Electromagnetic couplings of elementary vector particles

On the basis of the three fundamental principles of (i) Poincar{e} symmetry of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector particles, i.e., massive spin-1 particles transforming in the /1/2,1/2) representation space of the Homogeneous Lorentz Group (HLG). We make the point that the first two symmetries alone do not fix the electromagnetic couplings uniquely but solely prescribe a general Lagrangian depending on two free parameters, here denoted by xi and g. The first one defines the electric-dipole and the magnetic-quadrupole moments of the vector particle, while the second determines its magnetic-dipole and electric-quadrupole moments. In order to fix the parameters one needs an additional physical input suited for the implementation of the third principle. As such, one chooses Compton scattering off a vector target and requires the cross section to respect the unitarity bounds in the high energy limit. In result, we obtain the universal g=2, and xi=0 values which completely characterize the electromagnetic couplings of the considered elementary vector field at tree level. The nature of this vector particle, Abelian versus non-Abelian, does not affect this structure. Merely, a partition of the g=2 value into non-Abelian, g_{na}, and Abelian, g_{a}=2-g_{na}, contributions occurs for non-Abelian fields with the size of g_{na} being determined by the specific non-Abelian group appearing in the theory of interest, be it the Standard Model or any other theory.