  The recent experimental discovery of ${\rm Cd_3 As_2}$ and ${\rm Na_3 Bi}$
Dirac semimetals enables the study of the properties of chiral quasi-particles
in three spatial dimensions. As demonstrated by photoemission, Dirac semimetals
are characterized by a linear dispersion relation for fermion quasi-particles,
and thus represent three dimensional analogs of graphene. While the distinctive
behavior of chiral fermions (e.g. Klein tunneling) is already evident in two
dimensional graphene, the physics of chirality in three dimensions opens a
number of new possibilities. In this paper we investigate the properties of the
collective plasmon excitations in Dirac semimetals by using the methods of
relativistic field theory. We find a strong and narrow plasmon excitation whose
frequency is in the terahertz (THz) range which may be important for practical
applications. The properties of the plasmon appear universal for all Dirac
semimetals, due to the large degeneracy of the quasi-particles and the small
Fermi velocity, $v_F \ll c$. This universality is closely analogous to the
phenomenon of "dimensional transmutation", that is responsible for the
emergence of dimensionful scales in relativistic field theories such as Quantum
Chromodynamics, the modern theory of nuclear physics.
