  We study global quenches in a number of interacting quantum field theory
models away from the conformal regime. We conduct a perturbative
renormalization at one-loop level and track the modifications of the quench
protocol induced by the renormalization group flow. The scaling of various
observables at early times is evaluated in the regime of rapid quench rates,
with a particular emphasis placed on the leading order effects that cannot be
recovered using the finite order conformal perturbation theory. We employ the
canonical ideas of effective action to verify our results and discuss a
potential route towards understanding the late time dynamics.
