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

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: $(f_{D^{+}}-f_{D^0})/f_D=0.0047(6)$, $(f_{D^{\ast +}}-f_{D^{\ast 0}})/f_{D^{\ast }}=0.0068(9)$, $(f_{B^0}-f_{B^{+}})/f_B=0.0047(6)$, and $(f_{B^{\ast 0}}-f_{B^{\ast +}})/f_{B^{\ast }}=0.0045(5)$, which yield: $f_{D^{+}}-f_{D^0}=0.97\pm 0.13$ MeV, $f_{D^{\ast +}}-f_{D^{\ast 0}}=1.73\pm 0.27$ MeV, $f_{B^0}-f_{B^{+}}=0.90\pm 0.13$ MeV, $f_{B^{\ast 0}}-f_{B^{\ast +}}=0.81\pm 0.11$ 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.

arXiv comment8 pages, 1 figure; this version matches the published one

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• Heavy-Light Mesons in the Non-Relativistic Quark Model Using Laplace Transformation Method
• Isospin splittings in the decuplet baryon spectrum from dynamical QCD+QED
• Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy-light mesons
• Radiative Decays of Heavy-light Mesons and the $f_{H,H^{\ast },H_1}^{(T)}$ Decay Constants
• Strong Isospin Breaking in Heavy-Meson Decay Constants: Employing Borelized QCD Sum Rules in Local-Duality Limit
• Strong Isospin Breaking in the Decay Constants of Heavy-Light Mesons from Local-Duality QCD Sum Rules
• Radiative Decays of Vector Mesons with Light-Cone Sum Rules