Collins effect in the collinear factorization approach

1. 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

2. Outline: 1: Brief review 2: Collins function in the collinear factroization approach 3: Summary & outlook

3. L π p p R Single spin asymmetry Naive parton model: 1978, Kane, Pumplin, Repko

4. ST (zk+pT) ~pTXsT kT Two mechanisms in QCD ST (PXkT) P • 1:Transverse momentum dependent (TMD) factorizaion Sivers distribution function f1T┴ (x,kT2)Sivers 90 Collins fragmentation function H1┴(x,kT2)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

5. 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

6. kT-odd TMD distributions at large KT Generally speaking, TMD distributions can be calculated by using collinear approach radiated 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 !

7. Collins function and its kT moment • Kt-moment defines a twist-3 fragmentation function

8. F-type fragmentation gluon pole combining with the different matrix elements E1(z, z1) + process dependent process independent twist-3 correlation function contribute to Collins function iH1(z, z1) X.Ji, PRD94; Koike, 02-06 Yuan-Zhou, 09 It is not ruled out by time reversal invariance argument ! The imaginary phase necessary for nonzero SSA comes up automatically ! correspondingly define: EF(z,z1), HF(z,z1)

9. Universality of the Collins Fragmentation pp--> jet(->Pi) X ep--> e Pi X e+e--> Pi Pi X Metz 02, Collins-Metz 02, Yuan 07, 08 Gamberg-Mukherjee-Mulders 08 Conjecture: the Collins function should be the same among the different processes, such as e^+e^- , SIDIS and pp.

10. 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)

11. Collins function at large kt typpical diagrams: where we changed the normalizationof HF(z,z1)

12. 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

13. Summary • We have identified the correspondent collinear twist-three fragmentation function for the Collins effects • The Collins function calculated from this twist-three function isuniversal, 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 Xusing collinear factorization approach • SSA in the process pp--> jet(->Pi) X from fragmentation effect using collinear factroization appraoch Thank you for your attention.