Detailed derivation of the $\mathbf{^3P_0}$ strong decay model applied to baryons

TL;DR

This paper derives a detailed $^3P_0$ decay model for baryons, extending previous meson analyses, and successfully predicts the $ ext{Δ}(1232) o ext{π}N$ decay width using a consistent formalism and experimental data.

Contribution

It provides a comprehensive derivation of the $^3P_0$ decay model for baryons, linking decay widths to hadron radii and using a unified approach with previous meson studies.

Findings

Accurately predicts the $ ext{Δ}(1232) o ext{π}N$ decay width.

Establishes a connection between decay matrix elements and hadron radii.

Uses a single free parameter for pair creation strength, consistent with experimental data.

Abstract

We provide an in-detail derivation through the $^3P_0$ pair creation model of the transition matrix for a baryon decaying into a meson-baryon system. The meson's analysis was conducted in Ref. [1] and we extend the same formalism to the baryon sector, focusing on the $\Delta(1232)\to \pi N$ strong decay width because all hadrons involved in the reaction are very well established, the two hadrons in the final state are stable, avoiding further analysis, all quarks are light and so equivalent, and the decay width of the process is relatively well measured. Taking advantage of a Gaussian expansion method for the hadron's radial wave functions, the expression of the invariant matrix element can be related with the mean-square radii of hadrons involved in the decay. We use their experimental measures in such a way that only the strength of the quark-antiquark pair creation from the vacuum is a free parameter. This is then taken from our previous study of strong decay widths in the meson sector, obtaining a quite compatible result with experiment for the calculated $\Delta(1232)\to \pi N$ decay width.