
HERMES

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-leading-power (1/Q)
Mismatch at low and high transverse momentum SIDIS at 1/Q
Bacchetta-Boer-Diehl-Mulders,
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
4/25/2017

28. Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
Markus Diefenthaler
DIS Workshop
Munich, April 2007 x
4/25/2017

29. Non-universality: Dijet-correlation at RHIC
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/ , hep-ph/ , hep-ph/ , hep-ph/
Qiu-Vogelsang-Yuan, arXiv: ;
Collins-Qiu, arXiv:  
Voglesang-Yuan, arXiv:
Collins, arXiv:
Bomhof-Mulders, arXiv:
Factorization? Universality?

30. The simple picture does not hold for two-gluon exchanges
Qiu,Collins, ;
Vogelang-Yuan, ;
Collins,
Integrated over transverse momentum
Becchetta-Bomhof-Mulders-Pijlman, 04-06
4/25/2017

31. 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
4/25/2017

32. Color-singlet model
Final state interactions with quark and anti-quark cancel out each
other, no SSA in color-singlet model
4/25/2017

33. Color-octet model
Final state interactions can be summarized into a gauge link to infinity, nonzero SSA
4/25/2017

34. pp scattering
Color-singlet model: only initial state interaction, non-zero SSA
Color-octet model: initial and final state interactions cancel out, no SSA
4/25/2017

36. 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
4/25/2017
DPN Meeting 2007

37. JPARC prediction Final A_N depends on the weight of the quark-channel
contribution
Proportional to the sum of u- and d- quark Sivers function: fitted to HERMES data, Vogelsang-Yuan 05
4/25/2017
DPN Meeting 2007

38. Heavy quark SSA ~1/4Nc ~(Nc^2-2)/4Nc ~2/4Nc
ISI: contribute to quark and anti-quark
~1/4Nc
FSI: contribute to quark
~(Nc^2-2)/4Nc
FSI: contribute to anti-quark
~2/4Nc
4/25/2017
DPN Meeting 2007

39. A factor ~4 difference between charm and anticharm
At JPARC, the quark channel contributes ~60% for charm cross sections
4/25/2017
DPN Meeting 2007

40. FAIR at GSI
4/25/2017
DPN Meeting 2007

41. 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, NPB03
Brodsky-Yuan, PRD06

43. 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

44. 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

45. New challenge from STAR data (2006)
Talks by Ogawa and Nogach in SPIN2006
4/25/2017
Users Meeting, BNL

46. 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

47. SIDIS cross sections at large Pt

48. Transition from Perturbative region to Nonperturbative region?
Compare different region of PT
Nonperturbative TMD
Perturbative region

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

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