The role of the next-to-leading order triangle-shaped diagram in   two-body hadronic decays
  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. 
Jonas Schneitzer, Thomas Wolkanowski and Francesco Giacosa
hep-ph