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Blast-wave-Tsallis-power model for $p_{\rm T}$-spectra and elliptic flow $v_2$ of hadrons in collisions of identical nuclei at energies available at the Large Hadron Collider

Smbat Grigoryan

TL;DR

The paper extends the blast-wave-Tsallis-power model (BWTPM) to simultaneously describe midrapidity $p_T$-spectra and elliptic flow $v_2$ across AA collisions, leveraging an anisotropic, elliptical freeze-out surface and azimuthal flow modulation. Centrality is absorbed into a compact parametrization based on the charged-particle multiplicity $M_{ m ch}$, reducing the number of free parameters and enabling robust predictions across Pb–Pb, Xe–Xe, and OO collisions, as well as lower-energy RHIC data. A comprehensive global fit to diverse hadron species (including resonances and heavy quark states) demonstrates good agreement with $p_T$-spectra, integrated yields, mean $p_T$, and $v_2(p_T)$ over a wide $p_T$ range, with clear physical interpretation in terms of radial flow, resonance decays, and hard-process contributions. The model also provides predictive power for new collisions and for deformed nuclei, with explicit guidance on particle-type dependencies and potential future extensions to light nuclei production.

Abstract

A generalization of the phenomenological blast-wave-Tsallis-power model, recently proposed by the author for the hadrons transverse momentum ($p_\textrm{T}$) spectra measured at the LHC, is developed to also describe the hadrons $p_\textrm{T}$-differential elliptic flow coefficients $v_2$ in identical nuclei collisions of different centralities. The model describes well the available data on $p_\textrm{T}$-spectra and $v_2$ for any $p_\textrm{T}$ of various particles, from pions to charmonia, in Pb--Pb at $\sqrt{s_\mathrm{NN}}=$ 2.76 and 5.02~TeV, and in Xe--Xe at $\sqrt{s_\mathrm{NN}}=$ 5.44~TeV. Also, predictions for OO collisions at $\sqrt{s_\mathrm{NN}}=$ 5.36~TeV are given. While the model is mainly targeting the LHC energies, it also works at much lower RHIC energies.

Blast-wave-Tsallis-power model for $p_{\rm T}$-spectra and elliptic flow $v_2$ of hadrons in collisions of identical nuclei at energies available at the Large Hadron Collider

TL;DR

The paper extends the blast-wave-Tsallis-power model (BWTPM) to simultaneously describe midrapidity -spectra and elliptic flow across AA collisions, leveraging an anisotropic, elliptical freeze-out surface and azimuthal flow modulation. Centrality is absorbed into a compact parametrization based on the charged-particle multiplicity , reducing the number of free parameters and enabling robust predictions across Pb–Pb, Xe–Xe, and OO collisions, as well as lower-energy RHIC data. A comprehensive global fit to diverse hadron species (including resonances and heavy quark states) demonstrates good agreement with -spectra, integrated yields, mean , and over a wide range, with clear physical interpretation in terms of radial flow, resonance decays, and hard-process contributions. The model also provides predictive power for new collisions and for deformed nuclei, with explicit guidance on particle-type dependencies and potential future extensions to light nuclei production.

Abstract

A generalization of the phenomenological blast-wave-Tsallis-power model, recently proposed by the author for the hadrons transverse momentum () spectra measured at the LHC, is developed to also describe the hadrons -differential elliptic flow coefficients in identical nuclei collisions of different centralities. The model describes well the available data on -spectra and for any of various particles, from pions to charmonia, in Pb--Pb at 2.76 and 5.02~TeV, and in Xe--Xe at 5.44~TeV. Also, predictions for OO collisions at 5.36~TeV are given. While the model is mainly targeting the LHC energies, it also works at much lower RHIC energies.

Paper Structure

This paper contains 10 sections, 28 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Description of BWTPM
  3. parametrization of $M_{\rm ch}$
  4. parametrization of BWTPM
  5. Fitted data and parameters
  6. Discussion of the results
  7. Hadrons $p_{\textrm{T}}$-spectra, integrated yields, and $\langle p_{\textrm{T}}\xspace\rangle$
  8. Hadrons $p_{\textrm{T}}$-differential and averaged $v_{2}$
  9. Study of hadrons not used in the global fit
  10. Conclusions

Figures (15)

  • Figure 1: Fit of the midrapidity charged-particle multiplicity density data measured for various AA collisions at different centralities $x_c$ and energies $\sqrt{s_\mathrm{NN}}$ by the ALICE alic4alic5alic6alic536, PHOBOS phob and PHENIX phen1 experiments. The dashed line shows the prediction (multiplied by 0.5 for better visibility) for the OO collisions at $\sqrt{s_\mathrm{NN}}\xspace=$5.36 TeV. The data/fit ratio demonstrates the quality of the fits.
  • Figure 2: Fit of the midrapidity charged-particle multiplicity density in inelastic pp collisions by Eq. (\ref{['eq:dNdetapp']}) as a function of $\sqrt{s}$. Six higher energy data points are from Refs. alic7alic8alic9 and the remaining data points are from Refs. phobT77.
  • Figure 3: Fit of $p_{\textrm{T}}$-spectra with highest $p_{\textrm{T}}$ reached in $\textrm{Pb--Pb}$ collisions for charged particles at $\sqrt{s_\mathrm{NN}}$$=$2.76 TeV alic12atl1 and 5.02 TeV alic12cms1 and for ${\mathrm D}^{0}$ at $\sqrt{s_\mathrm{NN}}$$=$5.02 TeV cms2alic19.
  • Figure 4: Fit of pion, kaon, and proton $p_{\textrm{T}}$-spectra at $|y| <$ 0.5 for different centrality classes (centrality intervals) in $\textrm{Pb--Pb}$ collisions at $\sqrt{s_\mathrm{NN}}$$=$ 5.02 TeV alic5. The data points and fitting curves in the top panels are scaled, for better visibility, by the numbers given in the parentheses.
  • Figure 5: Similar to the Fig. \ref{['idpPbPbvsM']} but for $\textrm{Xe--Xe}$ collisions at $\sqrt{s_\mathrm{NN}}$$=$ 5.44 TeV alic29. In addition, the dashed lines in the top panels show the predictions (scaled down by 0.0002 for better visibility) for 0-5 % centrality OO collisions at $\sqrt{s_\mathrm{NN}}\xspace=$5.36 TeV.
  • ...and 10 more figures