  We will consider the most general least-order derivative action for the
torsional completion of gravitational backgrounds filled with left-handed and
right-handed semi-spinorial fields, accounting for all parity-even as well as
parity-odd contributions; we will proceed by performing the customary analysis,
decomposing torsion and substituting it in terms of the semi-spinorial density
currents, in order to obtain the effective action with the torsionally-induced
self-interacting potentials among the chiral fermionic fields: we shall see
that the resulting effective non-linear potentials will turn eventually out to
be parity conserving after all.
