A fresh look into the heavy quark-mass values

Abstract

Using the recent {\it world average} ${\alpha }_s(M_Z^2)=0.118\pm 0.006$, we give the {\it first direct extraction} from the $\Psi$ and ${\rm Y}$ data of the values of the {\it running heavy quark masses} within QCD spectral sum rules to two-loops in the $\overline{MS}$-scheme: $\mr_b(M^{PT2}_b)$ = $(4.23{}_{-0.04}^{+0.03}\pm 0.02)$ GeV and $\mr_c(M^{PT2}_c)$ = $(1.23{}_{-0.04}^{+0.02}\pm 0.03)$ GeV, (the errors are respectively due to $\alf$ and to the gluon condensate), and the corresponding value of the {\it short-distance perturbative pole masses to two-loops}: $M_b^{PT2}=(4.62\pm 0.02)$ GeV, $M_c^{PT2}=(1.41\pm 0.03)$ GeV, which we compare with the updated values of the {\it non-relativistic pole masses} re-extracted {\it directly} from the two-loop non-relativistic sum rules: $M_b^{NR}=(4.69{}_{+0.02}^{-0.01}\pm 0.02)$ GeV and $M_c^{NR}=(1.44\pm 0.02\pm 0.03)$ GeV. It is also informative to compare the {\it three-loop} values of the short-distance pole masses: $M_b^{PT3}=(4.87\pm 0.05\pm 0.02)$ GeV and $M_c^{PT3}=(1.62\pm 0.07\pm 0.03)$ GeV, with the {\it dressed mass} $M_b^{nr}=(4.94\pm 0.10\pm 0.03)$ GeV, entering into the {\it non-relativistic Balmer formula} including higher order $\alf$ corrections. The $small$ mass-differences $M_b^{NR}-M_b^{PT2}\simeq M_b^{nr}-M_b^{PT3}\simeq 70$ MeV and $M_c^{NR}-M_c^{PT2}\simeq (30\pm 20)$ MeV {\it can measure the size} of the non-perturbative effect induced by {\it renormalon} type-singularities. An analogous analysis is pursued for the heavy-light mesons, where a simultaneous {\it re-fit} of the $B$ and $B^{\ast }$ masses from relativistic sum rules leads to: $M_b^{PT2}=(4.63\pm 0.08)$ GeV,

15 pages in latex file + 3 figures in 3 ps-files appended at the end of the paper, CERN-TH.7405/94 (replace 9408376 : compressed abstract)

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• QCD Matching Conditions at Thresholds
• Precise Determination of {$f_{P_s}/f_P$}} {\bf and Measurement of the ``Perturbative'' Pole Mass from {$f_P$}}
• QSSR estimate of the $B_B$ parameter at next-to-leading order

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