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

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 $Dto l u_l$ and $D_sto l u_l$ measurements, reveals a tension between the bound and current experimental value of $f_{D_s}$.