A novel method for the physical scale setting on the lattice and its application to $N_f$=4 simulations

This letter reports on a new procedure for the lattice spacing setting that takes advantage of the very precise determination of the strong coupling in Taylor scheme. Although it can be applied for the physical scale setting with the experimental value of $Lambda_{overline{rm MS}}$ as an input, the procedure is particularly appropriate for relative calibrations. The method is here applied for simulations with four degenerate light quarks in the sea and leads to prove that their physical scale is compatible with the same one for simulations with two light and two heavy flavours.