  We investigate the low-energy scaling behavior of an interacting 3D Weyl
semimetal in the presence of disorder. In order to achieve a renormalization
group analysis of the theory, we focus on the effects of a
short-ranged-correlated disorder potential, checking nevertheless that this
choice is not essential to locate the different phases of the Weyl semimetal.
We show that there is a line of fixed-points in the renormalization group flow
of the interacting theory, corresponding to the disorder-driven transition to a
diffusive metal phase. Along that boundary, the critical disorder strength
undergoes a strong increase with respect to the noninteracting theory, as a
consequence of the unconventional screening of the Coulomb and disorder-induced
interactions. A complementary resolution of the Schwinger-Dyson equations
allows us to determine the full phase diagram of the system, showing the
prevalence of a renormalized semimetallic phase in the regime of intermediate
interaction strength, and adjacent to the non-Fermi liquid phase characteristic
of the strong interaction regime of 3D Weyl semimetals.
