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

Abstract We study the interaction of a kaon with the $$f_1(1285)$$ f 1 ( 1285 ) resonance, assuming that the $$f_1(1285)$$ f 1 ( 1285 ) is a molecular state generated by the $$K \bar{K}^*, \bar{K} K^*$$ K K ¯ ∗ , K ¯ K ∗ interaction, evaluating the scattering amplitude, the scattering length and effective range of the $$K f_1$$ K f 1 system. The scattering amplitude develops a resonant structure approximately 56 MeV below the $$K f_1$$ K f 1 threshold, with a width of around 123 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 $$K f_1$$ K f 1 system differs significantly from the one obtained assuming that the $$f_1(1285)$$ f 1 ( 1285 ) is an ordinary, non-molecular, particle. This provides motivation to continue the search for these observables, already initiated by the measurement of the $$p f_1(1285)$$ p f 1 ( 1285 ) correlation function by the ALICE collaboration.