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Higher order net-baryon number cumulants and baryon-strangeness correlations: Comparing QCD results on thepseudo-critical line with RHIC-BES II results on the freeze-out line

Jishnu Goswami, Frithjof Karsch

TL;DR

This work uses high-statistics lattice QCD calculations to study higher-order net-baryon cumulants and baryon–strangeness correlations along the (2+1)-flavor pseudo-critical line and compares them to STAR BES-II data and HRG models. By expanding the QCD pressure in a Taylor series and parameterizing the pseudo-critical line, the authors constrain the possible location of a QCD critical point and test the validity of a non-interacting HRG description up to moderate values of $\mu_B/T$. They find that $R_{12}^B=\chi_1^B/\chi_2^B$ matches STAR net-proton results down to $\sqrt{s_{NN}}\approx11.5$ GeV, while higher cumulant ratios $R_{31}^B$ and $R_{42}^B$ show no signs of critical behavior and deviate from HRG predictions, suggesting the HRG description fails for $\mu_B/T>1$ and arguing against a CEP in the BES-II collider-accessible region. Baryon–strangeness correlations exhibit energy-dependent agreement with STAR and ALICE data, but deviations at lower energies point to missing strange resonances and feed-down uncertainties, underscoring the need for controlled corrections. Overall, the study provides robust lattice-based constraints that the QCD critical point, if it exists, lies outside the BES-II collider range and highlights the role of resonance content in strange-baryon correlations for heavy-ion phenomenology.

Abstract

We present lattice QCD results for ratios of net-baryon number cumulants along the pseudo-critical line and compare them with STAR measurements from the RHIC BES-II program. The ratio of first and second order cumulants, $R_{12}^B$, agrees well with corresponding net-proton number cumulants down to $\sqrt{s_{NN}}=11.5$ GeV or baryon chemical potentials $μ_B/T \le 2$. Likewise higher-order cumulant ratios, $R_{31}^B$ and $R_{42}^B$, show no sign for the existence of a critical point in the parameter range explored with these cumulant ratios. A QCD critical point is unlikely to occur within the BES-II range in collider mode. Moreover, the results demonstrate that a non-interacting HRG description breaks down for $μ_B/T > 1$. We further analyze baryon-strangeness correlations normalized by strangeness fluctuations, finding consistency with STAR data at large beam energies but deviations at lower energies. Comparisons of electric-charge and strangeness correlations with STAR and ALICE data also show agreement at high energies, while the deviations at lower energies emphasize the role of unobserved strange resonances and the need for controlled feed-down corrections in baryon-strangeness correlations.

Higher order net-baryon number cumulants and baryon-strangeness correlations: Comparing QCD results on thepseudo-critical line with RHIC-BES II results on the freeze-out line

TL;DR

This work uses high-statistics lattice QCD calculations to study higher-order net-baryon cumulants and baryon–strangeness correlations along the (2+1)-flavor pseudo-critical line and compares them to STAR BES-II data and HRG models. By expanding the QCD pressure in a Taylor series and parameterizing the pseudo-critical line, the authors constrain the possible location of a QCD critical point and test the validity of a non-interacting HRG description up to moderate values of . They find that matches STAR net-proton results down to GeV, while higher cumulant ratios and show no signs of critical behavior and deviate from HRG predictions, suggesting the HRG description fails for and arguing against a CEP in the BES-II collider-accessible region. Baryon–strangeness correlations exhibit energy-dependent agreement with STAR and ALICE data, but deviations at lower energies point to missing strange resonances and feed-down uncertainties, underscoring the need for controlled corrections. Overall, the study provides robust lattice-based constraints that the QCD critical point, if it exists, lies outside the BES-II collider range and highlights the role of resonance content in strange-baryon correlations for heavy-ion phenomenology.

Abstract

We present lattice QCD results for ratios of net-baryon number cumulants along the pseudo-critical line and compare them with STAR measurements from the RHIC BES-II program. The ratio of first and second order cumulants, , agrees well with corresponding net-proton number cumulants down to GeV or baryon chemical potentials . Likewise higher-order cumulant ratios, and , show no sign for the existence of a critical point in the parameter range explored with these cumulant ratios. A QCD critical point is unlikely to occur within the BES-II range in collider mode. Moreover, the results demonstrate that a non-interacting HRG description breaks down for . We further analyze baryon-strangeness correlations normalized by strangeness fluctuations, finding consistency with STAR data at large beam energies but deviations at lower energies. Comparisons of electric-charge and strangeness correlations with STAR and ALICE data also show agreement at high energies, while the deviations at lower energies emphasize the role of unobserved strange resonances and the need for controlled feed-down corrections in baryon-strangeness correlations.

Paper Structure

This paper contains 5 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. QCD critical point constraints from the pseudo-critical line of (2+1)-flavor QCD
  3. Net-baryon number fluctuations on the pseudo-critical line
  4. Baryon--strangeness number correlations on the pseudo-critical line
  5. Summary

Figures (2)

  • Figure 1: Left The ratio $R_{12}^B$ obtained in QCD and HRG-model calculations as function $\mu_B/T$ on the $T_{pc}$. Right: Skewness ($R_{31}^B$) and kurtosis ($R_{42}^B$) ratios as function of $R_{12}^B$. Also shown are the corresponding STAR results for net-proton number fluctuations.
  • Figure 2: Baryon–strangeness (left) and electric charge–strangeness (right) correlations normalized by $\chi_2^S$ along $T_{pc}(\mu_B)$Bollweg:2024epj. Lattice QCD results are compared with preliminary heavy ion collision data from STAR presented at CPOD 2024 STAR-CPOD, and HRG model calculations using the QMHRG2020 list of hadrons. Also shown is a data point based on an analysis of data obtained by the ALICE collaboration Braun-Munzinger:2014lba.