Triangle singularity in $\tau \to f_1(1285)\pi\nu_\tau$ decay

We show that the $\tau^-$ decay into $f_1(1285)\pi^-\nu_\tau$ is dominated by a triangle loop mechanism with $K^*$, $\bar K^*$ and $K$ (or $\bar K$) as internal lines, which manifests a strong enhancement reminiscent of a nearby singularity present in the narrow $K^*$ limit. The $f_1(1285)$ is then produced by its coupling to the $K^*\bar K$ and $\bar K^*K$ which is obtained from a previous model where this resonance was dynamically generated as a molecular $K^*\bar K$ (or $\bar K^*K$) state using the techniques of the chiral unitary approach. We make predictions for the $f_1 \pi$ mass distribution which significantly deviates from the phase-space shape, due to the distortion caused by the triangle singularity. We find a good agreement with the experimental value within uncertainties for the integrated partial decay width, which is a clear indication of the importance of the triangle singularity in this decay and supports the dynamical origin of the $f_1(1285)$ as a $K^*\bar K$ and $\bar K^* K$ molecular state.