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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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