  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.
