Hadron Emission and Stopping in Heavy-Ion Collisions: Baryon-Rich Matter to Meson-Dominated Matter

Today’s accelerator facilities used for studies of relativistic heavy-ion collisions cover an energy range spanning over three orders of magnitude, from a few GeV up to a few TeV in center-of-mass energy per nucleon pair ($\sqrt{s_{NN}}$). We present a systematic overview of hadron emission in heavy-ion collisions across this entire energy range. The presented energy excitation functions of the approximated baryon and meson yields at mid-rapidity reflect the interplay between baryon stopping and particle production, both of which evolve continuously with increasing energy. At low energies (e.g., SIS18, AGS), strong nuclear stopping leads to high net-baryon densities at mid-rapidity and to the abundant formation of nuclear clusters. With increasing $\sqrt{s_{NN}}$, the relative baryon stopping power $\langle δy \rangle / y_p$ decreases, and meson production becomes dominant. The inelasticity, i.e. the fraction of the initial kinetic energy available converted in inelastic reactions into particle production and dynamics, is found to rise rapidly at low energies and then levels off at values around $0.7 - 0.8$. While at low energies up to $\sim 10$~GeV this available energy seems to be shared by equal amount between the production of new particles and the dynamics of the system, as well as radiation, the latter part starts to dominates at higher energies.

💡 Research Summary

This paper provides a comprehensive and systematic overview of hadron emission in relativistic heavy-ion collisions across an immense energy range, spanning from a few GeV to several TeV in center-of-mass energy per nucleon pair (√s_NN). The central theme is the evolving interplay between two fundamental processes: baryon stopping and particle production.

At low collision energies (e.g., at the SIS18 or AGS facilities), strong nuclear stopping occurs. This means the incoming nucleons lose most of their forward momentum in the collision, leading to a high density of net baryons (baryons minus antibaryons) around mid-rapidity (the center of the collision in momentum space). The system formed is baryon-rich, with abundant production of nuclear clusters. As the collision energy increases, the relative stopping power—the average rapidity loss of baryons divided by the beam rapidity—initially remains constant but eventually decreases at higher energies (e.g., at RHIC). This is because the kinematic gap between the projectile and target widens faster than the nucleons can be stopped. Consequently, the net-baryon density at mid-rapidity drops by over an order of magnitude from SIS18 to RHIC energies.

Simultaneously, the production of new particles, primarily mesons like pions and kaons, increases dramatically with energy. The mid-rapidity yield of pions rises smoothly from very low values at a few GeV to several units per participant nucleon at TeV energies. The proton yield reflects the competition between stopping (which brings initial protons to mid-rapidity, dominant at low energy) and pair production (which creates new proton-antiproton pairs, dominant at high energy). This causes the proton yield to first decrease, reach a minimum around √s_NN ≈ 40 GeV, and then increase again at higher energies. At the LHC (√s_NN = 5 TeV), protons and antiprotons are produced in equal numbers at mid-rapidity, indicating negligible transport of initial baryon number to that region.

By constructing the excitation functions for total baryon and meson yields at mid-rapidity, the paper identifies a clear transition. The meson yield, dominated by pions and kaons, increases monotonically. The baryon yield, after accounting for neutrons, hyperons, and light nuclei, decreases from its low-energy value to a minimum near 40 GeV before a slight rise due to pair production. The meson yield surpasses the baryon yield at approximately √s_NN ≈ 5 GeV. This marks the point where the matter formed in the collision zone transitions from being net-baryon dominated to being meson dominated.

The paper also performs a quantitative analysis linking stopping and production. It shows that the average energy carried by a net baryon increases linearly with √s_NN. Furthermore, it examines the inelasticity—the fraction of the initial kinetic energy converted into particle production and system dynamics (like collective flow). The inelasticity is found to rise rapidly at low energies and then saturate at a value of about 0.7-0.8. An intriguing observation is that up to energies of about 10 GeV, this available inelastic energy seems to be shared roughly equally between the production of new particles and the dynamics/radiation of the system. At higher energies, the share devoted to system dynamics and radiation becomes dominant.

In summary, this work synthesizes decades of experimental results to paint a coherent picture of how heavy-ion collisions evolve with energy. The continuous shift from a regime dominated by baryon stopping and baryon-rich matter at low energies to a regime dominated by particle (mostly meson) production at high energies is clearly demonstrated, offering fundamental insights into the changing nature of strong interaction matter under extreme conditions.