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

TL;DR

This study models the interaction of $\pi^0$ and $\eta$ with $f_1(1285)$, using a molecular state assumption and the Faddeev equations, to analyze scattering properties and possible resonance signals.

Contribution

It introduces a framework applying the fixed center approximation to Faddeev equations for $\pi^0$ and $\eta$ interactions with $f_1(1285)$, providing new insights into scattering and correlation functions.

Findings

Obtained scattering matrix, scattering length, and effective range.

Did not find clear signals for certain known resonances.

Observed a structure around 1500-1600 MeV and a cusp at 1833 MeV.

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.