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Defining TMD correlators

QCD workshop, JLAB, May 2012. Defining TMD correlators. Piet Mulders. m.g.a.buffing@vu.nl. mulders@few.vu.nl. Transverse moments. Remember for transverse moments s atisfying What happens before integration? (at least in cases that a gauge-linked TMD makes sense).

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Defining TMD correlators

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  1. QCD workshop, JLAB, May 2012 Defining TMD correlators Piet Mulders m.g.a.buffing@vu.nl mulders@few.vu.nl

  2. Transverse moments • Remember for transverse moments • satisfying • What happens before integration? (at least in cases that a gauge-linked TMD makes sense)

  3. A possible construction of TMDs • Expansion • Weighting

  4. Examples • Expansion • Example 1: unpolarized target

  5. Examples • Expansion • Example 1: unpolarized target

  6. Examples • Expansion • Example 2: TMD PDFs for spin ½ target

  7. Examples • Expansion • Example 3: TMD PFFs for spin ½ fragment

  8. TMDs for gluons • 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: Fg[-,-] Fg[+,+] Fg[+,-] Fg[-,+] C Bomhof, PJM, F Pijlman; EPJ C 47 (2006) 147 F Dominguez, B-W Xiao, F Yuan, PRL 106 (2011) 022301

  9. Higher 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 Fg[+,+]+Fg[-,-] and Fg[+,-]+Fg[-,+]are T-even with 2nd moments containing <[F,G] [G,F]> and <{F,G} {G,F}> operator terms respectively C Bomhof and PJ Mulders, NPB 795 (2008) 409 F Dominguez, J-W Qiu, B-W Xiao and F Yuan, PR D85 (2012) 045003

  10. 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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