  It is shown that the standard effective field theory of non-relativistic
superfluids, which includes only the leading order action in derivative
expansion, is in general inadequate for studying supersonic processes. Namely,
for a proper treatment of the latter the phonons with momenta greater than
$mc_s$ are relevant at times (with $m$ being the mass of the superfluid
constituent and $c_s$ denoting the sound-speed), which lie beyond the regime of
validity of the naive effective theory mentioned above. This is demonstrated on
a concrete example by recovering the known expression for the friction force as
a process of radiating phonons by a supersonic perturber. In particular, when
the impurity is heavier than superfluid constituents, it is indeed necessary to
extend the non-relativistic effective theory of superfluids to include
high-derivative corrections. For the light perturber, however, there is a
window of velocities for which high-derivative corrections are irrelevant.

High Energy Physics - Theory;Quantum Gases;High Energy Physics - Phenomenology