The ρ → γπ and ω → γπ 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 ρ(770) → γπ(140) and ω(780) → γπ(140) supposing all mesons (π, ρ, and ω) to be quark-antiquark states. The q q wave functions found for mesons and photon lead to a reasonably good description of data ( Γ ρ ^ ± → γ π ^ ±(exp ) = 68 ± 30 keV, Γ ρ ⁰ → γ π ⁰(exp ) = 77 ± 28 keV, Γ ω → γ π ⁰(exp ) = 776 ± 45 keV) which makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks g π ≡ g π (u → dπ). We have found two values for the pion bremsstrahlung coupling: |g π | = 16.7 ± 0.3 −2.3 +0.1 (Solution I) and |g π | = 3.0 ± 0.3 −2.1 +0.1 (Solution II). Within SU(6) symmetry for nucleons, Solution I gives us for πNN coupling the value 16.4 ≤ g 2 (4π) ≤ 23.2, which is in qualitative agreement with the πN scattering data, g 2 /(4π) }~ 14. For excited states, we have estimated the partial widths in Solution I as follows: Γ(ρ 2 ± → γπ) }~ 10–130 keV, Γ(ρ 2 0 → γπ) }~ 10–130 keV, Γ(ω 2S → γπ) }~ 60–1080 keV. The large uncertainties emphasize the necessity to carry out measurements of the meson radiative processes in the region of large masses.