  In this work, we investigate the preheating mechanism in a
disformally-coupled inflationary model where the scalar field $\phi$ (which is
the inflaton field) naturally coupled to another matter field $\chi$ induced by
the disformal transformation. In the present scenario, novel derivative
interactions mixing the kinetic terms of the two fields emerge inherently. We
start by deriving the evolution of the background system when the back reaction
on the background field is neglected. We examine the particle production due to
parametric resonances in the models and find in Minkowski space that the stage
of parametric resonances can be described by the Mathieu equation.
Interestingly, we discover that broad resonances in our models can be typically
achieved. Finally, we compare our results with previously studied model with
derivative couplings.
