General Method of Constructing Helicity Amplitudes Free from Kinematic Singularities and Zeros

A simple and straightforward method to identify and remove the kinematic singularities of helicity amplitudes is constructed from the Trueman-Wick crossing relations. A set of amplitudes free of all kinematic singularities and zeros is obtained for two-particle → two-particle reactions of any spins and masses, except that for boson-fermion interactions with general mass assignments there is still a kinematic $s^{\frac{1}{2}}$ singularity left in the amplitude.