Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes

Abstract

Helicity amplitudes are expressed via the spinor amplitudes in terms of the Joos invariant amplitudes which have been shown by Williams to be free from kinematical singularities. This procedure allows to analyze the kinematical singularities of helicity amplitudes and separate them out, which results in the definition of regularized helicity amplitudes. A crossing matrix for helicity amplitudes, is written down, corresponding to the continuation path used to cross spinor amplitudes. We verify explicitly that the corresponding crossing matrix for regularized helicity amplitudes is uniform, as it should be. Kinematical constraints which generalize, to the case of arbitrary spins and masses, relations which must hold between helicity amplitudes at some values of the energy variable in πN → πN, ππ → N N , and N N → N N reactions, appear as a consequence of the existence of poles in the crossing matrix between regularized helicity amplitudes.