Staggered chiral perturbation theory for heavy-light mesons

We incorporate heavy-light mesons into staggered chiral perturbation theory ($\mathrm{S}\chi \mathrm{PT}$), working to leading order in $1/m_Q$, where $m_Q$ is the heavy-quark mass. At first nontrivial 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 $\mathrm{S}\chi \mathrm{PT}$, 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 $\mathrm{S}\chi \mathrm{PT}$ prescription to represent this trick by insertions of factors of $1/4$ for each sea-quark loop.