On the two-photon decay width of the sigma meson

Abstract

We shortly report on the two-photon decay width of the light $\sigma$-meson interpreted as a quarkonium state. Results are given in dependence on the $\sigma$-mass and the constituent mass of the light quark. The triangle quark-loop diagram, responsible for the two-photon transition, is carefully evaluated: a term in the transition amplitude, often omitted in literature, results in destructive interference with the leading term. As a result we show that the two-photon decay width of the $\sigma $ in the quarkonium picture is less than 1 keV for the physical range of parameters.