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.