$f_2(1810)$ as a triangle singularity

Abstract

We perform calculations showing that a source producing $K^* \bar{K}^*$ in $J = 2$ and $L=0$ gives rise to a triangle singularity at $1810$ MeV with a width of about $200$ MeV from the mechanism $K^* \to \pi K$ and then $K\bar{K}^*$ merging into the $a_1(1260)$ resonance. We suggest that this is the origin of the present $f_2(1810)$ resonance and propose to look at the $\pi a_1(1260)$ mode in several reactions to clarify the issue.