Heavy meson chiral perturbation theory in finite volume

We study finite volume effects in heavy quark systems in the framework of heavy meson chiral perturbation theory for full, quenched, and partially quenched QCD. A novel feature of this investigation is the role played by the scales ${\Delta }_{*}$ and ${\delta }_s,$ where ${\Delta }_{*}$ is the mass difference between the heavy-light vector and pseudoscalar mesons of the same quark content, and ${\delta }_s$ is the mass difference due to light flavor $\mathrm{SU}\left(3\right)\mathrm{}$ breaking. The primary conclusion of this work is that finite volume effects arising from the propagation of Goldstone particles in the effective theory can be altered by the presence of these scales. Since ${\Delta }_{*}$ varies significantly with the heavy quark mass, these volume effects can be amplified in both heavy and light quark mass extrapolations (interpolations). As an explicit example, we present results for B parameters of neutral B meson mixing matrix elements and heavy-light decay constants to one-loop order in finite volume heavy meson chiral perturbation theory for full, quenched, and $N_f=2+1\mathrm{}$ partially quenched QCD. Our calculation shows that for high-precision determinations of the phenomenologically interesting $\mathrm{SU}\left(3\right)\mathrm{}$ breaking ratios, finite volume effects are significant in quenched and not negligible in partially quenched QCD, although they are generally small in full QCD.