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

In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($Γ^{(exp)}_{ρ^{\pm} \toγπ^{\pm}}=68\pm 30$ keV, $Γ^{(exp)}_{ρ^{0}\toγπ^0}=77\pm 28$ keV, $Γ^{(exp)}_{ω\toγπ^0}=776\pm 45$ keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks $g_π\equiv g_π(u\to d π)$. We have found two values for the pion bremsstrahlung coupling: $|g_π|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and $|g_π|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{πNN}^2/(4π) \le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{πNN}^2/(4π)\simeq 14$. For excited states, we have estimated the partial widths in Solution I as follows: $Γ(ρ_{2S}^\pm\to γπ)\simeq 10 - 130$ keV, $Γ(ρ_{2S}^0\to γπ)\simeq 10 -130$ keV, $Γ(ω_{2S}\to γπ)\simeq 60 - 1080$ keV. The large uncertainties emphasise the necessity to carry out measurements of the meson radiative processes in the region of large masses.