Scattering data and correlation function for the $K f_1(1285)$ interaction

TL;DR

This paper investigates the interaction between kaons and the $f_1(1285)$ resonance, modeling it as a molecular state, and predicts observable effects such as a resonant structure and correlation function shape.

Contribution

It provides a novel analysis of the $K f_1(1285)$ interaction assuming a molecular state, predicting specific scattering features and correlation functions.

Findings

Resonant structure appears 10 MeV below threshold

Correlation function indicates a near-threshold bound state

Interaction differs from elementary particle assumption

Abstract

We study the interaction of a kaon with the $f_1(1285)$ resonance, assuming that the $f_1(1285)$ is a molecular state generated by the $K \bar K^*, \bar K K^*$ interaction, evaluating the scattering amplitude, the scattering length and effective range of the $K f_1$ system. The scattering amplitude develops a resonant structure approximately $10$ MeV below the $K f_1$ threshold, with a width of around $15$ MeV. The corresponding correlation function has the distinctive shape of a system with a bound state close to threshold. We also show that the interaction of the $K f_1$ system is differs significantly from the one obtained assuming that the $f_1(1285)$ is an elementary particle. This provides motivation to continue the search for these observables, already initiated by the measurement of the $p f_1(1285)$ correlation function by the ALICE collaboration.