Azimuthal Asymmetry In The Unpolarized Drell-Yan Process Zhou Jian ShanDong University, China & LBNL,…

Azimuthal Asymmetry In The Unpolarized Drell-Yan Process

)2cos(

Zhou JianShanDong University, China & LBNL, US

Collaborators: Feng Yuan (LBNL, US) Zuo-tang Liang (ShanDong University, China)

Outline

1 Brief Review2 Focus on two soures: TMD factorization and higher twist Collinear factorizaion3 Conclusion and outlook

A general expression for Drell-Yan virtual photon decay angular distributions:

2 21 3 1 cos sin 2 cos sin cos 24 2

dd

*"Naive" Drell-Yan (transversely polarized , no transverse mo 1, 0, 0mentum)

In general : 1, 0, 0

*1 2

*( )h h x l l q qx

Θ and Φ are the decay polar and azimuthal angles of the μ+ in the dilepton rest-frame

2 21 3 1 cos sin 2 cos sin cos 24 2

dd

Actually , is pretty large

E866, PRL07

To account for non-zero azimuthal asymmetry, several mechanismshave 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, …)

),(),( TT pzfkxf Power suppresed by q_t^2/Q^2

Leading power

In the large lepton pair transverse momentum region ,QCD correction contribution dominateQqT But in the our most interested regime: small lepton pair transverse momentum region ..........

),(),( 11 TT pzhkxh

),(),( 1)(

1)( zzTxxT FF

The matrxi element defination of the and ),( 1)( xxTF

),(1 Tkxh

well-known relation because of the naive time-reversal odd property:YanDrell

TDIS

T ff 11 ),(),( 1

22

TDIS

TP

TTF kxfMkkdxxT

and

Similarly,YanDrelDIS hh 11 ),(),( 1

222)(

TDIS

P

TTF kxhMkkdxxT

and

D. Boer, P. J. Mulders and F. Pijilman 2003J. collins 2002

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 !

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

QqT ( But still ,ensuring the pertubative calculation make sense )QCDTq

In this limit, the final result reads,

On the TMD factroization side, the azimuthal asymmetry comes fromthe product of the two Boer-Mulders functions.

The above formula is valid for kinematical region: QqT

How to unify two schemes?

(Boer,99)

In the single spin asymmetry case, the consistency of formalisms have been confirmed

In the same spirit, two pictures can be unified for the case of azimuthal asymmetry in unpolarized Drell-Yan process.

(Voglesang, Beijing workshop, 08)

The key obervation: TMD distributions can be calcualted within perturbativeQCD as long as QCDTk

One of the well-known distributions: Siveres function

The perturbative calculation follow the similar procedure,

where

In this way, Boer-Mulders function can be expressed in terms of the ),( 1

)( xxTF 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.

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.

2

2

lnQqT

)2cos(

)2cos(