Invariant amplitudes for coherent electromagnetic pseudoscalar production from a spin-one target

Abstract

A set of 13 linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle is derived which respect Lorentz and gauge invariance. The $T$-matrix can be represented by a linear superposition of these amplitudes with invariant functions as coefficients, which depend on the Mandelstam variables only. Their explicit form is determined by the underlying dynamics. Nine of these amplitudes are purely transverse and describe photoproduction. The remaining four appear in electroproduction in addition, describing charge and longitudinal current contributions. Furthermore, a reduction of these amplitudes to operators acting in non-relativistic spin space is given.