Fine-tuning in scalar meson decay with bound-state corrections

TL;DR

This paper introduces a novel application of the Fock-Tani formalism to meson decay, incorporating bound-state corrections that refine decay amplitude calculations, exemplified through the $f_0(1500) o  $ decay channel.

Contribution

It presents an alternative approach using the Fock-Tani formalism to include bound-state corrections in meson decay calculations, offering a fine-tuning mechanism for decay amplitudes.

Findings

Bound-state corrections affect decay amplitude calculations.

The method provides a refined decay amplitude for the $f_0(1500) o  $ channel.

The approach offers a new tool for meson decay analysis.

Abstract

The glueball-quarkonia mixture decay amplitude has been evaluated, in the literature, by diagrammatic techniques for drawing quark lines and the quark-gluon vertex. In this paper we use an alternative approach which consists in a mapping technique, the Fock-Tani formalism, in order to obtain an effective Hamiltonian starting from microscopic interactions. An extra effect is present in this formalism associated to the extended nature of mesons: bound-state corrections, which introduces an additional decay amplitude and sets a fine-tuning procedure for general meson decay calculations. The $f_0(1500) \to \pi \pi$ channel shall be considered as numerical example of the procedure.