Triangle mechanism in τ → f1(1285)πντ decay

We show that the ${\tau }^{-}$ decay into $f_1\left(1285\right){\pi }^{-}{\nu }_{\tau }$ is dominated by a triangle loop mechanism with $K^{⁎}$, ${\overline{K}}^{⁎}$ and K (or $\overline{K}$) as internal lines, which manifests a strong enhancement reminiscent of a nearby singularity present in the narrow $K^{⁎}$ limit and the near ${\overline{K}}^{⁎}{K}^{⁎}$ threshold of the internal $K^{⁎}$ propagators. The $f_1\left(1285\right)$ is then produced by its coupling to the $K^{⁎}\overline{K}$ and ${\overline{K}}^{⁎}K$ which is obtained from a previous model where this resonance was dynamically generated as a molecular $K^{⁎}\overline{K}$ (or ${\overline{K}}^{⁎}K$) 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 mechanism and the $K^{⁎}\overline{K}$ threshold. 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 mechanism in this decay and supports the dynamical origin of the $f_1\left(1285\right)$ as a $K^{⁎}\overline{K}$ and ${\overline{K}}^{⁎}K$ molecular state.