  In quasi single field inflation there are massive fields that interact with
the inflaton field. If these other fields are not much heavier than the Hubble
constant during inflation ($H$) these interactions can lead to important
consequences for the cosmological energy density perturbations. The simplest
model of this type has a real scalar inflaton field that interacts with another
real scalar $S$ (with mass $m$). In this model there is a mixing term of the
form $\mu {\dot \pi} S$, where $\pi$ is the Goldstone fluctuation that is
associated with the breaking of time translation invariance by the time
evolution of the inflaton field during the inflationary era. In this paper we
study this model in the region $(\mu/H )^2 +(m/H)^2 >9/4$ and $m/H \sim {\cal
O}(1)$ or less. For a large part of the parameter space in this region standard
perturbative methods are not applicable. Using numerical and analytic methods
we derive a number of new results. In addition we study how large $\mu/H$ has
to be for the large $\mu/H$ effective field theory approach to be applicable.
