Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice

TL;DR

This paper calculates two-loop renormalization functions for vector, axial-vector, and tensor fermion bilinear operators on the lattice, providing results in multiple schemes and for various fermion representations.

Contribution

It presents the first two-loop renormalization functions for these operators in the RI' scheme on the lattice, including both singlet and nonsinglet cases, with results in MSbar for continuum comparison.

Findings

Provides polynomial expressions in $c_{SW}$ for renormalization functions.

Includes results in the MSbar scheme for continuum matching.

Addresses superficial divergence issues in integrals.

Abstract

We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\bar{\psi}\Gamma\psi$, where $\Gamma$ corresponds to the Vector, Axial-Vector and Tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MSbar scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the Appendices.