Bottom Quark Mass from Upsilon Mesons: Charm Mass Effects

TL;DR

This paper investigates how finite charm quark mass influences bottom quark mass determinations from Upsilon sum rules, providing refined calculations at NNLO and order αs^3, resulting in updated bottom quark mass values.

Contribution

It introduces a detailed calculation of charm mass effects on bottom quark mass determinations at NNLO and order αs^3, improving precision over previous massless quark approximations.

Findings

Finite charm mass shifts bottom 1S mass by about -20 MeV.

Finite charm mass shifts MSbar bottom mass by -30 to -35 MeV.

Calculated bottom 1S mass as 4.69 ± 0.03 GeV.

Abstract

The effects of the finite charm quark mass on bottom quark mass determinations from $\Upsilon$ 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 $\Upsilon$ 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 $\Upsilon$ 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.