The $K \bar K \pi$ decay of the $f_1(1285)$ and its nature as a $K^* \bar K -cc$ molecule

TL;DR

This paper models the decay of the $f_1(1285)$ meson as a dynamically generated state from $K^* ar{K}$ interactions, successfully predicting decay widths and mass distributions that support its molecular nature.

Contribution

It provides a theoretical framework treating $f_1(1285)$ as a $K^* ar{K}$ molecule, including final state interactions, and matches experimental decay widths.

Findings

Partial decay width agrees with experimental data

Mass distributions differ from phase space predictions

Final state interactions influence mass distribution shapes

Abstract

We investigate the decay of $f_1(1285) \to \pi K \bar K$ with the assumption that the $f_1(1285)$ is dynamically generated from the $K^* \bar{K} - cc$ interaction. In addition to the tree level diagrams that proceed via $f_1(1285) \to K^* \bar{K} - cc \to \pi K \bar K$, we take into account also the final state interactions of $K \bar K \to K \bar K$ and $\pi K \to \pi K$. The partial decay width and mass distributions of $f_1(1285) \to \pi K \bar K$ are evaluated. We get a value for the partial decay width which, within errors, is in fair agreement with the experimental result. The contribution from the tree level diagrams is dominant, but the final state interactions have effects in the mass distributions. The predicted mass distributions are significantly different from phase space and tied to the $K^* \bar{K} - cc$ nature of the $f_1(1285)$ state.