1. Transversity: Opportunities Now and Future
Feng Yuan
Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
3/27/2017

2. 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

3. Outline Transversity and transverse spin physics
Universality of the Collins Mechanism
Non-universality of the Sivers effects
Conclusion
3/27/2017

4. Parton distributions In DIS, Quark distribution matrix (P,k)
Gauge links
3/27/2017

5. 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

6. 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

7. 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

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

9. 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

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

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

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

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 αSmq/Q
We have to go beyond this naïve picture

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 kT ST .
Sivers function ~ ST (PXkT) P

15. 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

16. Universality of the Collins Fragmentation
3/27/2017
HALL A Meeting 2007

17. Collins effects in e+e-
Reliable place to extract the information on the Collins fragmentation function
Belle Col.,
PRL 06
3/27/2017

18. Collins asymmetry in pp collisions
Collins Fragmentation function
Quark transversity distribution
FY, arXiv:  [hep-ph]
3/27/2017

19. 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

20. One-gluon exchange (gauge link)?
Metz 02, Collins-Metz 02:
Universality of the Collins function!!
3/27/2017

21. 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

22. Extend to two-gluon exchange
Universality preserved
3/27/2017
HALL A Meeting 2007

23. 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

24. 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

25. 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

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

27. 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)

28. 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

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

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

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

32. 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?

33. 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

34. 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

35. Failure or Opportunity?
Collins,Qiu,
3/27/2017
HALL A Meeting 2007

36. 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

37. 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

38. 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

39. SIDIS cross sections at large Pt

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

41. 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

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

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

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

45. 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

46. New challenge from STAR data (2006)
Talks by Ogawa and Nogach in SPIN2006
3/27/2017
Users Meeting, BNL

47. 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?

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

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

52. Two-hadron interference frag. fun.
In DIS
Collins,Heppelmann,Ladinsky, 94
Jaffe,Jin,Tang, 97
Bacchetta,Radici, 04,06
3/27/2017