Bottom Quark Mass from Upsilon Mesons: Charm Mass Effects

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The effects of the finite charm quark mass on bottom quark mass determinations from Υ 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 Υ sum rules and at order αₛ³ for the determination of the bottom MSbar mass. For the bottom 1S mass, which is extracted from the Υ sum rules directly, we obtain Mb¹ˢ=4.69± 0.03 GeV with negligible correlation to the value of the strong coupling. For the bottom MSbar mass we obtain Mb(Mb) = 4.17± 0.05 GeV taking αₛ⁽ⁿˡ⁼⁵⁾(MZ)=0.118± 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, Mb¹ˢ, by about -20 MeV and the MSbar mass, Mb(Mb), by -30 to -35 MeV.