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

Abstract

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 (${\Gamma }_{{\rho }^{\pm }\to \gamma {\pi }^{\pm }}^{(exp)}=68\pm 30$ keV, ${\Gamma }_{{\rho }^0\to \gamma {\pi }^0}^{(exp)}=77\pm 28$ keV, ${\Gamma }_{\omega \to \gamma {\pi }^0}^{(exp)}=776\pm 45$ keV) that makes it possible to 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 pion bremsstrahlung coupling: $|g_{\pi }|=16.7\pm 0.3_{-2.3}^{+0.1}$ (Solution I) and $|g_{\pi }|=3.0\pm 0.3_{-2.1}^{+0.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4\le g_{\pi NN}^2/(4\pi )\le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{\pi NN}^2/(4\pi )\simeq 14$. For excited states, we have estimated 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 out measurements of the meson radiative processes in the region of large masses.

Comments: 23 pages in IOP format