# Analytical coalescence formula for particle production in relativistic heavy-ion collisions

## TL;DR

This paper derives an improved analytical coalescence formula for particle yields in relativistic heavy-ion collisions, incorporating relativistic effects and finite size corrections, aiding predictions of cluster production such as light nuclei and exotic hadrons.

## Contribution

It introduces a new analytical coalescence formula that accounts for longitudinal momentum, relativistic corrections, and finite size effects, enhancing yield predictions in heavy-ion collisions.

## Key findings

- The formula accurately predicts light nuclei yields in Pb+Pb collisions.
- Application to strangeness factor $S_3$ shows consistency with experimental data.
- Predictions for exotic hadron production align with other models.

## Abstract

Based on a covariant coalescence model with a blast-wave-like parametrization for the phase-space configuration of constituent particles at freeze-out, we derive an approximate analytical formula for the yields of clusters produced in relativistic heavy-ion collisions. Compared to previous existing formulae, the present work additionally considers the contributions from the longitudinal dimension in momentum space, the relativistic corrections and the finite size effects of the produced clusters relative to the spatial distribution of constituent particles at freeze-out. The new analytical coalescence formula provides a useful tool to evaluate the yield of produced clusters, such as light nuclei from nucleon coalescence and hadrons from quark coalescence, in heavy-ion collisions. As a first application of the new analytical formula, we explore the strangeness population factor $S_3 = ^3_{\Lambda}$H/($^3$He$\times \Lambda/$p) based on nucleon/$\Lambda$ coalescence as well as the production of exotic hadrons based on quark coalescence, in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The results are compared with the predictions from other models.