Transversity: Opportunities Now and Future

1
Transversity Opportunities Now and Future

• Feng Yuan
• Lawrence Berkeley National Laboratory
• RBRC, Brookhaven National Laboratory

2
Transverse spin physics
RHIC
RHIC
Bunce,Lambda
E704,pp to Pi
JLab
COMPASS
HERMES

BELLE
BHS
Factorization
unify
(non)Universality
Efremove-Teryav
Sivers
Jaffe-Ji
Collins
Mulders et al.
CSS
Ralston-Soper
Collins-Soper
Collins
Qiu-Sterman
BJY
3
Outline

• Transversity and transverse spin physics
• Universality of the Collins Mechanism
• Non-universality of the Sivers effects
• Conclusion

4
Parton distributions

• In DIS,

Quark distribution matrix ?(P,k)
Gauge links
5
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
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

7
Drell-Yan is an ideal place

• Combining two transversity distributions in
  Drell-Yan lepton pair production

-

? qT
? qT

-
Double Transverse spin asymmetry
8
Opportunity at RHIC
Vogelsang, et al, PRD, 1999
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

(zkpT)
(k,sT)
pTXsT
10
Whats 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 aSmq/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 02Belitsky-Ji-Yuan,NPB03
• Factorization Ji-Ma-Yuan,PRD04Collins,Metz,04
• Twist-3 quark-gluon correlations (coll.)
• Efremov-Teryaev, 82, 84
• Qiu-Sterman, 91,98

.
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
16
Universality of the Collins Fragmentation
17
Collins effects in ee-

• Reliable place to extract the information on the
  Collins fragmentation function

Belle Col., PRL 06
18
Collins asymmetry in pp collisions
Collins Fragmentation function
Quark transversity distribution
FY, arXiv0709.3272 hep-ph
19
Simple model a la Collins 93
Phase information in the vertex or the quark
propagator Collins-93
Universality of the Collins Function!!
20
One-gluon exchange (gauge link)?
Metz 02, Collins-Metz 02 Universality of the
Collins function!!
21
Similar arguments for pp collisions
Conjecture the Collins function will be the same
as ee- and SIDIS
22
Extend to two-gluon exchange
Universality preserved
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

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
PRL 94, 202002 (2005) and Nucl.Phys.B76531-70,200
7

• 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

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
  .97082002,2006

31
Experiment SIDIS vs Drell Yan
HERMES Sivers Results
RHIC II Drell Yan Projections
0
Markus Diefenthaler DIS Workshop Munich, April
2007
0
0.1 0.2 0.3 x
http//spin.riken.bnl.gov/rsc/
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/0406099,
  hep-ph/0505268, hep-ph/0601171, hep-ph/0609206
• Qiu-Vogelsang-Yuan, arXiv0704.1153 0706.1196
• Collins-Qiu, arXiv0705.2141 
• Voglesang-Yuan, arXiv0708.4398
• Collins, arXiv0708.4410
• Bomhof-Mulders, arXiv0709.1390
• Factorization? Universality?

33
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, 0708.4398 Qiu,Collins,
0705.4121 Collins, 0708.4410
Integrated over transverse momentum
Similar calculations can be Shown for QCD
35
Failure or Opportunity?
Collins,Qiu,0705.2141
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

37
Different PT Region

• 12GeV

• Integrate out PT (w/o weight)
• -- normal factorization, similar to inclusive
  DIS
• Large PT (gtgt?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
1/Pt2
1/Pt4
1/Pt3
1/Pt5
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

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?ltltQ)

• The collinear gluons dominate

q?ltltQ
Transverse Momentum Dependent distributions Sivers
, 90, Collins, 93,02 Brodsky-Hwang-Schmidt,02 Ji-Q
iu-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
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 Pi0 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
51
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52
Two-hadron interference frag. fun.

• In DIS

Collins,Heppelmann,Ladinsky, 94 Jaffe,Jin,Tang,
97 Bacchetta,Radici, 04,06