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04/10/23 1
Transversity: Opportunities Now and Future
Feng Yuan Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
Transverse spin physics
04/10/23 HALL A Meeting 2007 2
3 04/10/23
Outline
Transversity and transverse spin physics
Universality of the Collins Mechanism Non-universality of the Sivers effects Conclusion
In DIS,
4 04/10/23
Parton distributions
Quark distribution matrixP,k)
Gauge links
5 04/10/23
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
6 04/10/23
Measuring transversity is difficult
Have to multiply another chiral-odd object (distribution or fragmentation)Drell-Yan and other processes in
hadronic collisionsTwo-hadron production in DISSemi-inclusive single hadron production
in DIS
7 04/10/23
Drell-Yan is an ideal place
Combining two transversity distributions in Drell-Yan lepton pair production
+
-
-
+qT
qT
Double Transverse spin asymmetry
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Opportunity at RHIC
Vogelsang, et al, PRD, 1999
9 04/10/23
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
(k,sT)(zk+pT)
~pTXsT
10
What’s Single spin asymmetry?
Single Transverse SpinAsymmetry (SSA)
Final state particle isAzimuthal symmetric
Transverse plane
11
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!!
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
P
kTST
Sivers function ~ 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
Universality of the Collins Fragmentation
04/10/23 HALL A Meeting 2007 16
17 04/10/23
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:Universality 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.
Extend to two-gluon exchange
04/10/23 HALL A Meeting 2007 22
Universality preserved
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
04/10/23 HALL A Meeting 2007 23
24
Collins from HERMES Large, positive asymmetries:
no surprise from u-quark dominance
Large, negative asymmetries:first a surprise, now understood by large, negative disfavored Collins function
25
Collins from COMPASS
Smaller asymmetries than in proton case
PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007
First extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data
By Anselmino et al., PRD 75 (07)
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)
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”
04/10/23 HALL A Meeting 2007 28
29
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
04/10/23 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/
32
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, 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
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
This simple picture does not hold for two-gluon exchanges
04/10/23 34DPN Meeting 2007
Vogelang-Yuan, 0708.4398; Qiu,Collins, 0705.4121;Collins, 0708.4410
Integrated over transverse momentumSimilar calculations can be
Shown for QCD
Failure or Opportunity?
04/10/23 HALL A Meeting 2007 35
Collins,Qiu,0705.2141
Future opportunities at JLab
Transverse spin physics with proton and neutron targetsCrucial to extract the quark transversity
Detailed mapping of TMDs at 12 GeV upgrade
04/10/23 HALL A Meeting 2007 36
37
Different PT Region 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
12GeV
38
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
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
04/10/23 HALL A Meeting 2007 41
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, NPB03Brodsky-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 CorrelationsEfremov-Teryaev, 82, 84Qiu-Sterman, 91,98
Kane et al., hard parton model
+++
-+++
-
45
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
4604/10/23 Users Meeting, BNL
New challenge from STAR data (2006)Talks by Ogawa and Nogach in SPIN2006
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, 98Kouvaris,Qiu,Vogelsang,Yuan, 06See also Koike, et al., 06,07
49
Twist-3 Fit to data
E704
STAR
Kouvaris,Qiu,Vogelsang,Yuan, 06
RHIC
BRAMHS
50
Compare to 2006 data from RHIC
J.H. Lee, SPIN 2006
51
52 04/10/23
Two-hadron interference frag. fun. In DIS
Collins,Heppelmann,Ladinsky, 94Jaffe,Jin,Tang, 97Bacchetta,Radici, 04,06