[Paper Review] Strangeness Saturation: Energy- and System-Size Dependence

J. Cleymans, B. Kämpfer+2 more|ArXiv.org|Dec 23, 2002

Machine Learning in Materials Science3 citations

TL;DR

This paper investigates the energy- and system-size dependence of strangeness saturation in relativistic heavy-ion collisions using thermal statistical models. It shows that the strangeness saturation factor $\gamma_s$ increases with participant number in Pb+Pb and Au+Au systems at SPS and RHIC energies, with mid-rapidity data revealing higher $\gamma_s$ than 4$\pi$-integrated data, and finds that $f_2$, the fraction of multiply-struck participants, remarkably tracks $\gamma_s$ scaling in Au+Au collisions at RHIC.

ABSTRACT

Relativistic heavy-ion collisions lead to a final state which has a higher degree of strangeness saturation than those of elementary collisions. A systematic analysis of this phenomenon, based on the strangeness saturation factor, is made for C+C, Si+Si and Pb+Pb collisions at the CERN SPS collider and for Au+Au collisions at RHIC energies. Strangeness saturation is shown to increase with the number of participants within a colliding system, at both CERN SPS and RHIC energies. The saturation observed in central collisions of lighter nuclei deviates from that seen in peripheral collisions of heavier nuclei with an equivalent participant number, which could be due to the difference in nuclear density.

Motivation & Objective

• To understand the system-size and energy dependence of strangeness saturation in relativistic heavy-ion collisions.
• To compare strangeness saturation levels between fully-integrated and mid-rapidity hadron yields in Pb+Pb and Au+Au collisions.
• To investigate whether peripheral Pb+Pb collisions are equivalent to central collisions of lighter nuclei in terms of strangeness saturation.
• To examine the role of nuclear density and participant dynamics in strangeness production via the $f_2$ parameter.
• To assess the consistency of thermal model parameters across different collision systems and energies.

Proposed method

• Uses the grand-canonical thermal model with a phenomenological strangeness saturation factor $\gamma_s$ to describe hadron multiplicities.
• Applies the Boltzmann approximation to particle number densities, incorporating the Breit-Wigner distribution for resonances.
• Analyzes $4\pi$-integrated yields from central C+C, Si+Si, and Pb+Pb collisions at 158 AGeV (SPS) and mid-rapidity yields from Au+Au at $\sqrt{s}_{NN} = 130$ GeV (RHIC).
• Fixes temperature at 165 MeV for all systems and uses canonical formalism for baryon and charge conservation in small systems.
• Compares results from 4$\pi$-integrated data and mid-rapidity data, excluding $\phi$ in one 4$\pi$ analysis to ensure consistency.
• Introduces the $f_2$ parameter, representing the fraction of multiply-struck participants, to parametrize system-size dependence of $\gamma_s$.

Experimental results

Research questions

• RQ1 How does the strangeness saturation factor $\gamma_s$ vary with the number of participants in heavy-ion collisions at SPS and RHIC energies?
• RQ2 Are peripheral Pb+Pb collisions equivalent to central collisions of lighter nuclei (C+C, Si+Si) in terms of strangeness saturation?
• RQ3 Why is the degree of strangeness saturation higher in mid-rapidity regions than in fully-integrated phase space?
• RQ4 How does the Wróblewski factor $\lambda_s$, measuring $s\bar{s}$ pair production, evolve with collision energy and system size?
• RQ5 Can the $f_2$ parameter effectively describe the system-size dependence of $\gamma_s$ in Au+Au collisions at RHIC?

Key findings

• The strangeness saturation factor $\gamma_s$ increases with participant number in both Pb+Pb (SPS) and Au+Au (RHIC) collisions.
• Central C+C and Si+Si collisions exhibit higher $\gamma_s$ than peripheral Pb+Pb collisions with comparable participant numbers, indicating a deviation from equivalence.
• Mid-rapidity $\gamma_s$ values are consistently higher than those extracted from 4$\pi$-integrated data, suggesting stronger strangeness saturation in the central rapidity region.
• The $f_2$ parameter, representing the fraction of multiply-struck participants, provides an excellent parametrization of the $N_{\rm part}$-dependence of $\gamma_s$ in Au+Au collisions at RHIC.
• The Wróblewski factor $\lambda_s$ decreases with increasing collision energy from 40 to 158 AGeV, while remaining above the $pp$ value of 0.2.
• The $\gamma_s$ values extracted from mid-rapidity data at 158 AGeV are significantly higher than those from 4$\pi$-integrated data, even after excluding $\phi$ mesons for consistency.