Triangle Singularity as the Origin of the $a_1(1420)$

TL;DR

The paper demonstrates that the observed $a_1(1420)$ signal can be explained by a triangle singularity involving known mesons, challenging the interpretation of it as a new resonance.

Contribution

It introduces a dispersion relation-based approach to model triangle singularities and shows this can account for the $a_1(1420)$ signal without new resonances.

Findings

The $a_1(1420)$ signal is explained by rescattering effects, not a new resonance.

The triangle singularity model fits the data better than the resonance hypothesis.

This is the first demonstration of a light-meson structure explained by a triangle singularity.

Abstract

The COMPASS experiment recently discovered a new isovector resonance-like signal with axial-vector quantum numbers, the $a_1(1420)$, decaying to $f_0(980)\pi$. With a mass too close to and a width smaller than the axial-vector ground state $a_1(1260)$, it was immediately interpreted as a new light exotic meson, similar to the $X$, $Y$, $Z$ states in the hidden-charm sector. We show that a resonance-like signal fully matching the experimental data is produced by the decay of the $a_1(1260)$ resonance into $K^\ast(\to K\pi)\bar{K}$ and subsequent rescattering through a triangle singularity into the coupled $f_0(980)\pi$ channel. The amplitude for this process is calculated using a new approach based on dispersion relations. The triangle-singularity model is fitted to the partial-wave data of the COMPASS experiment. Despite having less parameters, this fit shows a slightly better quality than the one using a resonance hypothesis and thus eliminates the need for an additional resonance in order to describe the data. We thereby demonstrate for the first time in the light-meson sector that a resonance-like structure in the experimental data can be described by rescattering through a triangle singularity, providing evidence for a genuine three-body effect.