Collectivity Signatures in High-Multiplicity pp Collisions from Hybrid Hydro+Tsallis Modeling of Pion Spectra

TL;DR

This work investigates collectivity signatures in high-multiplicity pp collisions at $\sqrt{s}=7$ TeV by analyzing pion $p_T$ spectra with two fitting strategies: a Tsallis-Pareto distribution and a hybrid Hydro+Tsallis framework that couples a soft Boltzmann-Gibbs Blast Wave component to a hard Tsallis tail. The Hydro+Tsallis model provides a superior description across most multiplicity classes and enables simultaneous extraction of kinetic and non-extensive freeze-out parameters, including $T_0$, $\beta_T$, $T$, and $q$, from which a suite of thermodynamic quantities ($\varepsilon$, $n$, $s$, $P$, $C_V$, $c_s^2$, $\lambda$, $K_n$, $\kappa_T$, $\alpha$) is computed at freeze-out. The results show systematic increases of $T$, $\beta_T$, $\langle p_T\rangle$, $N_0$, and various densities with higher $dN_{ch}/d\eta$, while $T_0$, $q$, $\lambda$, $K_n$, and $\kappa_T$ decrease, suggesting a gradual transition toward collectivity and partial thermalization in high-multiplicity pp events. Correlations among parameters (e.g., strong linear $T$ vs $dN_{ch}/d\eta$ and negative $T_0$–$\beta_T$ correlation) support a picture of enhanced collective dynamics in small systems, though the authors caution that these trends do not constitute unambiguous evidence for deconfined QGP. The study provides a self-consistent framework to disentangle soft and hard production and motivates extensions to heavier hadrons for a more complete picture of collectivity in pp collisions.

Abstract

The transverse momentum (pT) distributions up to pT = 20 GeV/c for pions produced in the ten different multiplicity classes (MCs) of symmetric pp collisions at sqrt(s) = 7 TeV have been investigated. Two distinct models, the Tsallis-Pareto type function (model) and the combined BGBW model and Tsallis-Pareto type model have been employed to fit the pT distributions via the minimum chi-square method. The combined Hydro+Tsallis model is more reliably describing the pT spectra than the Tsallis-Pareto model. The Tsallis temperature (T), non-extensivity parameter (q), normalization constant (N0), Kinetic freeze-out temperature (T0), transverse flow velocity (betaT), and (mean pT) have been extracted through the fitting procedure via the employed models. The Tsallis-Pareto model gives T, q, N0 and mean pT while Hydro+Tsallis model gives T0, betaT, T, q, N0 and mean pT. Incorporating the values of the extracted T and q the thermodynamic quantities and response functions, including energy density (epsilon), particle density (n), entropy density (s), pressure (P), specific heat at constant volume (CV), squared speed of sound (cs2), mean free path (lambda), Knudsen number (Kn), isothermal compressibility (kappaT), and expansion coefficient (alpha) have been calculated at the freeze-out stage. It has been observed that T, betaT, mean pT, N0, epsilon, n, s, P, CV, cs2, and alpha increase with increasing(decreasing) the charged particles multiplicity density dNch/deta(MCs). While T0, q, lambda, Kn, and kappaT decrease with increasing(decreasing) dNch/deta(MCs). These systematic variations in the trends of parameters might suggest the gradual transition towards collectivity and thermal equilibration in the high multiplicity pp events, possibly signalling enhanced collective dynamics and partial thermalization in small collision systems.

Figures (7)

• Figure 1: Double differential $p_T$ distribution of charged pions produced in pp collisions at $\sqrt{s}$=7 TeV in different multiplicity classes. The various geometrical shapes and colours are used for the experimental data identified while the solid lines are used for (a) the Tsallis model and (b) the Hydro+Tsallis model.
• Figure 2: (a) $\chi^2/NDF$ (reduced-$\chi^2$), (b) Akaike Information Criterion ($AIC$), and (c) Bayesian Information Criterion ($BIC$) as a function of MCs and $dN_{ch}/d\eta$.
• Figure 3: (a) $T$, (b) $q$, (c) $N_0$ and (d) $\langle p_T\rangle$, extracted from the Tsallis and Hydro+Tsallis models, as a function of MCs and $dN_{ch}/d\eta$. The solid fit lines are the results of different models, indicated in each plot.
• Figure 4: (a) $T_0$ and (b) $\beta_T$, obtained from the Hydro+Tsallis model, as a function of MCs and $dN_{ch}/d\eta$. Plot (c) displays the correlation between $T_0$ and $\beta_T$. Different solid and dotted lines are used for the fitting results of different models, indicated in each plot.
• Figure 5: (a) $\varepsilon$, (b) $n$, (c) $s$, (d) $p$, (e) $C_V$, and (f) ${c_s}^2$, calculated from the Tsallis and Hydro+Tsallis models, as a function of MCs and $dN_{ch}/d\eta$. The solid and dotted lines are used for the fit results of different models.