Description of composite systems in the spectral integration technique: The gauge invariance and analyticity constraints for the radiative decay amplitudes

The constraints following from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems, when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S → γS and V → γS, with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of false kinematical singularities. Furthermore, we explain how to generalize this consideration for quark-antiquark systems, in particular, for the reaction φ(1020) → γf0(980). Here, we also consider in more detail the quark-model nonrelativistic approach for this reaction.