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

摘要

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 ± 0.13 ?MeV , f D ? + ? f D ? 0 = 1.73 ± 0.27 ?MeV , f B 0 ? f B + = 0.90 ± 0.13 ?MeV , f B ? 0 ? f B ? + = 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.