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Multiplicity dependence of thermal parameters in pp collisions at $\sqrt{s}=7$ TeV from statistical hadronization fits

R. C. Baral

Abstract

We perform a systematic thermal analysis of identified hadron yields measured by the ALICE Collaboration in proton-proton collisions at $\sqrt{s}=7$ TeV across charged-particle multiplicity classes within the statistical hadronization model using the Thermal-FIST framework. Global fits are used to extract the chemical freeze-out temperature $T$, system volume $V$, and strangeness saturation parameter $γ_S$. The extracted temperature remains approximately constant at $T \simeq 155$-$165$ MeV across multiplicity, while the volume exhibits an approximately linear increase with event activity. In contrast, $γ_S$ shows a clear rise with multiplicity, indicating a progressive reduction of strangeness suppression. Derived thermodynamic quantities obtained within the model show that the energy density increases with multiplicity, while the average energy per particle increases from $\sim 0.85$ GeV to $\sim 0.99$ GeV, remaining close to $1$ GeV. Particle-to-pion ratios exhibit a hierarchy with strangeness content consistent with ALICE measurements. A systematic comparison of fits constrained by hidden- and open-strangeness hadrons reveals a persistent offset in $γ_S$ at the $\sim 4σ$ level, indicating a tension between $φ$- and $Ω$-constrained fits. These results suggest that while high-multiplicity proton-proton collisions approach thermal-like behavior, a single global freeze-out description may not fully capture the strange sector.

Multiplicity dependence of thermal parameters in pp collisions at $\sqrt{s}=7$ TeV from statistical hadronization fits

Abstract

We perform a systematic thermal analysis of identified hadron yields measured by the ALICE Collaboration in proton-proton collisions at TeV across charged-particle multiplicity classes within the statistical hadronization model using the Thermal-FIST framework. Global fits are used to extract the chemical freeze-out temperature , system volume , and strangeness saturation parameter . The extracted temperature remains approximately constant at - MeV across multiplicity, while the volume exhibits an approximately linear increase with event activity. In contrast, shows a clear rise with multiplicity, indicating a progressive reduction of strangeness suppression. Derived thermodynamic quantities obtained within the model show that the energy density increases with multiplicity, while the average energy per particle increases from GeV to GeV, remaining close to GeV. Particle-to-pion ratios exhibit a hierarchy with strangeness content consistent with ALICE measurements. A systematic comparison of fits constrained by hidden- and open-strangeness hadrons reveals a persistent offset in at the level, indicating a tension between - and -constrained fits. These results suggest that while high-multiplicity proton-proton collisions approach thermal-like behavior, a single global freeze-out description may not fully capture the strange sector.

Paper Structure

This paper contains 12 sections, 2 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Statistical Hadronization Model and Thermal-FIST Framework
  3. Results and Discussion
  4. Fit Quality
  5. Chemical Freeze-out Temperature
  6. Strangeness Saturation
  7. Volume Scaling
  8. Energy Density and Average Energy per Particle
  9. Multiplicity dependence of particle-to-pion ratios
  10. $\Omega$-$\phi$ Tension
  11. Tables of Fit Results
  12. Conclusions

Figures (4)

  • Figure 1: Measured hadron yields and corresponding thermal model predictions for the combined high-multiplicity classes I and II in proton--proton collisions at $\sqrt{s}=7$ TeV. The upper panel shows the experimental data from ALICE and the results of global fits obtained within the statistical hadronization framework using Thermal-FIST. The lower panel displays the ratio of data to model predictions, with the horizontal line indicating unity. Error bars represent the experimental uncertainties.
  • Figure 2: Extracted thermal parameters as functions of the charged-particle multiplicity $\langle dN_{\mathrm{ch}}/d\eta \rangle$ in pp collisions at $\sqrt{s}=7$ TeV. (a) Chemical freeze-out temperature $T$, (b) strangeness saturation parameter $\gamma_S$, and (c) system volume $V$. Results are obtained from global fits to identified hadron yields using the statistical hadronization model within the Thermal-FIST framework. Different markers correspond to fits performed using the $\phi$ and $\Omega$ multiplicity class selections. Error bars represent fit uncertainties.
  • Figure 3: Energy density $\varepsilon$ (left) and average energy per particle $E/N$ (right) as functions of charged-particle multiplicity $\langle dN_{\mathrm{ch}}/d\eta \rangle$ in pp collisions at $\sqrt{s}=7$ TeV. Different markers correspond to the $\phi$ and $\Omega$ multiplicity class selections. The solid line in the right panel indicates the empirical freeze-out condition $E/N = 1$ GeV.
  • Figure 4: Multiplicity dependence of particle-to-pion yield ratios in pp collisions at $\sqrt{s}=7$ TeV. The ratios $K_S^0/\pi$, $\Lambda/\pi$, $\Xi/\pi$, $\Omega/\pi$, and $\phi/\pi$ are shown as functions of $\langle dN_{ch}/d\eta \rangle$. The experimental data (solid markers) with uncorrealted systematic uncertainties (vertical bars) are compared with thermal model calculations obtained using two different fit configurations within the Thermal-FIST framework: one including the $\phi$ meson and excluding the $\Omega$ baryon, and the other including the $\Omega$ baryon and excluding the $\phi$ meson.