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 q̅ wave functions found for mesons and photon lead to a reasonably good description of data ( Γ _ρ ^ ±→γπ ^ ±^(exp ) = 68 ± 30 keV, Γ _ρ ^0 →γπ ^0 ^(exp ) = 77 ± 28 keV, Γ _ω→γπ ^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 πNN 2 (4 π ) ≤ 23.2, which is in qualitative agreement with the πN scattering data, g πNN 2 /(4 π ) 14. For excited states, we have estimated the partial widths in Solution I as follows: Γ( ρ 2 S ± → γπ ) 10–130 keV, Γ( ρ 2 S 0 → γπ ) 10–130 keV, Γ( ω 2 S → 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.