Correcting the $B_A$ coalescence factor at GSI-HADES and RHIC-BES energies

TL;DR

This paper identifies necessary corrections to coalescence factors at low energies in heavy-ion collisions, significantly improving volume estimates and consistency between different measurement methods.

Contribution

It introduces a model-independent correction method for coalescence factors, accounting for primordial nucleon densities and specific yield ratios, enhancing interpretation at low energies.

Findings

Corrected $B_2$ and $B_3$ reduce volume discrepancies.

Corrections are substantial below 6 GeV but negligible above.

Method relies only on measured protons, clusters, and pions.

Abstract

We investigate the coalescence factors $B_2$ and $B_3$ at low collision energies ($\sqrt{s_\mathrm{NN}}<6$ GeV) with special focus on the HADES and RHIC-BES experiments. It is shown that, in order to properly interpret the coalescence factors $B_A$, two important corrections are necessary: I) $B_2$ has to be calculated using the proton $\times$ neutron yields in the denominator, instead of the square of the proton yield, and II) the primordial proton (neutron) densities have to be used for the normalization and not the final state (free) protons (neutrons). Both effects lead to a drastic reduction of $B_2$ and $B_3$ at low energies. This reduction decreases the discrepancy between the volumes extracted from HBT measurements and the volumes extracted from the coalescence factor ($V\propto 1/B_2$). While at HADES and low RHIC-BES energies these corrections are substantial, they become irrelevant above $\sqrt{s_\mathrm{NN}}>6$ GeV. The proposed correction method is model independent and is only based on the measurement of protons, clusters and charged pions.