Deep Inelastic Scattering in Improved Lattice QCD. II. The second moment of structure functions

TL;DR

This paper computes renormalization constants for lattice QCD operators relevant to the second moment of DIS structure functions using improved clover action, aiding more accurate lattice calculations.

Contribution

It provides the 1-loop perturbative renormalization constants and mixing coefficients for third-rank quark operators in improved lattice QCD, focusing on the second moment of DIS.

Findings

Calculated renormalization constants for rank three operators.

Demonstrated the feasibility of lattice computations for higher-rank operators.

Discussed operator transformation properties under hypercubic group.

Abstract

In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions. We have employed in our calculations the nearest-neighbor improved ``clover-leaf'' lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order $a$ ($a$ being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators. We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form.