On the mass spectrum of the two-dimensional O(3) sigma model with theta term

TL;DR

This paper investigates the mass spectrum of the two-dimensional O(3) sigma model with a topological term near θ=π, revealing a stable triplet and a singlet particle whose stability varies with θ.

Contribution

It applies Form Factor Perturbation Theory to analyze the non-integrable model and identifies the conditions under which the singlet particle remains stable or becomes a resonance.

Findings

The spectrum includes a stable triplet of massive particles for all θ.

A singlet state exists with higher mass, stable near θ=π.

The singlet becomes a resonance below a critical θ_c.

Abstract

Form Factor Perturbation Theory is applied to study the spectrum of the O(3) non--linear sigma model with the topological term in the vicinity of $\theta = \pi$. Its effective action near this value is given by the non--integrable double Sine--Gordon model. Using previous results by Affleck and the explicit expressions of the Form Factors of the exponential operators $e^{\pm i\sqrt{8\pi} \phi(x)}$, we show that the spectrum consists of a stable triplet of massive particles for all values of $\theta$ and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of $\theta$ close to $\pi$ whereas it becomes a resonance below a critical value $\theta_c$.