Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators

We present the method of calculation of radiative decays of composite quark–antiquark QQ̄ systems with different J : (QQ̄)in → γ(QQ̄)out. The method is relativistic invariant, it is based on the double dispersion relation integrals over the masses of composite mesons, it can be used for the high spin particles and provides us with the gauge invariant transition amplitudes. We apply this method to the case when the photon is emitted by a constituent in the intermediate state (additive quark model). We perform the momentum operator expansion of the spin amplitudes for the decay processes. The problem of nilpotent spin operators is discussed.