Interaction and correlation functions for $\pi f_1(1285)$, $\eta f_1(1285)$

Abstract

We have studied the interaction of $\pi^0 (\eta) f_1(1285)$ assuming the $f_1(1285)$ to be a molecular state of $K^* \bar K - \bar K^* K$. We use a framework in which a $\pi^0 (\eta) f_1(1285)$ optical potential is obtained, which is later used as the kernel of the Lippmann-Schwinger equation, following the standard method for the interaction of particles with nuclei. The optical potential is obtained using the fixed center approximation to the Faddeev equations, where a cluster, here the $f_1(1285)$, remains unchanged during the interaction, appropriate to the situation that one has here. We have obtained the scattering matrix for this system, the scattering length and effective range, plus the correlation functions. The framework used has been previously tested in the study of the $p f_1(1285)$ interaction and has been shown to give results in agreement with the recent experimental measurement of the $p f_1(1285)$ correlation function. On the other hand, from this interaction we do not obtain clear signals for the $\pi_1(1400)$ or $\pi_1(1600)$, nor for the $\eta_1(1855)$ resonances, which in other approaches have been claimed to arise from the same dynamics. We, however, obtain a structure in the $\pi^0 f_1(1285)$ amplitude around $1500-1600$ MeV and a strong cusp at the $\eta f_1(1285)$ threshold of $1833$ MeV.