Vector and Axial Currents in Wilson Chiral Perturbation Theory

TL;DR

This paper refines the construction and renormalization of vector and axial-vector currents in Wilson Chiral Perturbation Theory, highlighting the impact of finite renormalization and chiral Ward identities on lattice QCD calculations.

Contribution

It provides a detailed analysis of current renormalization in WChPT and computes the pion decay constant at one loop, revealing differences from previous results.

Findings

Finite renormalization affects the currents in WChPT.

Imposing Ward identities influences the axial-vector current at order a.

Computed pion decay constant differs from earlier published values.

Abstract

We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two flavor theory. Our result differs from previously published ones.