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In the framework of the relativistic and gauge invariant spectral integraltechnique, we calculate radiative decays rho(770)-> gamma pi(140) andomega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to bequark-antiquark states. The q anti-q wave functions found for mesons and photonlead to a reasonably good description of data ($\Gamma^{(exp)}_{\rho^{\pm}\to\gamma\pi^{\pm}}=68\pm 30$ keV,$\Gamma^{(exp)}_{\rho^{0}\to\gamma\pi^0}=77\pm 28$ keV,$\Gamma^{(exp)}_{\omega\to\gamma\pi^0}=776\pm 45$ keV) that makes it possibleto estimate the coupling for the bremsstrahlung emission of pion by quarks$g_\pi\equiv g_\pi (u\to d \pi)$. We have found two values for the pionbremsstrahlung coupling: $|g_\pi|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and$|g_\pi|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry fornucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{\piNN}^2/(4\pi) \le 23.2$ that is in qualitative agreement with the pi Nscattering data, $g_{\pi NN}^2/(4\pi)\simeq 14$. For excited states, we haveestimated the partial widths in Solution I as follows: $\Gamma(\rho_{2S}^\pm\to \gamma\pi)\simeq 10 - 130$ keV, $\Gamma (\rho_{2S}^0\to\gamma\pi)\simeq 10 -130$ keV, $\Gamma (\omega_{2S}\to \gamma\pi)\simeq 60 -1080$ keV. The large uncertainties emphasise the necessity to carry outmeasurements of the meson radiative processes in the region of large masses.

The rho -> gamma pi and omega -> gamma pi decays in quark-model approach and estimation of coupling for pion emission by quark