SPIN2006, Kyoto

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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