Heavy quark masses from sum rules in four-loop approximation

Abstract

New data for the total cross section σ(e + e − → hadrons) in the charm and bottom threshold region are combined with an improved theoretical analysis, which includes recent four-loop calculations, to determine the short distance MS charm and bottom quark masses. A detailed discussion of the theoretical and experimental uncertainties is presented. The final result for the MS-masses, m c (3 GeV) = 0.986(13) GeV and m b (10 GeV) = 3.609(25) GeV, can be translated into m c (m c ) = 1.286(13) GeV and m b (m b ) = 4.164 (25) GeV. This analysis is consistent with but significantly more precise than a similar previous study.

Heavy-quark masses from low-energy moments of heavy-quark currents

“…[7][8][9]. It is based on the direct comparison of the theoretical and experimental evaluations of the contributions to the derivatives of the polarization function Π Q (q 2 ), the former evaluated in perturbative QCD, the latter through moments of the measured cross section for heavy-quark production in electron-positron annihilation.…”

Quark masses and the strong coupling from recent $R(s)$ measurements

“…For detailed numerical results including a dedicated error analysis we refer to Ref. [15]. It is nicely seen that the results for m Q further stabilize when going from three to four loops.…”

“…The analysis performed in Ref. [15] is restricted to n = 1, 2, 3 and 4. Note that precise mass values can only be obtained for the three lowest moments since the non-perturbative contributions become too big already for n = 4.…”

“…In order to obtain R c one has to subtract the contribution from the light quarks which is explained in detail in Ref. [15]. Similarly, we refer to Ref.…”

“…Ref. [15]). We emphasize the remarkable consistency between the three results which we consider as additional confirmation of our approach.…”