NNLO unquenched calculation of the b quark mass

Abstract

By combining the first unquenched lattice computation of the B-meson binding energy with the recently calculated two-loop contribution to the lattice HQET mass, we determine the $\overline{MS}$ b-quark mass, ${\bar{m}}_b({\bar{m}}_b)$ at the NNLO. We find ${\bar{m}}_b({\bar{m}}_b)=(4.26\pm 0.03\pm 0.04\pm 0.05)\mathrm{GeV}$. The inclusion of the two-loop effects is one of the steps necessary to extract ${\bar{m}}_b({\bar{m}}_b)$ with a precision better than $\mathcal{O}({\Lambda }_{QCD})$, which is the uncertainty due to the presence of an IR renormalon singularity in the perturbative series of the residual mass. Our results have been obtained on a sample of 60 lattices of size $24^3\times 40$ at $\beta =5.6$, using the unquenched Wilson action with two degenerate sea quarks. The quark propagators have been computed using the unquenched links generated by the T$\chi$L Collaboration.

Comments: LATTICE99(Heavy Quarks), 3 pages