$f_2(1810)$ as a triangle singularity

TL;DR

The paper proposes that the $f_2(1810)$ resonance is generated by a triangle singularity involving $K^* ar{K}^*$ interactions, explaining its properties and suggesting experimental tests to confirm this mechanism.

Contribution

It introduces a novel interpretation of the $f_2(1810)$ as a triangle singularity, providing a specific mechanism and experimental proposal to verify this hypothesis.

Findings

Identifies a triangle singularity at 1810 MeV with a 200 MeV width.

Links the $f_2(1810)$ resonance to a triangle mechanism involving $K^*$ and $a_1(1260)$.

Suggests experimental searches in $ ext{π}a_1(1260)$ modes to test the hypothesis.

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.