The lattice scale at large β in quenched QCD

In this Letter we extend the estimate of the value of the lattice spacing a in units of the r0 scale at values of the bare coupling larger than those available. By using results from the computation of the renormalised coupling in the Schrödinger functional formalism we find that from β≃7 onward the behaviour predicted by asymptotic freedom at three loop describes very well the data if a value of r0Λ at the lower end of the error bar is used. We also show that, by sticking to the current value, an effective four loop term can describe as well the data. The systematic relative error on the lattice spacing induced by the choice of the procedure is between 1% and 3% for 6.92<β<8.5.