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

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 (md−mu), obtaining: (fD+−fD0)/fD=0.0047(6), (fD⁎+−fD⁎0)/fD⁎=0.0068(9), (fB0−fB+)/fB=0.0047(6), and (fB⁎0−fB⁎+)/fB⁎=0.0045(5), which yield: fD+−fD0=0.97±0.13 MeV, fD⁎+−fD⁎0=1.73±0.27 MeV, fB0−fB+=0.90±0.13 MeV, fB⁎0−fB⁎+=0.81±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 ≈3 standard deviations.