Renormalisation and off-shell improvement in lattice perturbation theory

TL;DR

This paper develops one-loop lattice perturbation theory calculations for improved quark operators, addressing off-shell effects and comparing clover and Ginsparg-Wilson fermions, including tadpole improvement.

Contribution

It provides a systematic method for off-shell improvement of lattice quark operators and compares different fermion formulations at one-loop order.

Findings

Calculated renormalisation factors and improvement coefficients for improved operators.

Demonstrated off-shell improvement by eliminating contact term effects.

Compared clover and Ginsparg-Wilson fermions, showing simpler off-shell improvement for the latter.

Abstract

We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg-Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.