Isospin breaking in the decay constants of heavy mesons from QCD sum rules

TL;DR

This paper investigates the isospin-breaking effects on decay constants of heavy mesons using QCD sum rules, providing precise ratios and differences that are compared with lattice QCD results, revealing some discrepancies.

Contribution

It introduces a QCD sum rule analysis of isospin-breaking effects on heavy meson decay constants, achieving high-precision ratios and differences, and compares findings with lattice QCD results.

Findings

Calculated isospin-breaking ratios for D and B mesons.

Found good agreement with lattice QCD for D mesons.

Identified a discrepancy for B mesons with lattice results.

Abstract

We present a study of the strong isospin-breaking (IB) effect, due in QCD to the difference between $u$- and $d$-quark masses, in the leptonic decay constants of charmed and beauty pseudoscalar and vector mesons using the method of QCD sum rules. We apply the sum-rule analysis to the decay constants of mesons containing one heavy quark and one light quark with the light mass in the range from the average $u/d$ quark mass to the strange-quark mass. We then analyse the dependence of the decay constants on the light quark mass and extract with good accuracy the IB ratios of decay constants at leading order in the mass difference $(m_d - m_u)$, obtaining: $(f_{D^+} - f_{D^0}) / f_{D} = 0.0047 (6)$, $(f_{D^{*+}} - f_{D^{*0}}) / f_{D^*} = 0.0068 (9)$, $(f_{B^0} - f_{B^+}) / f_{B} = 0.0047 (6)$, and $(f_{B^{*0}} - f_{B^{*+}}) / f_{B^*} = 0.0045 (5)$, which yield: $f_{D^+} - f_{D^0} = 0.97 \pm 0.13$ MeV, $f_{D^{*+}} - f_{D^{*0}} = 1.73 \pm 0.27$ MeV, $f_{B^0} - f_{B^+} = 0.90 \pm 0.13$ MeV, $f_{B^{*0}} - f_{B^{*+}} = 0.81 \pm 0.11$ MeV. In the case of the $D$-meson our finding is consistent with recent lattice QCD results, whereas it is much lower in the case of the $B$-meson showing a tension of $\approx 3$ standard deviations.