NNLO Unquenched Calculation of the b Quark Mass

TL;DR

This paper presents a high-precision unquenched lattice QCD calculation of the b-quark mass, incorporating two-loop corrections and systematic error analysis to improve accuracy over previous estimates.

Contribution

It provides the first unquenched lattice computation of the B-meson binding energy combined with two-loop residual mass corrections for a precise b-quark mass determination.

Findings

Estimated  mass: 4.26 b0 0.09 GeV

Two-loop corrections are crucial for precision

Systematic errors thoroughly analyzed

Abstract

By combining the first unquenched lattice computation of the B-meson binding energy and the two-loop contribution to the lattice HQET residual mass, we determine the (\bar{{MS}}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The inclusion of the two-loop corrections is essential to extract (\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal O}(\Lambda^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon singularities in the perturbative series of the residual mass. Our best estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we have combined the different errors in quadrature. A detailed discussion of the systematic errors contributing to the final number is presented. Our results have been obtained on a sample of (60) lattices of size (24^{3}\times 40) at (\beta =5.6), using the Wilson action for light quarks and the lattice HQET for the (b) quark, at two values of the sea quark masses. The quark propagators have been computed using the unquenched links generated by the T(\chi)L Collaboration.