The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays

Abstract

The next-to-leading-order contribution to the amplitude of a two-body decay process is a triangle-shaped diagram in which the unstable state is exchanged by the emitted particles. In this work we calculate this diagram in the framework of a scalar quantum field theory and we estimate its role in hadronic physics, i.e., we apply our results to the well-known scalar-isoscalar resonances $f_0(500)$, $f_0(980)$, $f_0(1370)$, $f_0(1500)$, $f_0(1710)$ and the scalar-isovector resonance $a_0(1450)$. It turns out that, with the exception of the broad resonance $f_0(500)$, the next-to-leading-order contribution is small and can be neglected.

Comments: 18 pages, 6 figures, 1 table