Correlation function for the $p ~f_1(1285)$ interaction

TL;DR

This paper develops a formalism to calculate the correlation function between a proton and a molecular resonance, applying it to the $f_1(1285)$, revealing a resonance below threshold that affects the correlation function.

Contribution

It introduces a method to evaluate the correlation function involving a stable particle and a molecular resonance using the fixed center approximation.

Findings

A resonance state below the $p ~ f_1(1285)$ threshold was found.

The correlation function shows depletion at small proton momenta.

The study provides insights into the nature of resonances and three-body bound states.

Abstract

We have addressed here the problem of calculating the correlation function of a stable particle with a resonance, in particular one resonance that qualifies as a molecular state of two components. The formalism used requires to evaluate the scattering matrix of the stable particle with the molecule, a nuclear problem which we address by means of the fixed center approximation. We have applied the method to the interaction of a proton with the $f_1(1285)$ resonance, presently under investigation by the ALICE collaboration, where the $f_1(1285)$ is taken as a $K^*\bar{K}-\bar{K}^*K$ molecule. We find that the $p ~ f_1(1285)$ interaction develops a resonance state below the $p ~ f_1(1285)$ threshold, which leads to a depletion in the $p ~ f_1(1285)$ correlation function for small values of the proton momentum. The discussion presented shows that these type of studies can provide much information on the nature of some resonances and the existence of three-body bound states involving mesons and baryons.