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 $\bar{ MS}$ b-quark mass, $\bar{ m}_{ b}(\bar{ m}_{ b})$ at the NNLO. We find $\bar{ m}_{ b}(\bar{ m}_{ b}) = (4.26\pm 0.03 \pm 0.04 \pm 0.05) { \rm GeV}$. 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 ${ \cal O}(\Lambda_{ QCD})$, 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.
Categories: hep-lat hep-ph