Strange quark mass from sum rules with improved perturbative QCD convergence

Abstract

The strange quark mass is determined from a QCD Finite Energy Sum Rule (FESR) optimized to reduce considerably the systematic uncertainties arising from the hadronic resonance sector, as well as from the poor convergence of the pseudoscalar correlator in perturbative QCD. The former is achieved by introducing a suitable integration kernel in the Cauchy integral in the complex squared energy plane. The latter is obtained by optimizing the perturbative expansion to accelerate its convergence. The result for the strange quark mass in the MS scheme at a scale of 2 GeV is m s (2 GeV) = 94 ± 9 MeV.

B meson decay constants f B c $$ {f}_{B_c} $$ , f B s $$ {f}_{B_s} $$ and f B from QCD sum rules

“…To understand the effect of the variation of s cont we estimated the contribution of the continuum near the physical threshold in the determination of f B , where some phenomenological information is available. We considered the phase space contribution of the Bππ and B * π intermediate states near threshold, with form factors taken from chiral perturbation theory [49]- [50] and LQCD [51], respectively. In both cases the contributions are negligible compared with the dominant pole contribution of the B meson.…”

“…In table II we show the change in the decay constants when m b (M S) is changed by ± 1σ. Despite the relatively large uncertainty in the s-quark mass [50,[54][55][56][57], m s (2 GeV) = 94 ± 9 MeV, it only has a small effect on f Bs , reflecting the relative smallness of this correction. The uncertainty in the larger c-quark mass m c (m c ) = 1.278 ± 0.009 GeV [54][55][56][57][58][59] has also a small impact on f Bc .…”

Analytical determination of the QCD quark masses

“…I now return to the problem with the PQCD convergence of the pseudoscalar correlator, and its impact on the strange-quark mass [49] (the impact on the up-and down-quark masses, leading to improved results, is currently under investigation [50]). For the integration kernel, Eq.…”

“…In fact, judging from the first five terms, this expansion is worse behaved than the non-convergent harmonic series. An integration kernel [49] shown to be better suited than Eq. (21) is…”