Meson decay in a corrected $3^P_0$ model

TL;DR

This paper introduces a corrected $3^P_0$ meson decay model using the Fock-Tani formalism, incorporating bound-state effects, and applies it to specific meson decay processes to improve theoretical predictions.

Contribution

It develops a new corrected $3^P_0$ decay model based on the Fock-Tani formalism, including bound-state corrections, for more accurate meson decay descriptions.

Findings

The corrected model accounts for meson extended nature.

Application to $b_{1} o ext{omega} ext{pi}$ decay.

Application to $a_{1} o ho ext{pi}$ decay.

Abstract

Extensively applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the $3^P_0$ model, in which $q\bar{q}$ pair production is the dominant mechanism. The pair production can be obtained from the non-relativistic limit of a microscopic interaction Hamiltonian involving Dirac quark fields. The evaluation of the decay amplitude can be performed by a diagrammatic technique for drawing quark lines. 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 same microscopic interaction. An additional effect is manifest in this formalism associated to the extended nature of mesons: bound-state corrections. A corrected $3^P_0$ is obtained and applied, as an example, to $b_{1}\to\omega\pi$ and $a_{1}\to\rho\pi$ decays.