azimuthal asymmetry in the unpolarized drell-yan process zhou jian shandong university, china &...
DESCRIPTION
A general expression for Drell-Yan virtual photon decay angular distributions: In general : Θ and Φ are the decay polar and azimuthal angles of the μ+ in the dilepton rest-frameTRANSCRIPT
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(