arXiv subjects

Swatantra Kumar Tiwari

Publications and source records attributed to Swatantra Kumar Tiwari.

At least 19 recordsLinked to original sources

arXiv2026

Transport of $D^0$ meson in hadronic matter in the domain of Non-Extensive statistics

In this work, we investigate the drag and diffusion coefficients of $D^0$ meson propagating through a hadronic thermal bath by employing the Fokker Planck equation within the framework of Tsallis non extensive statistics. The non extensive parameter, $q$ accounts for the deviation from equilibrium and provides a more realistic description of the medium that is not perfectly thermalized. The hadronic bath, consisting of various mesonic and baryonic species, is characterized by different mass cutoffs that control the spectral composition of the medium. Our analysis shows that both the drag, $F$ and momentum diffusion coefficients, $Γ$ increases with temperature and also increases with increasing $q$ and mass cutoff. The spatial diffusion coefficient, $D_x$ exhibits a decreasing trend with temperature $T$, $q$ and mass cutoff which highlights the significant influence of non-equilibrium effects and hadronic composition on the transport behaviour of $D^0$ meson, offering valuable insights into the thermal and dynamical properties of the hadronic phase in heavy ion collisions. In this study while calculating the spatial diffusion coefficient, $D_x$ we observe that beyond $q$ = 1.24, $D_x$ goes below to the lower limit proposed in Ads/CFT theory. This suggests that 1.24 is the upper limit of non extensive parameter, $q$.

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arXiv2026

Unified Functional-Holographic Theory of the QCD Critical End Point

We develop a thermodynamically consistent nonperturbative framework for equilibrium QCD criticality, unifying DSE quark propagation, FRG flow, and PNJL thermodynamics for coupled chiral/deconfinement order parameters. A holographic Maxwell-Chern-Simons sector supplies topological response; its topological susceptibility enters the FRG flow of the determinantal ('t Hooft) interaction, encoding axial-anomaly evolution across the phase diagram. At $μ_B=0$ we anchor to continuum-extrapolated lattice thermodynamics and conserved-charge susceptibilities through a lattice-calibrated Polyakov sector, enforcing exact thermodynamic identities by evaluating derivatives at the stationary grand-potential solution at each RG scale. Solving the coupled DSE-FRG-holographic system yields, at the present approximation level, an equilibrium critical end point at $T_{\mathrm{CEP}}\simeq130\text{--}135,\mathrm{MeV}$ and $μ_{B,\mathrm{CEP}}\simeq600,\mathrm{MeV}$, with quantified sensitivity to regulator, Polyakov-sector, and holographic-normalization choices. The critical region is organized by a nonperturbative map onto universal 3D Ising scaling variables, with anomalous-dimension effects absorbed into nonuniversal metric factors, yielding predictions for the hierarchy, nonmonotonicity, and sign structure of higher-order net-baryon cumulant ratios along smooth freeze-out trajectories and speed-of-sound softening. Comparisons to RHIC BES fluctuation measurements are qualitative consistency checks on correlated equilibrium trends and sign patterns, because finite size/lifetime, critical slowing down, baryon-number conservation, acceptance/efficiency corrections, net-proton-to-net-baryon conversion, and baryon transport can round or reshape experimental cumulants. The results provide a unified equilibrium baseline and controlled inputs for finite-size scaling and dynamical embeddings of heavy-ion data.

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arXiv2026

Geometric Baryogenesis with Chiral-Time Equivalence

The asymmetry between matter and antimatter demands a cause as simple as it is profound. Here we show that a single geometric principle Chiral-Time Equivalence (CTE)-suffices to generate and correlate the required CP violation with the time orientation of the cosmos. Promoting the Immirzi parameter to a pseudoscalar Nambu-Goldstone field $Φ$, CTE fixes the leading operators: a shift-symmetric derivative portal $((\partial_μΦ)J^μ_{B-L}/M_*)$ that acts as a dynamical chemical potential in FRW, and a topological term $(Φ\,R\tilde R)$ that imprints parity on tensor modes. In thermal equilibrium this structure produces gravity-assisted leptogenesis, whose magnitude is set at the decoupling temperature by susceptibilities rather than by tuned departures from equilibrium. A fully flavored Boltzmann network with curvature sources captures flavor transfer and washout, while slow-roll and resonant regimes are established via thermodynamic and Kubo formulas. Consistency is secured by an EFT analysis (stability, perturbative unitarity, and BBN safety), and by explicit elimination of EC torsion and control of dCS birefringence in the small-coupling domain. The most striking prediction is a sign locking among $η_B$, tensor chirality $χ_T$, and the drift of $Φ$, together with a tri-observable relation that ties $η_B$ to cosmic birefringence $Δα$ and $χ_T$. Thus a single, symmetry-protected geometric origin renders the baryon excess testable by TB/EB correlations and stochastic-wave chirality, and calculable within a minimal, ultraviolet-anchored effective theory.

