  In the context of general $SU(2)_L\otimes SU(2)_R\otimes U(1)$ models a
relatively light W' is still allowed in some scenarios with a heavy
right-handed neutrino and a quark mixing matrix $U^R$ close to unity. We
explore the consequences of the presence of this new charged current on the
parity violating spin asymmetries which could be induced in one-jet inclusive
production in polarized proton-proton or proton-neutron collisions. Such
measurements could be performed within a few years at the Brookhaven
Relativistic Heavy Ion Collider (RHIC) running part of the time as a polarized
hadronic collider.
