Heavy meson chiral perturbation theory in finite volume

TL;DR

This paper investigates how finite volume effects influence heavy meson properties in chiral perturbation theory across different QCD frameworks, highlighting the impact of specific mass scales on volume corrections.

Contribution

It introduces the role of the scales Delta and delta_s in finite volume effects and provides one-loop order calculations for B meson parameters in various QCD approximations.

Findings

Finite volume effects are amplified by the scale Delta, especially in heavy quark mass extrapolations.

Finite volume effects are significant in quenched QCD and non-negligible in partially quenched QCD.

In full QCD, finite volume effects are generally small, affecting high-precision determinations.

Abstract

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 flavour SU(3) 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 partially quenched QCD. Our calculation shows that for high-precision determinations of the phenomenologically interesting SU(3) breaking ratios, finite volume effects are significant in quenched and not negligible in partially quenched QCD, although they are generally small in full QCD.