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Positivity constraints, derived initially assuming parity conservation, forthe inclusive reaction of the type $A({spin 1/2})+B({spin 1/2})\to C+X$, wherethe spins of both initial spin-1/2 particles can be in any possible directionsand no polarization is observed in the final state, are generalized to the caseof parity violation. By means of a systematic method, we obtain non-trivialbounds involving all the spin observables of the reaction and we discuss somerelevant physics processes. Particularly we discover a non-trivial positivityconstraint 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 theongoing longitudinal spin program at RHIC.

General positivity bounds for spin observables in particle inclusive production