Staggered Chiral Perturbation Theory for Heavy-Light Mesons

TL;DR

This paper develops a theoretical framework combining heavy-light mesons with staggered chiral perturbation theory, analyzing taste violations and calculating decay constants at one-loop order in QCD.

Contribution

It introduces a novel heavy-light staggered chiral perturbation theory and performs one-loop calculations of meson decay constants including taste violation effects.

Findings

Taste violations affect chiral logarithms through light meson propagators.

New analytic terms arise from additional Lagrangian contributions.

Calculated B and D meson decay constants at one-loop order.

Abstract

We incorporate heavy-light mesons into staggered chiral perturbation theory, working to leading order in 1/m_Q, where m_Q is the heavy quark mass. At first non-trivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light staggered chiral perturbation theory, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the "fourth root trick" to reduce four staggered tastes to one, and of the prescription to represent this trick in the chiral theory by insertions of factors of 1/4 for each sea quark loop.