Azimuthal Asymmetry In The Unpolarized Drell-Yan Process

1. Azimuthal Asymmetry In The Unpolarized Drell-Yan Process Zhou Jian ShanDong University, China & LBNL, US Collaborators: Feng Yuan (LBNL, US) Zuo-tang Liang (ShanDong University, China)

2. Outline • 1 Brief Review • 2 Focus on two soures: TMD factorization and higher twist • Collinear factorizaion • 3 Conclusion and outlook

3. A general expression for Drell-Yan virtual photon decay angular distributions: Θ and Φ are the decay polar and azimuthal angles of the μ+ in the dilepton rest-frame In general :

4. Actually , is pretty large E866, PRL07

5. To account for non-zero azimuthal asymmetry, several mechanisms have been suggested: • Chan effect • Gluon radiation QCD correction effect (Collins, 77) • Boer-Mulders function (Based on TMD factorization, Boer 99) • Higher twist effect (Based on Collinear Factorizaiton, Qiu-Sterm, …) Power suppresed by q_t^2/Q^2 Leading power In the large lepton pair transverse momentum region ,QCD correction contribution dominate But in the our most interested regime: small lepton pair transverse momentum region ..........

6. The matrxi element defination of the and well-known relation because of the naive time-reversal odd property: and Similarly, and J. collins 2002 D. Boer, P. J. Mulders and F. Pijilman 2003

7. Double initial state interactions: Two typical diagrams (of 212) contribute to azimuthal asymmetry The factorization procedure is illustrated as the following figures All the transverse momnetun carried by incoming parton have been intergrated out !

8. The calculation based on the collinear factorization is valid for the whole the lepton pair transverse momentum spectrum. In order to make comparison with TMD approach, we take the limit ( But still ,ensuring the pertubative calculation make sense ) In this limit, the final result reads,

9. On the TMD factroization side, the azimuthal asymmetry comes from the product of the two Boer-Mulders functions. (Boer,99) The above formula is valid for kinematical region: How to unify two schemes?

10. In the single spin asymmetry case, the consistency of formalisms have been confirmed (Voglesang, Beijing workshop, 08) In the same spirit, two pictures can be unified for the case of azimuthal asymmetry in unpolarized Drell-Yan process.

11. The key obervation: TMD distributions can be calcualted within perturbative QCD as long as One of the well-known distributions: Siveres function The perturbative calculation follow the similar procedure, where

12. In this way, Boer-Mulders function can be expressed in terms of the which allow us to make comparsion between two mechanisms. It turns out to yield the identical result in the overlap region where they both apply. Notice:As we claimed previously, the contribution at the intermediate transverse momentum is not power suppressed.

13. Summary and outlook: • We investigated the higher twist origin of azimuthal asymmetry in the unpolarized Drell-Yan process • The consistence between the TMD factorizaiton approach and collinear factorization approach has been verified. • The azimuthal asymmetry in the other processes such as e-e+ and SIDIS can be addressed in the context of higher twist collinear factorization. • The large logarthim require the resummation.