Upper bounds on $f_D$ and $f_{D_s}$ from two-point correlation function in QCD

Abstract

The correlation function of two pseudoscalar charmed quark currents with a positive hadronic spectral density is employed to obtain upper bounds on the decay constants of $D$ and $D_s$ mesons. Including all known terms of the operator-product-expansion of this correlation function in QCD and taking into account the estimated uncertainties, we obtain $f_D<230$ MeV and $f_{D_s}<270$ MeV. Comparison with the decay constants determined from $D\to l{\nu }_l$ and $D_s\to l{\nu }_l$ measurements, reveals a tension between the bound and current experimental value of $f_{D_s}$.

8 pages, 3 figures, a few comments,a table and references added, version to appear in Phys.Rev.D

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• Interpretation of the "$f_{D_s}$ puzzle" in SM and beyond