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

TL;DR

This paper calculates the next-to-leading-order triangle diagram in two-body hadronic decays within scalar quantum field theory, assessing its significance for various scalar resonances, and finds it negligible except for the broad $f_{0}(500)$.

Contribution

The work provides a detailed calculation of the NLO triangle diagram in scalar QFT and evaluates its impact on specific scalar meson resonances in hadronic physics.

Findings

NLO contribution is small for most resonances

Negligible impact on narrow resonances

Significant only for broad $f_{0}(500)$

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.