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

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 $K^{\ast }\bar{K}$, the $K^{\ast }$ 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.