Analyticity properties of two-body helicity amplitudes for reactions involving massless particles

Abstract

Taking into account gauge conditions, helicity amplitudes for processes involving massless particles are expressed via the spinor amplitudes in terms of the Joos invariant amplitudes which have been shown to be free from kinematical singularities if at least one particle is massive. This procedure allows us to analyse 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, which corresponds to a well-defined crossing path for spinor amplitudes. Such a path is assumed to exist when massless particles are involved. It is shown that this matrix can be obtained from the matrix for the massive case by putting some masses equal to zero. Kinematical constraints which generalize to the case of arbitrary spin relations which must hold between helicity amplitudes at some values of the energy variable in\(\gamma \pi \to \mathcal{N}\bar {\mathcal{N}}\),\(\gamma K \to \Lambda \bar {\mathcal{N}}\) reactions, appear as a consequence of the existence of poles in the crossing matrix between regularized helicity amplitudes.