Convergence of the $ppp$ correlation function within the hyperspherical adiabatic basis

TL;DR

This paper analyzes the convergence of the hyperspherical adiabatic basis in calculating the three-particle $ppp$ correlation function, demonstrating the need for high angular momentum states for accurate modeling at higher energies.

Contribution

It provides a detailed study of the convergence properties of the hyperspherical adiabatic basis for the $ppp$ correlation function across a range of energies, highlighting the importance of including states up to $J^=21/2^-$.

Findings

Including states up to $J^=21/2^-$ is necessary for accurate correlation tail description.

Convergence improves with higher energy, matching experimental data well.

Higher angular momentum states can be considered as free, simplifying calculations.

Abstract

The computation of the three-particle correlation function involving three hadrons started just recently after the first publications of ALICE measurements. Key elements to be considered are the correct description of the asymptotics, antisymmetrization issues and, in most cases, the treatment of the Coulomb interaction. In the case of the $ppp$ correlation function, a first analysis was done where the hyperspherical adiabatic method was used to determine the $ppp$ wave function at different energies. Although the asymptotic behavior, antisymmetrization issues and the treatment of the Coulomb interaction were discussed in detail, the convergence properties of the adiabatic basis were studied at low energies around the formation of the correlation peak determined mainly by the $J^\pi=1/2^-$ and $3/2^-$ three-body states. Since many and very precise data have been taken or are planned to be measured at energies beyond the peak, we present an analysis of the convergence characteristics of the basis as the energy of the process increases. We show that in order to describe correctly the correlation tail it is necessary to consider three-body states up to $J^\pi=21/2^-$ whereas higher states can be considered as free. Once those states are incorporated solving the associate dynamical equations, the agreement with the experimental data is found to be excellent.