Lambda-parameter of lattice QCD with the overlap-Dirac operator

We compute the ratio ${\mathrm{\Lambda }}_L\mathrm{/}{\mathrm{\Lambda }}_{\overline{MS}}$ between the scale parameter ${\mathrm{\Lambda }}_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and ${\mathrm{\Lambda }}_{\overline{MS}}$ of the $\overline{\mathrm{M}\mathrm{S}}$ renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the $\bar{{\rm MS}}$ scheme is calculated, using the lattice background field technique.