The vector and axial currents in Wilson chiral perturbation theory

TL;DR

This paper analyzes the construction and matching of vector and axial currents in Wilson Chiral Perturbation Theory, emphasizing the effects of finite renormalization and chiral Ward-Takahashi identities on physical quantities like the pion decay constant.

Contribution

It provides a detailed examination of current matching in WChPT, revealing additional O(a) terms from Ward identities and presenting a corrected one-loop calculation of the pion decay constant.

Findings

Additional O(a) terms in axial current from Ward identities

Explicit one-loop calculation of pion decay constant

Differences from previous results in literature

Abstract

We reconsider the construction and matching of the vector and axial currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. In particular, we discuss in detail the impact of the finite renormalization of the currents on their matching from the lattice theory to WChPT.We explicitly show that imposing chiral Ward-Takahashi identities on the currents leads, in general, to additional terms of O(a) in the axial current. We illustrate the impact on physical quantities by computing the pion decay constant to one-loop order in the two flavor theory. Our result differs from previously published ones.