C,b quark masses and f,f decay constants from pseudoscalar sum rules in full QCD to order α2

Abstract

Abstract The pseudoscalar sum rules of the heavy–light quark systems are used for extracting simultaneously the c,b quark masses and the decay constants fD(s),fB(s) of the D(s),B(s) mesons. To order αs2, one obtains the running quark masses: m c (m c )=(1.10±0.04) GeV, m b (m b )=(4.05±0.06) GeV implying m b (M Z )=(2.65±0.05) GeV; the perturbative pole masses: Mc=(1.46±0.04) GeV, Mb=(4.69±0.06) GeV; and the decay constants: fD=(205±20) MeV, fB=(203±23) MeV and fDs=(235±24) MeV, fBs=(236±30) MeV, in the normalization where fπ=130.56 MeV. The fitted values of the pole and running masses satisfy quite well their three-loop perturbative relation. The value fD≃fB confirms earlier findings from the sum rule that the 1/ M P heavy quark symmetry scaling law is affected by large 1/MP corrections.