Invariant amplitudes for coherent electromagnetic pseudoscalar production from a spin-one target (II): crossing, multipoles and observables

The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are discussed in detail. Since not all of the amplitudes have simple crossing behaviour, we introduce an alternative set of basic amplitudes which are either symmetric or antisymmetric under crossing. The multipole decomposition is given, and the representation of the multipoles as integrals over the invariant functions weighted with Legendre polynomials is derived. Furthermore, differential cross section and polarization observables are expressed in terms of the corresponding invariant functions.