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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
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Outline:
1: Brief review2: Collins function in the collinear factroization approach3: Summary & outlook
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Single spin asymmetry
Xπpp )(
p p
πL
R
Naive parton model:1978, Kane, Pumplin, Repko
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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
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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
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kT-odd TMD distributions at large KTGenerally speaking,
TMD distributions can be calculated by using collinear approach
radiated gluon lead to large kT gluon rescattering lead to
asymm
etry 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 !
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Collins function and its kT
moment
Kt-moment defines a twist-3 fragmentation function
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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
ix
1)(
1
gluon pole
),(1
1zziHx
P Fg
),()( 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) +
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Universality of the Collins Fragmentation
ep--> e Pi X e+e--> Pi Pi X pp--> jet(->Pi) X
Metz 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.
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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)
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Collins function at large kt
typpical diagrams:
where we changed the normalizationof HF(z,z1)
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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
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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 t
he 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.