Transcript International Workshop on Transversity: New Developments in Nucleon Spin Structure

International Workshop on Transversity:
New Developments in Nucleon Spin Structure
13-18 June 2004
Vrije Universiteit Amsterdam
Color Gauge Invariance in Hard Processes
Fetze Pijlman
in collaboration with
•A. Bacchetta
•D. Boer
•C.J. Bomhof
•P.J. Mulders
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.B396:161, 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. C18:639, 2001
Mulders, Tangerman, Nucl.Phys. B461:197, 1996
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Calculation of the hadronic tensor
1. assume factorization
2. make an expansion in M/Q
Resumming all
+
If
then
gluons
coming from the proton
give leading contributions
(leading twist)
gluons coming from the proton
+
+
Efremov, Radyushkin, Theor.Math.Phys. 44:774, 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.B656:165,2003
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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. B667:201,2003
3) links could spoil the Lorentz Invariance Relations such as
Goeke, Metz, Pobylitsa, Polyakov, Phys.Lett.B567:27,2003
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. B667:201,2003
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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:
large momentum:
difference is exactly
a gluonic pole
C.J. Bomhof, P.J. Mulders, F.P., hep-ph/0406099
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Summary and outlook
1) 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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