defining tmd correlators
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Defining TMD correlatorsDefining TMD correlators
QCD workshop, JLAB, May 2012QCD workshop, JLAB, May 2012
mulders@few.vu.nl
Piet MuldersPiet Mulders
m.g.a.buffing@vu.nl
Transverse momentsTransverse moments
Remember for transverse moments
satisfying
What happens before integration? (at least in cases that a gauge-linked TMD makes sense)
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A possible construction of TMDsA possible construction of TMDs
Expansion
Weighting
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ExamplesExamples
Expansion
Example 1: unpolarized target
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ExamplesExamples
Expansion
Example 1: unpolarized target
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ExamplesExamples
Expansion
Example 2: TMD PDFs for spin ½ target
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ExamplesExamples
Expansion
Example 3: TMD PFFs for spin ½ fragment
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TMDs for gluonsTMDs for gluons
2[ , '] . [ ] [ ']
[ ,0] [0, ]3 . 0
( . )( , ; )
(2 )(0) ( )C C i p C CT
g Tn
n
nd P dx p n e P U U F PF
The TMD gluon correlators contain two links, which can have
different paths. Note that standard field displacement involves C = C’
Basic (simplest) gauge links for gluon TMD correlators:
[ ] [ ][ , ] [ , ]( ) ( )C CF U F U
g g
g g
C Bomhof, PJM, F Pijlman; EPJ C 47 (2006) 147F Dominguez, B-W Xiao, F Yuan, PRL 106 (2011) 022301
C Bomhof, PJM, F Pijlman; EPJ C 47 (2006) 147F Dominguez, B-W Xiao, F Yuan, PRL 106 (2011) 022301
Higher azimuthal asymmetries and gluonsHigher azimuthal asymmetries and gluons
When construtin moments of these TMDs one needs operators <F F>, <F [F,F]>, <F, {F,F}>, <[F,F] [F,F]>, <{F,F} {F,F}> etc. again with increasing twist and several gluonic poles. Relevant in study of linearly polarized gluons in proton
Both g[+,+] + g
[] and g[+,] + g
[,+] are T-even with 2nd moments containing <[F,G] [G,F]> and <{F,G} {G,F}> operator terms respectively
9C Bomhof and PJ Mulders, NPB 795 (2008) 409F Dominguez, J-W Qiu, B-W Xiao and F Yuan, PR D85 (2012) 045003
C Bomhof and PJ Mulders, NPB 795 (2008) 409F Dominguez, J-W Qiu, B-W Xiao and F Yuan, PR D85 (2012) 045003
Beware!Beware!
Our treatment does not show factorization into TMDs with process-dependent gauge links!
It only concerns the study of transverse moments of TMDs and possible full definition of universal TMD distribution functions
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