Abstract
Using recent values of the QCD (non-)perturbative parameters given in Table 1 and an estimate of the N3LO QCD perturbative contributions based on the geometric growth of the PT series, we re-use QCD spectral sum rules (QSSR) known to N2LO PT series and including all dimension-six NP condensate contributions in the full QCD theory, for improving the existing estimates of m¯c,b and fD(s),B(s) from the open charm and beauty systems. We especially study the effects of the subtraction point on “different QSSR data” and use (for the first time) the Renormalization Group Invariant (RGI) scale-independent quark masses in the analysis. The estimates [rigourous model-independent upper bounds within the SVZ framework] reported in Table 8: fD/fπ=1.56(5)[⩽1.68(1)], fB/fπ=1.58(5)[⩽1.80(3)] and fDs/fK=1.58(4)[⩽1.63(1)], fBs/fK=1.50(3)[⩽1.61(3.5)], which improve previous QSSR estimates, are in perfect agreement (in values and precisions) with some of the experimental data on fD,Ds and on recent lattice simulations within dynamical quarks. These remarkable agreements confirm both the success of the QSSR semi-approximate approach based on the OPE in terms of the quark and gluon condensates and of the Minimal Duality Ansatz (MDA) for parametrizing the hadronic spectral function which we have tested from the complete data of the J/ψ and ϒ systems. The values of the running quark masses m¯c(mc)=1286(66) MeV and m¯b(mb)=4236(69) MeV from MD,B are in good agreement though less accurate than the ones from recent J/ψ and ϒ sum rules.
Highlights
Introduction and a short historical reviewThescalar meson decay constants fP are of prime interests for understanding the realizations of chiral symmetry in QCD
We may have improved the accuracy of our predictions by introducing more model-dependent new parameters for parametrizing the continuum contribution, which we would not do as, in addition to the test performed in Section 2, we want to check the degree of accuracy of the Minimal Duality Ansatz (MDA) parametrization for the heavy-light systems by confronting the results obtained in this paper with the some known data on fP or from lattice simulations
We have used as inputs, the recent values of the QCDperturbative parameters given in Table 1 and the renormalization group invariant quark and spontaneous masses in Eqs. (18) and (19)
Summary
The (pseudo)scalar meson decay constants fP are of prime interests for understanding the realizations of chiral symmetry in QCD. It has been completed by the PT α2s N2LO corrections of Chetyrkin and Steinhauser [17] in the case of one heavy and one massless quarks This result has been completed by the inclusion of the NP contributions up to dimension-six [11] and of the light quark mass corrections to LO by [11, 18]. We shall use for the B-meson, the moments obtained after deriving n + 1-times the two-point function and evaluated at Q2 = 0 [3], where an expansion in terms of the on-shell mass Mb can be used.
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