Analysis of the decay constants of the heavy pseudoscalar mesons with QCD sum rules

In this article, we recalculate the contributions of all vacuum condensates up to dimension-6, in particular the one-loop corrections to the quark condensates alpha(s)<(q) over barq > and partial one-loop corrections to the four-quark condensates alpha(2)(s)<(q) over barq >(2), in the operator product expansion. Then we study the masses and decay constants of the heavy pseudoscalar mesons D, D-s, B and B-s using the QCD sum rules with two choices: I we choose the (MS) over bar masses by setting m = m(mu) and take perturbative corrections up to the order O(alpha(s)); II we choose the pole masses m, take perturbative corrections up to the order O(alpha(2)(s)) and set the energy-scale to be the heavy quark pole mass mu = m(Q). In the case of I, the predictions f(D) = (208 +/- 11) MeV and f(B) = (189 +/- 15) MeV are consistent with the experimental data within uncertainties, while the prediction f(Ds) = (241 +/- 12) MeV is below the lower bound of the experimental data f(Ds) = (260.0 +/- 5.4) MeV. In the case of II, the predictions f(D) = (211 +/- 14) MeV, f(B) = (190 +/- 17) MeV, f(Ds) = (258 +/- 13) MeV and f(Ds) /f(D) = 1.22 +/- 0.08 are all in excellent agreements with the experimental data within uncertainties.