The bottom quark mass from sum rules at next-to-next-to-leading order

Abstract

We determine the bottom MS quark mass m b and the quark mass in the potential subtraction scheme from moments of the bb production cross section and from the mass of the Upsilon 1S state at next-to-next-to-leading order in a reorganized perturbative expansion that sums Coulomb exchange to all orders. We find m b (m b ) = (4.25 ± 0.08) GeV and m b,PS (2 GeV) = (4.59 ± 0.08) GeV for the potential-subtracted mass at the scale 2 GeV, adopting a conservative error estimate.

Bottom quark mass from $ \varUpsilon $ sum rules to $ \mathcal{O}\left( {\alpha_s^3} \right) $

“…For µ = 4.20 GeV the analysis [4] gives the value m b (m b ) = 4.22 ± 0.07 consistent with refs. [21,32] and eq. (3.5).…”

“…At the same time the high-moment sum rules have been evaluated only through the next-to-next-to-leading order (NNLO) [13][14][15][16][17][18][19][20][21] though the effect of higher order logarithmically enhanced terms have been considered [22,23]. In this paper we present the complete O(α 3 s ) corrections to the heavy quarkonium parameters required for the N 3 LO analysis of the nonrelativistic Υ sum rules and apply the result to the determination of the bottom quark mass.…”

“…Formally all the terms of this expansion beyond the N 3 LO are suppressed according to the √ n ∼ 1/α s power counting and can be neglected in our approximation. Such an expansion, however, merely violates the cancellation of the large perturbative corrections related to the infrared renormalon in the series for the binding energy (2.15) and for the pole mass (3.2) [18,20,21,[53][54][55]. This spoils the convergence of the resulting series for m b since the factorial growth of the coefficients e (k) m beats the 1/ √ n suppression.…”

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

“…[14]. Thus, the renormalon effect brings down the extracted central value of m b [43] Υ sum rules NNLO 4.21 ± 0.11 MY98 [42] Υ sum rules NNLO 4.20 ± 0.10 BS99 [67] Υ sum rules NNLO 4.25 ± 0.08 H00 [57] Υ sum rules NNLO 4.17 ± 0.05 KS01 [68] Υ sum rules NNLO 4.209 ± 0.050 CH02 [69] Υ sum rules NNLO 4.20 ± 0.09 E02 [70] Υ sum rules NNLO 4.24 ± 0.10 P01 [13] spectrum, Υ(1S) NNLO 4.210 ± 0.090 ± 0.025 BSV01 [55] spectrum, Υ(1S) NNLO 4.190 ± 0.020 ± 0.025 PS02 [35] spectrum, Υ(1S) N 3 LO 4.349 ± 0.070 L03 [14] spectrum, Υ(1S) N 3 LO 4.19 ± 0.04 this work, Eq. (56) spectrum, Υ(1S) N 3 LO 4.241 ± 0.070 reference order E tt (GeV) PS02 [35] N 3 LO −3.065 ± 0.157 (S = 1, 0) L03 [14] N 3 LO −3.21 ± 0.15 (S = 1) this work, Eq.…”

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).…”