Precise determination of the bottom-quark on-shell mass using its four-loop relation to the MS̄-scheme running mass

In this paper, we explore the properties of the bottom-quark on-shell mass (Mb) by using its relation to the MS̄ mass (mb). At present, this MS̄-on-shell relation has been known up to four-loop QCD corrections, which however still has a ~ 2% scale uncertainty by taking the renormalization scale as mb( mb) and varying it within the usual range of [ mb( mb)/2, 2 mb( mb)]. The principle of maximum conformality (PMC) has been adopted to achieve a more precise MS̄-on-shell relation by eliminating such scale uncertainty. As a step forward, we also estimate the magnitude of the uncalculated higher-order terms by using the Pad\'{e} approximation approach. Numerically, by using the MS̄ mass mb( mb)=4.183±0.007 GeV as an input, our predicted value for the bottom-quark on-shell mass becomes Mb 5.372+0.091-0.075 GeV, where the uncertainty is the squared average of the ones caused by Δ αₛ(MZ), Δ mb( mb), and the estimated magnitude of the higher-order terms.