  We analyze a modified $f(R)$ theory of gravity in the Palatini formulation,
when an Holst term endowed with a dynamical Immirzi field is included. We study
the basic features of the model, especially in view of liminating the torsion
field via the Immirzi field and the scalar-tensor degrees of freedom of the
$f(R)$ model. The main task of this study is the investigation of the
morphology of the gravitational wave polarization when their coupling to a
circle of test particles is considered. We first observe that the dynamics of
the scalar mode of the $f(R)$ Lagrangian is frozen out, since its first order
term identically vanishes. This allows a detailed characterization of the
linearized theory, which outlines the emergence of a modified Newtonian
potential in the static limit, and when time independence is relaxed a standard
gravitational wave plus the scalar wave associated to the Immirzi field.
Investigating the effect of the coupling of this scalar-tensor wave on a circle
of test particles, we arrive to define two effective gravitational
polarizations, corresponding to an equivalent phenomenological wave, whose
morphology is anomalous with respect the standard case of General Relativity.
In fact, the particle circle suffers modifications as it was subjected to
modified plus and cross modes, whose specific features depend on the model free
parameters and are, in principle, detectable via a data analysis procedure.
