Matrix elements of the complete set of \Delta B = 2 and \Delta C = 2 operators in heavy meson chiral perturbation theory

TL;DR

This paper calculates the light quark-mass and volume dependence of matrix elements relevant for meson mixing and width differences using heavy meson chiral perturbation theory, aiding lattice QCD extrapolations.

Contribution

It provides detailed chiral perturbation theory results for elta B=2 and elta C=2 operators in heavy meson systems, including non-standard model cases.

Findings

Chiral extrapolations are more complex for beyond Standard Model operators.

Results are applicable for lattice QCD extrapolations to physical quark masses.

Analysis includes volume dependence and partially quenched effects.

Abstract

Using heavy meson chiral perturbation theory, we consider the light quark-mass and spatial volume dependence of the matrix elements of \Delta B=2 and \Delta C=2 four-quark operators relevant for B^{0}_{(s)}{-}\bar{B}^{0}_{(s)} and D^{0}{-}\bar{D}^{0} mixing, and the B_{s} meson width difference. Our results for these matrix elements are obtained in the N_{f}=2+1 partially quenched theory, which becomes full QCD in the limit where sea and valence quark masses become equal. They can be used in extrapolation of lattice calculations of these matrix elements to the physical light quark masses and to infinite volume. An important conclusion of this paper is that the chiral extrapolations for matrix elements of heavy-light meson mixing beyond the Standard Model, and those relevant for the B_s width difference are more complicated than that for the Standard Model mixing matrix elements.