Isotopic Symmetry Breaking in the $\eta(1405)\to f_0 (980)\pi^0\to\pi^+\pi^-\pi^0$. Decay through a $K\bar K$ Loop Diagram and the Role of Anomalous Landau Thresholds

TL;DR

This paper investigates how anomalous Landau thresholds and the nonzero width of $K^*$ mesons influence isotopic symmetry breaking in the decay of $ ext{eta}(1405)$ to three pions, revealing the importance of these effects in decay mechanisms.

Contribution

It introduces a detailed analysis of isotopic symmetry breaking via triangle singularities and Landau thresholds, emphasizing the role of $K^*$ width in decay processes.

Findings

Anomalous Landau thresholds significantly affect decay amplitudes.

Nonzero $K^*$ width is crucial for accurate symmetry breaking quantification.

Different $K^+-K^0$ mass difference scales impact the symmetry breaking effects.

Abstract

Anomalous isotopic symmetry breaking in the $\eta(1405)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$ decay through a mechanism featuring anomalous Landau thresholds in the form of logarithmic triangle singularities, i.e., through the $\eta(1405)\to (K^*\bar K+\bar K^*K)\to(K^+K^-+K^0\bar K^0)\pi^0\to f_0(980)\pi^0 \to\pi^+\pi^- \pi^0$ transition, has been analyzed. It has been shown that this effect can be correctly quantified only by taking into account the nonzero $K^*$ width. Different scales of isotopic symmetry breaking associated with the $K^+-K^0$ mass difference are compared.