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 f0(500)f0(500), f0(980)f0(980), f0(1370)f0(1370), f0(1500)f0(1500), f0(1710)f0(1710) and the scalar–isovector resonance a0(1450)a0(1450). It turns out that, with the exception of the broad resonance f0(500)f0(500), the next-to-leading-order contribution is small and can be neglected.