Determination of the Lambda parameter from full lattice QCD

Abstract

We present a determination of the QCD parameter $\ensuremath{\Lambda}$ in the quenched approximation (${n}_{f}=0$) and for two flavors (${n}_{f}=2$) of light dynamical quarks. The calculations are performed on the lattice using $O(a)$ improved Wilson fermions and include taking the continuum limit. We find ${\ensuremath{\Lambda}}_{{n}_{f}=0}^{\overline{MS}}=259(1)(19)\text{ }\text{ }\mathrm{MeV}$ and ${\ensuremath{\Lambda}}_{{n}_{f}=2}^{\overline{MS}}=261(17)(26)\text{ }\text{ }\mathrm{MeV}$, using ${r}_{0}=0.467\text{ }\text{ }\mathrm{fm}$ to set the scale. Extrapolating our results to five flavors, we obtain for the running coupling constant at the mass of the $Z$ boson ${\ensuremath{\alpha}}_{s}^{\overline{MS}}({m}_{Z})=0.112(1)(2)$.