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

摘要

We discuss the leptonic decay constants of heavy-light mesons by means ofBorel QCD sum rules in the local-duality (LD) limit of infinitely large Borelmass parameter. In this limit, for an appropriate choice of the invariantstructures in the QCD correlation functions, all vacuum-condensatecontributions vanish and all nonperturbative effects are contained in only onequantity, the effective threshold. We study properties of the LD effectivethresholds in the limits of large heavy-quark mass $m_Q$ and small light-quarkmass $m_q$. In the heavy-quark limit, we clarify the role played by theradiative corrections in the effective threshold for reproducing the pQCDexpansion of the decay constants of pseudoscalar and vector mesons. We showthat 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 theperturbative spectral densities. Making use of the lattice QCD results for thedecay constants of nonstrange and strange pseudoscalar and vector heavy mesons,we obtain solid predictions for the decay constants of heavy-light mesons asfunctions of $m_q$ in the range from a few to 100 MeV and evaluate thecorresponding strong isospin-breaking effects: $f_{D^+} - f_{D^0}=(0.96 \pm0.09) ~ {\rm MeV}$, $f_{D^{*+}} - f_{D^{*0}}= (1.18 \pm 0.35) ~ {\rm MeV}$,$f_{B^0} - f_{B^+}=(1.01 \pm 0.10) ~ {\rm MeV}$, $f_{B^{*0}} - f_{B^{*+}}=(0.89\pm 0.30) ~ {\rm MeV}$.