Isospin Breaking in Heavy-Meson Decay Constants

TL;DR

This paper uses a novel QCD sum rule approach in the local-duality limit to analyze how heavy-light meson decay constants depend on the light quark mass, revealing that nonperturbative effects vanish and perturbative contributions dominate.

Contribution

It introduces an alternative method using local-duality limit of QCD sum rules to isolate perturbative effects in heavy-light meson decay constants, highlighting isospin breaking effects.

Findings

Isospin breaking in decay constants is about 1 MeV for charm and beauty mesons.

Nonperturbative vacuum condensate contributions vanish in the local-duality limit.

Perturbative QCD determines the light-quark mass dependence of decay constants.

Abstract

Evaluation of Borelized QCD sum rules in the so-called local-duality limit of infinitely large Borel mass parameter provides an alternate route for extraction of the dependence of the decay constants of heavy-light mesons on the mass $m_q$ of the involved light quark $q$: For appropriate choices of the two-point correlation functions of currents interpolating the hadrons under study, the local-duality limit forces all nonperturbative contributions parametrized by vacuum condensates to such kind of correlator to vanish. As a consequence, the sought $m_q$ dependence of the heavy-light meson decay constants proves to be controlled primarily by the correlator contributions from perturbative QCD. Our knowledge of the analytic behaviour of the latter as functions of $m_q$ enables us to derive the $m_q$ dependence of the decay constants of both pseudoscalar and vector heavy-light mesons, for which we estimate strong isospin breaking to be of the order of 1 MeV for both charm and beauty sectors.