MS-bar definition of parton distribution functions
The parton distribution functions are defined as matrix elements of
certain operators:
Here |P,s> represents a proton state, and we normally
average over the spin state. The operators O are made of quark
and gluon fields. The operators need renormalization to make
them well defined. The renormalization is performed using the
MS-bar convention. (This gives the mu dependence of the parton
distribution functions.)
Details may be found in Handbook of perturbative QCD by
the CTEQ Collaboration (Sterman et al.), published in
Reviews of Modern Physics, 67 (1995) 157 or in Parton Distribution Functions, a talk by D. E. Soper at the Lattice 96 Conference
(206 Kbytes, gzipped Postscript). More details can be found in
J. C. Collins and D. E. Soper, Nucl. Phys. B194 (1982) 445 and in
G. Curci, W. Furmanski and R. Petronzio, Nucl. Phys. B 175 (1980) 27.
Davison E. Soper and Parvez Anandam
Institute of Theoretical Science,
University of Oregon, Eugene OR 97403 USA
soper@bovine.uoregon.edu
anandam@darkwing.uoregon.edu