Vector meson masses in 2+1 flavor Wilson Chiral Perturbation Theory

TL;DR

This paper derives the dependence of vector meson masses on quark masses and lattice spacing in 2+1 flavor Wilson chiral perturbation theory at next-to-leading order, accounting for lattice artifacts.

Contribution

It extends heavy vector meson chiral perturbation theory to include lattice cutoff effects in 2+1 flavor Wilson fermions at NLO.

Findings

Derived quark mass and lattice cutoff dependence of vector meson masses.

Established a consistent power counting scheme including O(a^2) terms.

Provided formulas applicable to lattice QCD simulations.

Abstract

We calculate the vector meson masses in $N_{\rm f} = 2+1$ Wilson chiral perturbation theory at next-to-leading order. Generalizing the framework of heavy vector meson chiral perturbation theory, the quark mass and the lattice cutoff dependence of the vector meson masses is derived. Our chiral order counting assumes that the lattice cut-off artifacts are of the order of the typical pion momenta, $p \sim a\Lambda_{\rm QCD}^{2}$. This counting scheme is consistent with the one in the pseudo scalar meson sector where the O($a^2$) terms are included in the leading order chiral Lagrangian.