Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy-light mesons

Abstract: We discuss the leptonic decay constants of heavy--light mesons by means of Borel QCD sum~rules in the local-duality (LD) limit of infinitely large Borel mass parameter. In this limit, for an appropriate choice of the invariant structures in the QCD correlation functions, all vacuum-condensate contributions vanish and all nonperturbative effects are contained in only one quantity, the effective threshold. We study properties of the LD effective thresholds in the limits of large heavy-quark mass $m_Q$ and small light-quark mass $m_q$. In the heavy-quark limit, we clarify the role played by the radiative corrections in the effective threshold for reproducing the pQCD expansion of the decay constants of pseudoscalar and vector mesons. We show that the dependence of the meson decay constants on $m_q$ arises predominantly (at the level of 70--80%) from the calculable $m_q$-dependence of the perturbative spectral densities. Making use of the lattice QCD results for the decay constants of nonstrange and strange pseudoscalar and vector heavy mesons, we obtain solid predictions for the decay constants of heavy--light mesons as functions of $m_q$ in the range from a few to 100 MeV and evaluate the corresponding strong isospin-breaking effects: $f_{D^+} - f_{D^0}=(0.96 \pm 0.09) ~ {\rm MeV}$, $f_{D^{*+}} - f_{D^{*0}}= (1.18 \pm 0.35) ~ {\rm MeV}$, $f_{B^0} - f_{B^+}=(1.01 \pm 0.10) ~ {\rm MeV}$, $f_{B^{*0}} - f_{B^{*+}}=(0.89 \pm 0.30) ~ {\rm MeV}$.