Collins effect in the collinear factorization approach

Jian Zhou(ShanDong University, China & LBNL, US)

Collaborators: Feng Yuan (LBNL, US)

Based on the paper: e-Print: arXiv:0903.4680

Outline:

1: Brief review2: Collins function in the collinear factroization approach3: Summary & outlook

Single spin asymmetry

Xπpp )(p p

π L

R

Naive parton model:1978, Kane, Pumplin, Repko

Two mechanisms in QCD

1: Transverse momentum dependent (TMD) factorizaion Sivers distribution function f1T

┴ (x,kT2) Sivers 90

Collins fragmentation function H1┴(x,kT

2) Collins 93

2: Collinear higher-twist factorization twist-3 distribution function TF(x,x1) Qiu-Sterman 91; Efremov-Teryaev 82, 84 twist-3 fragmentation function EF(x,x1) ? Koike 02; Meissner; Metz 08

kTST

P ST (PXkT)(zk+pT)

~pTXsT

The unification of two mechanisms

Twist-three: QCD<< PT assuring the perturbative calculation make sense

TMD: low PT, require additional hard scale like Q2 in DIS and Drell-Yan, PT<<Q Overlap: QCD<< PT<<Q, unifying these two Mechanisms

Crucial step: TMD distributions at large kT

X. Ji, J.W. Qiu, W.Vogelsang, F. Yuan, 06

kT-odd TMD distributions at large KTGenerally speaking,

TMD distributions can be calculated by using collinear approachradiated gluon lead to large kT

gluon rescattering lead to

asymmetry kT distribution

factorized into twist-3 collinear functions accordingly, TF(x,x1), TF

(σ)(x,x1) ,etc.

The calculation of Collins function follows the similar procedure,but with significant difference !

Collins function and its kT moment

Kt-moment defines a twist-3 fragmentation function

Yuan-Zhou, 09

twist-3 correlation function contribute to Collins function

X.Ji, PRD94;Koike, 02-06

iH1(z, z1)

It is not ruled out by time reversal invariance argument ! The imaginary phase necessary

fornonzero SSA comes up automatically !

gg

g xPxi

ix1)(1

gluon pole

),(11zziH

xP F

g

),()( 1zzExi Fg process dependent

process independent

combining with the different matrix elements

F-type fragmentation correspondingly define: EF(z,z1), HF(z,z1)

E1(z, z1) +

Universality of the Collins Fragmentation

ep--> e Pi X e+e--> Pi Pi X pp--> jet(->Pi) XMetz 02, Collins-Metz 02,Yuan 07, 08Gamberg-Mukherjee-Mulders 08

Conjecture: the Collins function should be the same among the different processes, such as e^+e^- , SIDIS and pp.

Universality of the Collins Fragmentation

The arguments of EF(z,z1) are fixed by picking up pole contribution soft gluon pole contribution z=z1 hard gluon pole contribution z1=zh, z>zh fortunately...

Thanks to its support properties: EF(z,z1)=0 when z=z1 or z>z1

S. Meißner A. Metz 08

Process dependent contribution to Collins function vanishes !

We are only left with contributions from HF \hat{H} (the moment of collins function)

Collins function at large kt

typpical diagrams:

where we changed the normalizationof HF(z,z1)

Collins contribution in SIDIS

This result can be reproduced by the TMD factorization with Collins function calculated, the quark transversity distribution This demonstrate that the TMD and collinear approaches are consistent in the intermediate transverse momentum region for the Collins effects

Summary We have identified the correspondent collinear twist-three fragmentation function for the Collins effects The Collins function calculated from this twist-three function is universal, does not dependent on the gauge link direction We have shown that the TMD and collinear approaches are consistent in the intermediate transverse momentum region.outlook cos(2φ) azimuthal asymmetry in the process e+e--> Pi Pi X

using collinear factorization approach SSA in the process pp--> jet(->Pi) X from fragmentation effect using collinear factroization appraoch

Thank you for your attention.