Determination of the Lambda parameter from full lattice QCD

We present a determination of the QCD parameter $\Lambda$ 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 ${\Lambda }_{n_f=0}^{\overline{MS}}=259(1)(19)\mathrm{MeV}$ and ${\Lambda }_{n_f=2}^{\overline{MS}}=261(17)(26)\mathrm{MeV}$, using $r_0=0.467\mathrm{fm}$ to set the scale. Extrapolating our results to five flavors, we obtain for the running coupling constant at the mass of the $Z$ boson ${\alpha }_s^{\overline{MS}}(m_Z)=0.112(1)(2)$.