Isospin Mass Differences of the $B$, $D$ and $K$

TL;DR

This paper calculates the electromagnetic mass differences of B, D, and K mesons using QCD sum rules, providing results consistent with experimental data despite large uncertainties.

Contribution

It introduces a novel application of double dispersion relations in QCD sum rules to compute meson mass differences, including quark mass corrections.

Findings

Results are consistent with experimental measurements.

Large uncertainties remain in the calculations.

Method successfully applies to different meson types.

Abstract

We compute the electromagnetic mass difference for the $B$-, $D$- and $K$-mesons using QCD sum rules with double dispersion relations. For the $B$- and $D$-mesons we also compute the linear quark mass correction, whereas for the $K$ the standard soft theorems prove more powerful. The mass differences, which have not previously been computed via a double dispersion, are fully consistent with experiment, albeit with large uncertainties.