Positivity constraints on initial spin observables in inclusive reactions

For any inclusive reaction of the type $A_1({spin} 1/2)+ A_2({spin} 1/2) \to B + X$, we derive new positivity constraints on spin observables and study their implications for theoretical models in view, in particular, of accounting for future data from the polarized $pp$ collider at BNL-RHIC. We find that the single transverse spin asymmetry $A_N$ for several processes, for example jet production, direct photon production, lepton-pair production, must be such that $|A_N| \lappeq 1/2$, rather than the usual bound $|A_N| \leq 1$.