General positivity bounds for spin observables in particle inclusive production

Positivity constraints, derived initially assuming parity conservation, for the inclusive reaction of the type $A({spin 1/2})+B({spin 1/2})\to C+X$, where the spins of both initial spin-1/2 particles can be in any possible directions and no polarization is observed in the final state, are generalized to the case of parity violation. By means of a systematic method, we obtain non-trivial bounds involving all the spin observables of the reaction and we discuss some relevant physics processes. Particularly we discover a non-trivial positivity constraint for the processes, $pp\to W^{\pm}/Z^0+X$ or $pp\to \ell^{\pm}+X$ where $\ell^{\pm}$ decayed from $W^{\pm}/Z^0$, which could be checked at the ongoing longitudinal spin program at RHIC.