Scattering data and correlation function for the $K{f}_1(1285)$ interaction

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 $K{\bar{K}}^{\ast },\bar{K}{K}^{\ast }$ 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.

Comments: Corrections done, new references added