The bottom $\bar{\rm MS}$ quark mass from sum rules at next-to-next-to-leading order

TL;DR

This paper accurately determines the bottom quark mass in the MS-bar and potential subtraction schemes using sum rules and the Upsilon 1S state at NNLO, improving precision in heavy quark mass measurements.

Contribution

It introduces a NNLO reorganized perturbative approach that sums Coulomb exchange to all orders for precise bottom quark mass determination.

Findings

MS-bar bottom quark mass: 4.25 ± 0.08 GeV

Potential-subtracted mass at 2 GeV: 4.59 ± 0.08 GeV

Method improves accuracy of heavy quark mass estimates.

Abstract

We determine the bottom $\bar{\rm MS}$ quark mass $\bar{m}_b$ and the quark mass in the potential subtraction scheme from moments of the $b\bar{b}$ 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 $\bar{m}_b(\bar{m}_b)=(4.25\pm 0.08) $GeV and $m_{b,\rm PS}(2 {GeV})=(4.59\pm 0.08) $GeV for the potential-subtracted mass at the scale 2 GeV, adopting a conservative error estimate.