Bottom and charm mass determinations with a convergence test

Abstract

We present new determinations of the MS charm quark mass using relativistic QCD sum rules at O(α 3 s ) from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e + e − collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain m c (m c ) = 1.288 ± 0.020 GeV from the vector correlator. The method is also applied to the extraction of the MS bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain m b (m b ) = 4.176 ± 0.023 GeV.

Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass

“…Namely, we reorganize the perturbative series in terms of α s (µ α ) and m c (µ m ) with µ α = µ m [27,28]. This can be done by inserting an expansion of α s (µ = µ m ) in terms of α s (µ α ) into the formula of r n (α s (µ), m c (µ)) and rearranging the perturbative series.…”

Perturbative corrections to B → D form factors in QCD

“…Likewise, we will adopt the intervals for the D-meson decay constant in QCD from lattice simulations f D = (209.2 ± 3.3) MeV [58] with N f = 2 + 1. In addition, we will employ the MS bottom quark mass m b (m b ) = (4.193 +0.022 −0.035 ) GeV [59] from non-relativistic sum rules and the MS charm quark mass m c (m c ) = (1.288 ± 0.020) GeV [60] from relativistic sum rules, employing the quark vector correlation function computed at O(α 3 s ). Following [15,41], the hard scales µ h1 and µ h2 are taken to be equal and will be varied in the interval [m b /2 , 2 m b ] around the default value m b , and the factorization scale is chosen as 1.0 GeV ≤ µ ≤ 2.0 GeV with the default value µ = 1.5 GeV.…”

Precise determination of αs from relativistic quarkonium sum rules

“…For the charm cross section the data above threshold spans a wide range of energies such that even for n = 1 the computed moment is fairly insensitive to how the continuum is treated [3]. On the other hand, bottom moments with low values of n do depend strongly on the continuum such that M V,1 b cannot be used for any competitive determination of the bottom-quark mass [4,5] -a situation that could change if data at larger energies became available. Here, since we are interested in a precise extraction of α s , the continuum contribution must be treated carefully, in a way that avoids any possible contamination of the extracted values.…”