Color Gauge Invariance in Hard Processes

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Color Gauge Invariance in Hard Processes
Vrije Universiteit Amsterdam
Fetze Pijlman
in collaboration with

• A. Bacchetta
• D. Boer
• C.J. Bomhof
• P.J. Mulders

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Contents

• transversity and transverse momentum dependent
  correlators
• gauge links appearing in hard scattering
  processes
• gauge links and their consequences
• gauge links in more complex hard QCD processes
• summary

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Transversity in semi-inclusive DIS

• cross-section

leading order in M/Q
transversity in the hadronic tensor
Collins, Nucl.Phys.B396161, 1993
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Example of a proper deconvolution concerning
transversity

• Longitudinal polarized target (beam direction)
• and unpolarized electron beam
• transverse moment of the Collins function

Bacchetta, Mulders, F.P., hep-ph/0405154 Korotkov,
Nowak, Oganessyan, Eur.Phys.J. C18639,
2001 Mulders, Tangerman, Nucl.Phys. B461197, 1996
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Calculation of the hadronic tensor

1. assume factorization
2. make an expansion in M/Q

If then gluons coming from
the proton give leading contributions (leading
twist)
Resumming all gluons coming from the
proton
...
Efremov, Radyushkin, Theor.Math.Phys. 44774, 1981
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Introduction of the gauge links

• Resummation of gluons
• in SIDIS at leading order

Resummation of gluons in Drell-Yan at
leading order
Belitsky, Ji, Yuan, Nucl.Phys.B656165,2003
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Relevance of gauge links

• 1) nice gauge invariant correlators, affects
  transverse moments
• 2) the origin of the Sivers effect and
  Qiu-Sterman mechanism in
• SIDIS and DY
• 
  Boer, Mulders, F.P., Nucl.Phys. B667201,2003
• 3) links could spoil the Lorentz Invariance
  Relations such as
• Goeke, Metz,
  Pobylitsa, Polyakov, Phys.Lett.B56727,2003
• 4) the link dependence might lead to additional
  distribution
• functions like
  Bacchetta, Mulders, F.P., hep-ph/0405154
• 5) for fragmentation there are 2 sources for
  T-odd effects which
• prohibit a simple sign relation between the
  functions measured in
• SIDIS and e e- annihilation
• 
  Boer, Mulders, F.P., Nucl.Phys.
  B667201,2003

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Input from the experimental side

• 1) a nonzero Sivers function proves the
  existence of
• T-odd distribution functions and gluonic
  poles. It would stress
• the importance of the link structure
• 2) a nonzero stresses the link
  dependency in correlators
• and indicates a violation of the Lorentz
  Invariance Relations.
• asymmetry for jet production in DIS
• (polarized beam, unpolarized target, quark
  masses neglected)

Bacchetta, Mulders, F.P., hep-ph/0405154
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Links in large transverse momentum in SIDIS

soft pole
hard pole
1) hard poles are cancelled and soft poles
remain and give the gauge link 2) link structure
is similar to ordinary SIDIS ( )
C.J. Bomhof, P.J. Mulders, F.P., hep-ph/0406099
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Introduction of a (Wilson) loop

• link for DY at large
• transverse momentum
• link for DY

transverse moments ordinary DY
difference is exactly large
momentum a gluonic
pole
C.J. Bomhof, P.J. Mulders, F.P., hep-ph/0406099
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Summary and outlook

• We found more complex link structures in hard
  scattering
• processes involving loops. The differences
  in link structures
• appear in azimuthal asymmetries as gluonic
  poles.
• 2) Nonzero gluonic poles imply T-odd
  distribution functions and
• require a link prescription to describe the
  asymmetries.
• 3) The link dependence leads to the introduction
  of new functions.
• One of these new functions ,
  can be measured in
• jet production in DIS.
• 4) We will study link structures and their
  consequences in more
• general scattering processes like pion
  production in proton proton
• scattering.

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