Testing the origin of the $f_1(1420)$ with the $bar K p to Lambda (Sigma) Kbar K pi$ reaction

We study the $bar K p to Y Kbar K pi$ reactions with $bar K = bar K^0, K^-$ and $Y=Sigma^0, Sigma^+, Lambda$, in the region of $Kbar K pi$ invariant masses of $1200-1550$ MeV. The strong coupling of the $f_1(1285)$ resonance to $K^* bar K$ makes the mechanism based on $K^*$ exchange very efficient to produce this resonance observed in the $Kbar K pi$ invariant mass distribution. In addition, in all the reactions one observes an associated peak at $1420$ MeV which comes from the $K^* bar K$ decay mode of the $f_1(1285)$ when the $K^*$ is placed off shell at higher invariant masses. We claim this to be the reason for the peak of the $K^* bar K$ distribution seen in the experiments which has been associated to the $f_1(1420)$ resonance.