Bottom Quark Mass from Upsilon Mesons: Charm Mass Effects

Abstract

The effects of the finite charm quark mass on bottom quark mass determinations from ${\rm Y}$ sum rules are examined in detail. The charm quark mass effects are calculated at next-to-next-to-leading order in the non-relativistic power counting for the ${\rm Y}$ sum rules and at order ${\alpha }_s^3$ for the determination of the bottom MSbar mass. For the bottom 1S mass, which is extracted from the ${\rm Y}$ sum rules directly, we obtain $M_b^{1S}=4.69\pm 0.03$ GeV with negligible correlation to the value of the strong coupling. For the bottom MSbar mass we obtain ${\bar{M}}_b({\bar{M}}_b)=4.17\pm 0.05$ GeV taking ${\alpha }_s^{(n_l=5)}(M_Z)=0.118\pm 0.003$ as an input. Compared with an analysis where all quarks lighter than the bottom are treated as massless, we find that the finite charm mass shifts the bottom 1S mass, $M_b^{1S}$, by about -20 MeV and the MSbar mass, ${\bar{M}}_b({\bar{M}}_b)$, by -30 to -35 MeV.

70 pages, latex, 21 postscript figures included

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