In-medium operator product expansion for heavy-light-quark pseudoscalar mesons

TL;DR

This paper develops an in-medium operator product expansion for heavy-light pseudoscalar mesons, addressing IR divergences and operator mixing, and compares the results with previous theoretical findings.

Contribution

It provides a detailed OPE framework for D- and B-mesons in medium, including IR-stable Wilson coefficients and operator mixing effects, with a comparison to prior results.

Findings

IR-stable Wilson coefficients derived

Operator mixing absorbed IR divergences

Disagreements found with previous theoretical results

Abstract

The operator product expansion (OPE) for heavy-light-quark pseudoscalar mesons (D-mesons and B-mesons) in medium is determined, both for a moving meson with respect to the surrounding medium as well as for a meson at rest. First of all, the OPE is given in terms of normal-ordered operators up to mass dimension 5, and the mass of the heavy-quark and the mass of the light-quark are kept finite. The Wilson coefficients of such an expansion are infrared (IR) divergent in the limit of a vanishing light-quark mass. A consistent separation of scales necessitates an OPE in terms of non-normal-ordered operators, which implies operator mixing, where the IR-divergences are absorbed into the operators. It is shown that the Wilson coefficients of such an expansion are IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details of the major steps for the calculation of the Wilson coefficients are presented. By a comparison with previous results obtained by other theoretical groups we have found serious disagreements.