Compton scattering off massive fundamental bosons of pure spin 1

Abstract

Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging; thus the challenge is to develop criteria which allow us to select those of them which relate to physically detectable particles. We here take the position that the unitarity of the Compton scattering cross sections in the ultrarelativistic limit, when predicted by a consistent method for a spin-$1$ description, could provide such a criterion. We analyze the properties of massive fundamental spin-$1$ bosons transforming as antisymmetric tensors of second rank, $(1,0)\oplus(0,1)$. For this purpose, we employ the Poincaré covariant projector method, which provides consistent, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for the description of spin-$1$ bosons, first from an in-built $g=1$ value of the gyromagnetic ratio to an unspecified $g\not=1$, and from, single-parity, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector-antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, and valid for $g=1$, while it is violated within the covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarelativistic limit requires us to consider the contributions of both parities in $(1,0)\oplus(0,1)$. On that basis, we conclude that massive spin-$1$ bosons transforming as antisymmetric tensors are physical parity doublets.