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Unique Description for SSAs in DIS and Hadronic Collisions. Feng Yuan RBRC, Brookhaven National Laboratory. Collaborators: Kouvaris, Ji, Qiu, Vogelsang. x. z. y. What is Single Spin Asymmetry?. - PowerPoint PPT Presentation
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SPIN2006, Kyoto
1
Unique Description for SSAs in DIS and Hadronic Collisions
Feng Yuan
RBRC, Brookhaven National Laboratory
Collaborators: Kouvaris, Ji, Qiu, Vogelsang
2SPIN 2006, Kyoto
What is Single Spin Asymmetry? Scattering a transverse spin polarized proton on
unpolarized target (another hadron or a photon)
the cross section contains a term
z
x
y
S?
P P’
K?
3SPIN 2006, Kyoto
Why Does SSA Exist?
Single Spin Asymmetry requiresHelicity flip: one must have a reaction
mechanism for the hadron to change its helicity (in a cut diagram)
Final State Interactions (FSI): to generate a phase difference between two amplitudes
The phase difference is needed because the structure S ·(p × k) violate the naïve time-reversal invariance
4SPIN 2006, Kyoto
Naïve Parton Model Fails to Explain Large SSAs
If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, PRL41, 1978) It is in general suppressed by αS mq/Q
We have to go beyond the naïve parton model to understand the large SSAs observed in hadronic reactions
5SPIN 2006, Kyoto
Two Mechanisms in QCD
Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations Sivers function, Sivers 90 Collins function, Collins 93 Gauge invariant definition of the TMDs: Brodsky, Hwang,
Schmidt 02; Collins 02 ; Belitsky, Ji, Yuan 02; Boer, Mulders, Pijlman, 03
The QCD factorization: Ji, Ma, Yuan, 04; Collins, Metz, 04 Twist-three Correlations (collinear factorization)
Efremov-Teryaev, 82, 84 Qiu-Sterman, 91,98 Kanazawa-Koike, 00-04
6SPIN 2006, Kyoto
How Do They Contribute?
TMD: the quark orbital angular momentum leads to hadron helicity flip
The factorizable final state interactions --- the gauge link provides the phase
Twist-three: the gluon carries spin, flipping hadron helicity
The phase comes from the poles in the hard scattering amplitudes
7SPIN 2006, Kyoto
Global Picture for SSAs
TMD
Quark-gluon correlation
SIDIS
Drell-Yan
Gluon SiversCharmonium
Dijet-Corr.
Single Inclusiveat RHIC
Dijet at RHIC
Large q?
Drell-Yan
Large P?
SIDIS
8SPIN 2006, Kyoto
Territories and unification
Twist-three: the single inclusive hadron production in pp, require large P?
TMD: low P?, require additional hard scale like Q2 in DIS and Drell-Yan, P?¿ Q
Connecting these two, at the matrix elements level
TF(x,x)=s d2k |k|2 qT(x,k)
Boer, Mulders, Pijlman 03
Qiu-Sterman Sivers
9SPIN 2006, Kyoto
Unifying the Two Mechanisms (P? dependence of SSAs)
At low P?, the non-perturbative TMD Sivers function will be responsible for its SSA
When P?» Q, purely twist-3 contributions
For intermediate P?, QCD¿ P?¿ Q, we should see the transition between these two
An important issue, at P?¿ Q, these two should merge, showing consistence of the theory
(Ji, Qiu, Vogelsang, Yuan, PRL97, 082002;PRD73,094017; PLB638,178, 2006)
10SPIN 2006, Kyoto
Recall the TMD Factorization
11SPIN 2006, Kyoto
SIDIS: at Large P?
When q?ÀQCD, the Pt dependence of the TMD parton distribution and fragmentation functions can be calculated from pQCD, because of hard gluon radiation
Single Spin Asymmetry at large P? is not suppressed by 1/Q, but by 1/P?
12SPIN 2006, Kyoto
SSA in the Twist-3 approach
Twist-3 quark-gluon Correlation: TF(x1,x2)
Fragmentation function:\hat q(x’)
Collinear Factorization:
Qiu,Sterman, 91
13SPIN 2006, Kyoto
Factorization guidelines
Reduced diagrams for different regions of the gluon momentum: along P direction, P’, and soft Collins-Soper 81
14SPIN 2006, Kyoto
Final Results
P? dependence
Which is valid for all P? range
Sivers function at low P? Qiu-Sterman Twist-three
15SPIN 2006, Kyoto
Transition from Perturbative region to Nonperturbative region? Compare different region of P?
Nonperturbative TMD Perturbative region
16SPIN 2006, Kyoto
More over
At low P?¿ Q, the second term vanishes, use the Sivers function only
P?-moment of the asymmetry can be calculated from twist-three matrix element In SIDIS, for the Sivers asymmetry
Boer-Mulders-Tangelmann, 96,98
17SPIN 2006, Kyoto
Compare to the HERMES data TF from the fit to single
inclusive hadron asymmetry data (fixed target & RHIC) See Vogelsang’s talk,
Kouvaris-Qiu-Vogelsang-Yuan
, hep-ph/0609238 Indicate the consistency
of SSAs in DIS and hadron collisions
not corrected for acceptance and smearing
See also, Efremov, et al., PLB612,233 (20005)
18SPIN 2006, Kyoto
Dijet-correlation at RHIC Proposed by Boer-Vogelsang Initial state and/or final state interactions?
Bacchetta-Bomhof-Mulders-Pijlman,04-06 We can illustrate the initial and final state
interactions in a model-independent way, at nonzero leading order, for example
19SPIN 2006, Kyoto
At this order, the asymmetry can be related to that in DIS, in leading power of q?/P?
qTDIS--- Sivers function from DIS
q?--- imbalance of the dijet
Hsivers depends on subprocess (see Bomhof’s talk)
20SPIN 2006, Kyoto
Predictions for dijet-correlation AN
VY05: Vogelsang-Yuan, Phys.Rev.D72:054028,2005 Sivers functions fit to the HERMES data
Model II: uT(1/2)/u=-0.75x(1-x),dT
(1/2)/d=2.76x(1-x) Cautions: Scale difference, HERMES <Q2>~2GeV2
Sudakov effects may affect the asymmetry, Boer-Vogelsang 04
VY05
Modified Initial/final
u-quark
d-quark
21SPIN 2006, Kyoto
Global Picture for SSAs
TMD
Quark-gluon correlation
SIDIS
Drell-Yan
Gluon SiversCharmonium
Dijet-Corr.
Single Inclusiveat RHIC
Dijet at RHIC
Large q?
Drell-Yan
Large P?
SIDIS
22SPIN 2006, Kyoto
Summary
We are in the early stages of a very exciting era of transverse spin physics studies
Many data are coming out, and new experiments are proposed to provide a detailed understanding of the spin degrees of freedom, especially for the quark orbital motion
We will learn more about nucleon structure from these studies