αSfromΥspectroscopy with dynamical Wilson fermions

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 ${\alpha }_S$ at a scale set by the $2S-1S$ and $1P-1S$ 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 $N_f=2\mathrm{}$ result with the quenched result at equal lattice spacing we extrapolate to the physical number of light flavors to find a value of ${\alpha }_{\overline{\mathrm{MS}}}^{\mathrm{}\left(5\right)\mathrm{}}{(m}_Z)=0.1118\mathrm{}(17).$ 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.