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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 proceedsvia 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 asingularity at a mass of the $a_1(1260)$ around 1420 MeV, producing a peak inthe cross section of the $\pi p$ reaction, used to generate the mesonic finalstate, which provides a natural explanation of all the features observed in theCOMPASS experiment, where a peak observed at this energy is tentativelyassociated to a new resonance called $a_1(1420)$. On the other hand, thetriangular singularity studied here gives rise to a remarkable feature, where apeak is seen for a certain decay channel of a resonance at an energy about 200MeV higher than its nominal mass.

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