Scattering data and correlation function for the K f₁(1285) interaction

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 \R{$56$ MeV} below the $K f_1$ threshold, with a width of around \R{$123$ MeV} 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 differs significantly from the one obtained assuming that the $f_1(1285)$ is an \R{ordinary, non-molecular,} 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.