The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$

TL;DR

This paper explains the observed peak at 1420 MeV in the $a_1(1260)$ decay channel as a triangular singularity effect, rather than a new resonance, aligning with COMPASS experiment observations.

Contribution

It demonstrates that the $a_1(1420)$ peak arises from a triangular singularity mechanism in the decay process, offering a natural explanation without invoking a new resonance.

Findings

The peak at 1420 MeV is explained by a triangular singularity.

The mechanism reproduces features observed in the COMPASS experiment.

A peak appears about 200 MeV above the nominal resonance mass.

Abstract

We study the decay mode of the $a_1(1260)$ into a $\pi^+$ in p-wave and the $f_0(980)$ that decays into $\pi^+ \pi^-$ in s-wave. The mechanisms proceeds via a triangular mechanism where the $a_1(1260)$ decays into $K^* \bar K$, the $K^*$ decays to an external $\pi^+$ and an internal $K$ that fuses with the $\bar K$ to produce the $f_0(980)$ resonance. The mechanism develops a singularity at a mass of the $a_1(1260)$ around 1420 MeV, producing a peak in the cross section of the $\pi p$ reaction, used to generate the mesonic final state, which provides a natural explanation of all the features observed in the COMPASS experiment, where a peak observed at this energy is tentatively associated to a new resonance called $a_1(1420)$. On the other hand, the triangular singularity studied here gives rise to a remarkable feature, where a peak is seen for a certain decay channel of a resonance at an energy about 200 MeV higher than its nominal mass.