Bottom Mass from Nonrelativistic Sum Rules at NNLL

TL;DR

This paper determines the bottom quark mass using nonrelativistic sum rules with renormalization group improvement at NNLL order, resulting in stabilized theoretical predictions and precise mass values.

Contribution

It introduces a NNLL order analysis with RGI in vNRQCD, improving the stability and accuracy of bottom quark mass determinations from sum rules.

Findings

Stable sum rule moments with respect to scale variations.

Precise bottom 1S mass: 4.755 GeV with quantified uncertainties.

Bottom MSbar mass: 4.235 GeV with quantified uncertainties.

Abstract

We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) Upsilon sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI computed in the vNRQCD framework leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M_b^{1S}=4.755 +- 0.057(pert) +- 0.009(alpha_s) +- 0.003(exp) GeV for the bottom 1S mass and m_b(m_b)= 4.235 +- 0.055(pert) +- 0.003(exp) GeV for the bottom MSbar mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.