The vector and axial vector current in Wilson ChPT

TL;DR

This paper constructs vector and axial vector currents in Wilson Chiral Perturbation Theory, addressing explicit chiral symmetry breaking effects at finite lattice spacing and demonstrating their impact on physical quantities like f_pi.

Contribution

It introduces a modified construction of currents in WChPT that accounts for O(a) lattice artifacts and finite renormalization effects, differing from continuum ChPT.

Findings

Derived expressions for currents including O(a) corrections

Computed f_pi at one loop with renormalized axial current

Showed some O(a) effects are absorbed by renormalization

Abstract

We construct the vector and axial vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. Our construction is slightly different compared to ChPT in continuum QCD, where the currents are essentially the (partially) conserved currents associated with the chiral symmetries. In WChPT, due to explicit chiral symmetry breaking at non-zero lattice spacing, there appear O(a) terms in the expressions for the currents which do not stem from the effective action. In addition, the finite renormalization of the currents needs to be taken into account in order to properly match the currents of the effective theory. As an illustration we compute f_pi to one loop with the renormalized axial vector current for a particular renormalization condition. It turns out that for this particular condition some of the O(a) corrections are taken care of by the renormalization.