OMS-bar scheme of UV renormalization in the presence of unstable fundamental particles

A generalization of the on-mass-shell scheme of UV renormalization (the $\bar{OMS}$ scheme) to the case of presence of unstable fundamental particles (like W and Z bosons) is proposed. Its basic ingredients are as follows: (i) the renormalized mass coincides with a real part of the position of the complex pole of the corresponding propagator, (ii) the imaginary part of the on-shell self-energy coincides with the imaginary part of the complex pole position. The latter property implies the gauge-invariance of the imaginary part of the on-shell self-energy in the $\bar{OMS}$ scheme and its connection with the lifetime of an unstable particle. Starting with the three-loops this connection becomes nontrivial.