  We explore the sensitivity and the physics interest of the measurement of
parity-violating spin asymmetries in one-jet production in the presence of a
new leptophobic neutral gauge boson Z', within polarized hadronic collisions at
the BNL RHIC. We focus on polarized neutron collisions which could be achieved
in a realistic upgrade of the RHIC-Spin program. We show that, in case of a
discovery, a compilation of the information coming from both polarized pp and
nn collisions should constrain the number of Higgs doublets and the presence or
absence of trilinear fermion mass terms in the underlying model of New Physics.
