Abstract
We extract (for the first time) the correlated values of the running masses m‾c and m‾b from MBc using QCD Laplace sum rules (LSR) within stability criteria where perturbative (PT) expressions at N2LO and non-perturbative (NP) gluon condensates at LO are included. Allowing the values of m‾c,b(m‾c,b) to move inside the enlarged range of recent estimates from charmonium and bottomium sum rules (Table 1) obtained using similar stability criteria, we deduce: m‾c(m‾c)=1286(16) MeV and m‾b(m‾b)=4202(8) MeV. Combined with previous estimates (Table 2), we deduce a tentative QCD Spectral Sum Rules (QSSR) average: m‾c(m‾c)=1266(6) MeV and m‾b(m‾b)=4197(8) MeV where the errors come from the precise determinations from J/ψ and ϒ sum rules. As a result, we present an improved prediction of fBc=371(17) MeV and the tentative upper bound fBc(2S)≤139(6) MeV, which are useful for a further analysis of Bc-decays.
Highlights
Extractions of the perturbative and nonperturbative quark and gluon condensates QCD parameters are very important as they will serve as inputs in different phenomenological applications of the-standard model
Lattice calculations are an useful tool for a such project but alternative analytical approaches based on QCD first principles (Chiral perturbation, effective theory and QCD spectral sum rules (QSSR)) are useful complement and independent check of the previous numerical simulations as they give insights for a better understanding of the-perturbative phenomena inside the hadron “black box”
In this note,1 we shall use the Laplace version [2,3,4,5,6,7] of QCD Spectral Sum Rules (QSSR) introduced by Shifman-Vainshtein-Zakharov (SVZ) [2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21] for a new extraction of the running quark masses mc and mb from the Bc(0−+)-meson mass which we shall use for improving the prediction on its decay constant f Bc done previously using similar approaches in [22,23,24,25,26,27] and for deriving a tentative upper bound on f Bc (2S)
Summary
Extractions of the perturbative (quark masses, αs) and nonperturbative quark and gluon condensates QCD parameters are very important as they will serve as inputs in different phenomenological applications of the (non)-standard model. Lattice calculations are an useful tool for a such project but alternative analytical approaches based on QCD first principles (Chiral perturbation, effective theory and QCD spectral sum rules (QSSR)) are useful complement and independent check of the previous numerical simulations as they give insights for a better understanding of the (non)-perturbative phenomena inside the hadron “black box”. We shall use the Laplace version [2,3,4,5,6,7] of QSSR introduced by Shifman-Vainshtein-Zakharov (SVZ) [2,3,8,9,10,11,12,13,14,15,16,17,18,19,20,21] for a new extraction of the running quark masses mc and mb from the Bc(0−+)-meson mass which we shall use for improving the prediction on its decay constant f Bc done previously using similar approaches in [22,23,24,25,26,27] and for deriving a tentative upper bound on f Bc (2S)
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