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

We consider the decays of omega and rho mesons, the (3)S(1)q (q) over bar states of constituent quark model: rho -> gamma pi, omega -> gamma pi and rho -> pi pi. The q (q) over bar 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 (Gamma((exp))(rho +/-->gamma pi +/-) = 68 +/- 30 keV, Gamma((exp))(rho 0 ->gamma pi 0) = 77 +/- 28 keV, Gamma(( exp))(omega ->gamma pi 0) = 776 +/- 45 keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks q -> q + pi. We have found two values for the pion bremsstrahlung coupling: vertical bar g(pi)vertical bar = 16.7 +/- 0.3(-02.3)(+0.1) (solution I) and vertical bar g(pi)vertical bar = 3.0 +/- 0.3(-2.1)(+0.1) (solution II). Within the SU(6) symmetry for nucleons, solution I gives us for pi NN coupling the value 16.4 <= g(pi NN)(2)/(4p) <= 23.2 that is in qualitative agreement with the pi N scattering data, g(pi NN)(2)/(4 pi) similar or equal to 14. The decay rho -> pi pi, being determined by the transition q (q) over bar -> pi pi, 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 + pi with a subsequent fusion q (q) over bar -> pi, and (ii) the direct transition q (q) over bar -> pi pi. With our knowledge of the bremsstrahlung radiation of the pion, g(pi), we estimate the amplitude q (q) over bar -> pi pi and its role in the confinement mechanism.