  We analyze theoretically the conductivity of Weyl semimetals within the
self-consistent Born approximation (SCBA) in the full range of disorder
strength, from weak to strong disorder. In the range of intermediate disorder,
we find a critical regime which separates the semimetal and diffusion regimes.
While the numerical values of the critical exponents are not expected to be
exact within the SCBA, the approach allows us to calculate functional
dependences of various observables (density of states, quasiparticle
broadening, conductivity) in a closed form. This sheds more light on the
qualitative behavior of the conductivity and its universal features in
disordered Weyl semimetals. In particular, we have found that the vertex
corrections in the Kubo formula are of crucial importance in the regime of
strong disorder and lead to saturation of the dc conductivity with increasing
disorder strength. We have also analyzed the evolution of the optical
conductivity with increasing disorder strength, including its scaling
properties in the critical regime.
