Analyticity Properties of Helicity Amplitudes and Construction of Kinematical Singularity-Free Amplitudes for Any Spin

The analyticity properties of helicity amplitudes for binary reactions of particles with arbitrary spins are studied using the following three properties: (i) the analyticity properties of scattering amplitudes, assuming these are correctly predicted by perturbation theory; (ii) the crossing relations of helicity amplitudes near $s=0\mathrm{}$; (iii) the threshold behavior of partial-wave amplitudes. Making use of these properties, kinematical singularity-free amplitudes for any spin are constructed by modifying helicity amplitudes. MacDowell reciprocity is generalized to arbitrary spin. Helicity amplitudes are proved to satisfy the Froissart limit at the high-energy limit.