  We study light propagation in a neutral Weyl semimetal with the Fermi level
lying at the Weyl nodes in the weak self-interacting regime. The nontrivial
topology induces a screening effect in one of the two transverse gauge fields,
for which we find two branches of attenuated collective excitations. In
addition to the known topologically gaped photon mode, a novel massless and
slightly damped excitation appears. Strikingly, at low energies this new
excitation has a linear dispersion and it propagates with the same velocity
than the electrons, while at energies well above the electron-hole continuum
threshold it behaves as a massive attenuated photon with velocity similar to
the speed of light in the material. There is a crossover at certain momentum in
the direction perpendicular to the separation of the Weyl nodes above which the
novel gapless mode enters into an overdamped regime. Regarding the unscreened
gauge field we show that it is also attenuated, which is a non-topological
property shared by Dirac semimetals as well.
