Statistical analysis of the sigma meson considered as two-pion resonance

TL;DR

This paper analyzes the sigma meson as a two-pion resonance using the linear sigma model, statistical methods, and spectral functions, showing consistency with experimental data and supporting its interpretation as a resonance.

Contribution

It provides a detailed statistical analysis and spectral function modeling that supports the sigma meson as a two-pion resonance, aligning theoretical predictions with experimental observations.

Findings

Predicted sigma-mass: 486±7 MeV

Predicted decay width: 340±20 MeV

Experimental data matches ~56% of predictions

Abstract

It was found that the most simple analysis in the linear \sigma- model, where the sigma meson couples in vacuum to two virtual pions, predicted the most typical values for the \sigma-mass and total decay width as 486+/-7MeV and 340+/-20MeV respectively. It was demonstrate, via statistical analysis, that the experimental values reported by the Fermilab (E791) Collaboration represents approximately 56% of the values predicted by the linear \sigma- model together with the Breit-Wigner formalism. Additional, it was created the spectral function, in terms of the \sigma-meson regularized self-energy, which is consistently with the Breit-Wigner distribution and it reproduces reasonably well the total width and observable mass given by the Fermilab (E791) Collaboration and Dalitz plot. The results are a strong evidence that the \sigma- meson can be considered as a two-pion resonance.