The decays ω → γπ, ρ → γπ, ππ and confinement singularity

We consider the decays of ω and ρ mesons, the states of constituent quark model: ρ → γπ, ω → γπ and ρ → ππ. The wavefunctions used in calculations were found previously in the spectral integral equation approach for meson masses. The performed calculations for the radiative decays lead to a reasonably good description of data keV, keV, keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks q → q + π. We have found two values for the pion bremsstrahlung coupling: | g π | = 16.7 ± 0.3 +0.1 − 2.3 (solution I) and | g π | = 3.0 ± 0.3 +0.1 − 2.1 (solution II). Within the SU (6) symmetry for nucleons, solution I gives us for π NN coupling the value 16.4 ⩽ g 2 π NN /(4π) ⩽ 23.2 that is in qualitative agreement with the π N scattering data, g 2 π NN /(4π) ≃ 14. The decay ρ → ππ, being determined by the transition , gives us information on the confinement interactions. One can specify in this decay two types of transitions: (i) the bremsstrahlung radiation of a pion q → q + π with a subsequent fusion , and (ii) the direct transition . With our knowledge of the bremsstrahlung radiation of the pion, g π , we estimate the amplitude and its role in the confinement mechanism.