Perturbative renormalization of the first moment of structure functions for domain-wall QCD

Abstract

Using the domain-wall formulation of lattice fermions, we have computed the one-loop renormalization factors of one-link operators which measure the first nontrivial moment of the unpolarized, polarized and transversity structure functions, in the flavor nonsinglet sector. The knowledge of these factors is necessary in order to extract physical numbers from domain-wall Monte Carlo simulations of parton distributions.We have automated the perturbative calculations by developing suitable FORM codes. The results show that in many instances the total renormalization factors are almost equal to one, and that hence the corresponding operators are, for the appropriate values of the Dirac mass M and the coupling g0, practically unrenormalized.

Chiral violations in domain-wall QCD from one-loop perturbation theory at finiteNs

“…When M is indeed close to 0.1 or 1.9, the numerical convergence of the integrals (which are computationally quite demanding, being in this case sums over a six-dimensional space) is much worse then when M is nearer to 1. This behavior had already been noticed in the calculations for the [40], however now the convergence is even slower than in that case, and it also tends to become worse when N s is small.…”

“…Towards this end we present here the results of some selected one-loop calculations which we have carried out using the Feynman rules which exactly correspond to the theory at finite N s . This is at variance with past domainwall perturbative calculations where, in place of the exact quark propagators, their asymptotic expressions for large N s were instead used [37,38,39,40]. The purpose of this work is to calculate with the exact Feynman rules the deviations from the N s = ∞ results in the case where N s is limited to small values of O (10), that is for situations which roughly correspond to present simulations.…”

“…[40] for N s = ∞. These codes are now able to compute matrix elements for general values of N s and M .…”

“…Here and in most of the paper we put a = 1, but in some contexts, like when discussing the residual mass, the lattice spacing will be explicitly shown. We refer to [38,39,40] for the Feynman rules which derive from this domain-wall action in the limit N s → ∞. In this article we always work at finite N s , and the expressions that we have to use for the quark propagators are then different.…”

“…It is easy to check that all the propagators that we have derived in this Section reduce to the expressions used in the calculations of Refs. [38,39,40] when N s is large. Notice also that the function E(p) introduced here tends in this approximation to the function F (p) as defined in those articles.…”