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QCD workshop, JLAB, May 2012. Defining TMD correlators. Piet Mulders. [email protected]. [email protected]. Transverse moments. Remember for transverse moments s atisfying What happens before integration? (at least in cases that a gauge-linked TMD makes sense). - PowerPoint PPT Presentation
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Defining TMD correlatorsDefining TMD correlators
QCD workshop, JLAB, May 2012QCD workshop, JLAB, May 2012
Piet MuldersPiet Mulders
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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