  Dirac and Weyl semimetals with linearly crossing bands are the focus of much
recent interest in condensed matter physics. Although they host fascinating
phenomena, their physics can be understood in terms of weakly interacting
electrons. In contrast, more than 40 years ago, Abrikosov pointed out that
quadratic band touchings are generically strongly interacting. We have
performed terahertz spectroscopy on films of the conducting pyrochlore
Pr$_2$Ir$_2$O$_7$, which has been shown to host a quadratic band touching. A
dielectric constant as large as $\tilde{\varepsilon }/\epsilon_0 \sim 180 $ is
observed at low temperatures. In such systems the dielectric constant is a
measure of the relative scale of interactions, which are therefore in our
material almost two orders of magnitude larger than the kinetic energy. Despite
this, the scattering rate exhibits a $T^2$ dependence, which shows that for
finite doping a Fermi liquid state survives, however with a scattering rate
close to the maximal value allowed.
