OPE, charm-quark mass, and decay constants of D and [Formula: see text] mesons from QCD sum rules

We present a sum-rule extraction of the decay constants of the charmed mesons D and [Formula: see text] from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running [Formula: see text] masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the [Formula: see text] mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the [Formula: see text]-mass correlator. Second, making use of the OPE in terms of the [Formula: see text] mass, we determine the decay constants of both D and [Formula: see text] mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.