Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions

Abstract

Using the overlap-Dirac operator proposed by Neuberger, we have computed in lattice QCD the one-loop renormalization factors of ten operators which measure the lowest two moments of unpolarized and polarized non-singlet quark distributions. These factors are necessary to extract physical numbers from Monte Carlo simulations made with overlap fermions. An exact chiral symmetry is maintained in all our results, and the renormalization constants of corresponding unpolarized and polarized operators which differ by a ${\gamma }_5$ matrix have the same value. We have considered two lattice representations for each continuum operator. The computations have been carried out using the symbolic language FORM, in a general covariant gauge. In some simple cases they have also been checked by hand.

23 pages, 1 Postscript figure, uses elsevier style. Small corrections made in eqs. (6), (7), (13), (15), (17), (19), (20), (21) and (A.8), with no influence on the results

References in corpus (8)

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• Comment on `Controversy concerning the definition of quark and gluon angular momentum' by Elliot Leader (arXiv:1101.5956, PRD 83, 096012 (2011))
• Perturbative renormalization in parton distribution functions using Overlap fermions and Symanzik improved gluons
• The Lattice Free Energy with Overlap Fermions: A Two-Loop Result
• Quenched Chiral Behavior of Hadrons with Overlap Fermions
• Chiral violations in domain-wall QCD from one-loop perturbation theory at finite $N_s$