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The correlation function of two pseudoscalar charmed quark currents with apositive hadronic spectral density is employed to obtain upper bounds on thedecay constants of $D$ and $D_s$ mesons. Including all known terms of theoperator-product-expansion of this correlation function in QCD and taking intoaccount 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 boundand current experimental value of $f_{D_s}$.

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