Triangle singularity in $\tau \to f_1(1285)\pi {\nu }_{\tau }$ decay

Abstract

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

Comments: 8 pages, 4 figures