Decay constants of the charmed vector mesons $D^*$ and $D^*_s$ from QCD sum rules

We present a sum-rule calculation of the decay constants of the charmed vector mesons $D^*$ and $D^*_s$ from the two-point correlator of vector currents. First, we show that the perturbative expansion in terms of the pole mass exhibits no sign of convergence whereas the reorganization of this expansion in terms of the $\overline{\rm MS}$ mass leads to a distinct hierarchy. Second, making use of the operator product expansion in terms of the $\overline{\rm MS}$ mass, we determine the decay constants of the $D^*$ and $D^*_s$ mesons with an emphasis on the uncertainties in these theoretically predicted quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Our results are $f_{D^*}=(252.2 \pm 22.3_{\rm OPE}\pm 4_{\rm syst})\; {\rm MeV}$ and $f_{D_s^*}=(305.5 \pm 26.8_{\rm OPE}\pm 5_{\rm syst})\; {\rm MeV}$. For the ratios of the vector-to-pseudoscalar decay constants we report $f_{D^*}/f_D= 1.221\pm 0.080_{\rm OPE}\pm 0.008_{\rm syst}$ and $f_{D^*_s}/f_{D_s}= 1.241\pm 0.057_{\rm OPE}\pm 0.007_{\rm syst}$.