Revising the $f_1(1420)$ resonance

TL;DR

This paper reinterprets the $f_1(1420)$ resonance as a manifestation of decay modes of the $f_1(1285)$, challenging its status as a genuine resonance based on theoretical analysis and experimental data.

Contribution

It provides a theoretical analysis showing that the $f_1(1420)$ is not a true resonance but a result of decay modes of the $f_1(1285)$, revising the understanding of this particle.

Findings

The shoulder around 1400 MeV is linked to a triangle singularity.

The peak at 1420 MeV with 60 MeV width matches experimental data.

A genuine $f_1(1420)$ would imply a 20 ext% decay to $\pi a_0(980)$, contradicting experiments.

Abstract

We have studied the production and decay of the $f_1(1285)$ into $\pi a_0(980)$ and $K^* \bar K$ as a function of the mass of the resonance and find a shoulder around 1400 MeV, tied to a triangle singularity, for the $\pi a_0(980)$ mode, and a peak around 1420 MeV with about 60 MeV width for the $K^* \bar K$ mode. Both these features agree with the experimental information on which the $f_1(1420)$ resonance is based. In addition, we find that if the $f_1(1420)$ is a genuine resonance, coupling mostly to $K^* \bar K$ as seen experimentally, one finds unavoidably about a 20\% fraction for $\pi a_0(980)$ decay of this resonance, in drastic contradiction with all experiments. Altogether, we conclude that the $f_1(1420)$ is not a genuine resonance, but the manifestation of the $\pi a_0(980)$ and $K^* \bar K$ decay modes of the $f_1(1285)$ at higher energies than the nominal one.