Renormalization-group improved sum rule analysis for the bottom-quark mass

Abstract

We study the effect of resumming large logarithms in the determination of the bottom quark mass through a non-relativistic sum rule analysis. Our result is complete at next-to-leading-logarithmic accuracy and includes some known contributions at next-to-next-to-leading logarithmic accuracy. Compared to finite order computations, the reliability of the theoretical evaluation is greatly improved, resulting in a substantially reduced scale dependence and a faster convergent perturbative series. This allows us to significantly improve over previous determinations of the MS bottom quark mass, m b , from non-relativistic sum rules. Our final figure reads m b (m b ) = 4.19 ± 0.06 GeV.

Heavy quark pair production near threshold with potential non-relativistic QCD

“…Likely, the theoretically cleanest observable on which one can use our results is non-relativistic sum rules, which has already been considered in Ref. [9], where an accurate determination of the bottom mass was obtained. Here we will consider inclusive electromagnetic decays (either to e + e − or to γγ) of the bottomonium ground state for which we will provide analytic formulae.…”

“…The numerical values of the bottom-quark mass to be used in the various schemes are take from Ref. [9] and are given by m PS (2 GeV) = 4.515 GeV, m RS (2 GeV) = 4.370 GeV, and m RS ′ (2 GeV) = 4.750 GeV. Apart from the different numerical values for m to be used, the first change in the formulae appears (at most) at NNLL (NNLO) and is due to the shift…”

“…Such a threshold scan allows for an extremely precise measurement of the top-quark mass and yields information on the top-quark width and the topHiggs Yukawa coupling. The analogous threshold scan for the bb sector is also fundamental for non-relativistic sum rules [4,5,6,7,8] and may lead to accurate determinations of the bottom quark mass [9].…”

“…We will report results on tt production near threshold, as well as elaborate on the computation of non-relativistic sum rules presented in Ref. [9]. Inclusive electromagnetic decays of heavy quarkonium will also be considered.…”

Neural network parametrization of the lepton energy spectrum in semileptonic B meson decays

“…This determination of the b quark mass is consistent with determinations from other analysis. The b quark mass has been determined using different techniques, like the sum rule approach, using either non-relativistic [34,35,37,38] or relativistic [39,40] sum rules, global fits of moments of differential distributions in B decays, [28,33,41], the renormalon analysis of Ref. [42], and several other methods related to heavy-quarkonium physics [43,44] (see [45] for a review).…”