Abstract
We update our perturbative determination of M̅S̅ mass m̅b(m̅b), by including the recently obtained four-loop coefficient in the relation between the pole and M̅S̅ mass. First the renormalon subtracted (RS or RS’) mass is determined from the known mass of the Y(1S) meson, where we use the renormalon residue Nm obtained from the asymptotic behavior of the coefficient of the 3-loop static singlet potential. M̅S̅ mass is then obtained using the 4-loop renormalon-free relation between the RS (RS’) and M̅S̅ mass. We argue that the effects of the charm quark mass are accounted for by effectively using Nf = 3 in the mass relations. The extracted value is m̅b(m̅b) = 4222(40) MeV, where the uncertainty is dominated by the renormalization scale dependence.
Highlights
The (MS) mass of the bottom (b) quark, mb ≡ mb(mb), is an important quantity in particle physics, free of renormalon ambiguities, and appears in many physical observables
We use the fact that the leading infrared (IR) renormalon ambiguity of 2mb cancels out with that of EΥ(1S) [1, 2, 3]
These proceedings are a brief review of our previous work [4], which we update by including in the analysis the recently calculated [5] four-loop coefficient of the relation between the pole mass and the MS mass
Summary
The (MS) mass of the bottom (b) quark, mb ≡ mb(mb), is an important quantity in particle physics, free of renormalon ambiguities, and appears in many physical observables. We use the fact that the leading infrared (IR) renormalon ambiguity of 2mb cancels out with that of EΥ(1S) [1, 2, 3]. We outline: (1) The correct treatment of charm quark mass effects in the perturbation expansion of mb/mb; (2) Asymptotic expressions for the coefficients in the perturbation expansion of the ratio mb/mb and of the static singlet potential V (r), and the extraction of the renormalon residue Nm; (3) The construction of the (modified) renormalonsubtracted mass mb,RS(′) (using Nm), and the renormalon-free relation between mb,RS(′) and mb; (4) Renormalon-free perturbation expansion for MΥ(t(h1)S) in terms of mb,RS(′), and extraction, from MΥ(t(h1)S) = 9.460 GeV, of the values of mb,RS(′) (⇒ mb).
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