Positivity Constraints on Initial Spin Observables in Inclusive Reactions

For any inclusive reaction of the type $A_1(\mathrm{\text{spin}}1/2)+A_2(\mathrm{\text{spin}}1/2)\to B+X$, 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 Brookhaven RHIC. We find that the single transverse spin asymmetry $A_N$, in the central region for several processes, for example, jet production, direct photon production, and lepton-pair production, is expected to be such that $|A_N|\lesssim 1/2$, rather than the usual bound $|A_N|\le 1$.