αSfromΥspectroscopy with dynamical Wilson fermions

Abstract

We estimate the QCD coupling constant from a lattice calculation of the bottomonium spectrum. The second order perturbative expansion of the plaquette expectation value is employed to determine ${\ensuremath{\alpha}}_{S}$ at a scale set by the $2S\ensuremath{-}1S$ and $1P\ensuremath{-}1S$ level splittings. The latter are computed in NRQCD in a dynamical gauge field background with two degenerate flavors of Wilson quarks at intermediate masses and extrapolated to the chiral limit. Combining the ${N}_{f}=2$ result with the quenched result at equal lattice spacing we extrapolate to the physical number of light flavors to find a value of ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}^{(5)}{(m}_{Z})=0.1118(17).$ The error quoted covers both statistical and systematic uncertainties in the scale determination. An additional $5%$ uncertainty comes from the choice of the underlying sea quark formulation and from truncation errors in perturbative expansions.