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arXiv2024

Exploring Anisotropic flow via the Boltzmann Transport Equation Employing the Tsallis Blast Wave Description at LHC energies

Anisotropic flows $i.e.$ azimuthal anisotropies in particle production are one of the important probes in characterizing the properties of the strongly interacting matter created in the relativistic heavy-ion collisions. These observables are sensitive to both the transport properties as well as the equation of state (EOS) of Quantum Chromodynamics (QCD) matter. We have adopted the Boltzmann transport equation (BTE) in the relaxation time approximation (RTA) to describe the experimental data for harmonic flows such as elliptic flow ($v_2$), triangular flow ($v_3$), quadrangular flow ($v_4$) obtained in heavy-ion collisions at Large Hadron Collider (LHC) energies. In this analysis, we have used Tsallis statistics as an initial distribution and the Tsallis Blast wave (TBW) description is used as the equilibrium distribution function while describing the evolution of the particle production in BTE. We have fitted the transverse momentum spectra, $v_2$, $v_3$, and $v_4$ of identified hadrons such as pion, kaon, and proton for Pb-Pb and Xe-Xe collisions at the LHC energies of $\sqrt{s_{NN}}$ = 5.02 TeV and $\sqrt{s_{NN}}$ = 5.44 TeV, respectively for various centralities. Our study offers a comparative analysis between the two distinct collision systems operating at comparable collision energies. The present formulation successfully fits the experimental data for $p_T$-spectra upto $p_T$ = 8 GeV and effectively explains the anisotropic flows data upto $p_T$ = 10 GeV with a very favourable $χ^2/ndf$. We observe that the average transverse flow velocity ($<β_r>$) and the kinetic freeze-out temperature ($T$) extracted in our analysis decrease as we go towards the peripheral collisions. The azimuthal modulation amplitudes ($ρ_a$) exhibit an increasing pattern as one moves from central to peripheral collisions in both the Pb-Pb and Xe-Xe nuclei interactions.

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arXiv2023

Nuclear Modification Factor in Pb-Pb and p-Pb collisions at $\sqrt{s_{NN}}$=5.02 TeV at LHC energies using Boltzmann Transport Equation with Tsallis Blast Wave Description

In this article, we have studied the nuclear modification factor measured in Pb-Pb collisions ($R_{PbPb}$) for $π^{\pm}$, $K^{\pm}$, $p+\bar{p}$, $K^{*0} + \bar{K^{*0}}$, $ϕ$ and in p-Pb collisions ($R_{pPb}$) for $π^{\pm}$, $K^{\pm}$, $p+\bar{p}$ at Large hadron collider (LHC) energy of $\sqrt{s_{NN}}$ = 5.02 TeV for the most central and peripheral collisions. We have also analysed the experimental data of transverse momentum ($p_T$) spectra for these identified hadrons at LHC for Pb-Pb as well as for p-Pb collisions. We have used Boltzmann transport equation (BTE) in relaxation time approximation (RTA) for this analysis. The Tsallis statistics is used as an initial distribution function and The Tsallis blast wave (TBW) model is employed as an equilibrium distribution in BTE. The present model fits the measured transverse momentum spectra, $R_{PbPb}$, and $R_{pPb}$ successfully upto $p_T$ = 8 GeV with a reasonable $χ^2/ndf$ for all the considered hadrons at various centralities. The experimental data for $R_{pPb}$ are generated using the particle yields at pPb and pp collisions where number of binary collisions are taken from Glauber model calculations. We find that the average transverse flow velocity ($<β_r>$) follows the mass and centrality ordering and decreases with the mass as well as when one move from the central collisions to peripheral collisions. These findings are inline with the results of the hydrodynamical calculations.

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arXiv2022

Possible Formation of a Perfect Fluid in $pp$, $p$-Pb, Xe-Xe and Pb-Pb Collisions at the Large Hadron Collider Energies: A Color String Percolation Approach

Isothermal compressibility ($κ_{\rm T}$) is an important thermodynamic observable which gives information about the deviation of a system from perfect fluid behavior. In this work, for the first time we have estimated the isothermal compressibility of QCD matter formed in high energy hadronic and nuclear collisions using color string percolation model (CSPM), where we investigate the change in $κ_{\rm T}$ as a function of final state charged particle multiplicity and initial percolation temperature across various collision species. The estimated initial percolation temperature for different collision systems at different collision energies helps us to have a better understanding of the system at the initial phase of evolution. The comparison of the CSPM results for isothermal compressibility with that for the well known fluids, indicates that the matter formed in heavy-ion collisions might be the {\it closest perfect fluid} found in nature. This estimation complements the well-known observation of minimum shear viscosity to entropy density ratio for a possible QGP medium created in heavy-ion collision experiments. A threshold of pseudorapidity density of charged particles, $\langle dN_{\rm ch}/dη\rangle \geq 20 $ in the final state event multiplicity is observed, after which one may look for a possible QGP formation at the LHC energies.

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arXiv2020

Elliptic flow of hadrons via quark coalescence mechanism using Boltzmann transport equation for Pb+Pb collision at $\sqrt{s_{NN}}$=2.76 TeV

Elliptic flow of hadrons observed at relativistic heavy-ion collision experiments at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC), provides us an important signature of possible de-confinement transition from hadronic phase to partonic phase. However, hadronization processes of de-confined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use coalescence mechanism also known as Recombination (ReCo) to combine quarks into hadrons. To get there, we have used Boltzmann transport equation in relaxation time approximation to transport the quarks into equilibration and finally to freeze-out surface, before coalescence takes place. A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy-ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as $π$, $K$, $p$ etc., produced in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified hadrons seems to be described quite well in the available $p_{\rm T}$ range. After the evolution of quarks until freeze-out time, has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

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arXiv2019

Wiedemann-Franz Law For Hot QCD Matter in a Color String Percolation Scenario

Transport coefficients serve as important probes in characterizing the QCD matter created in high-energy heavy-ion collisions. Thermal and electrical conductivities as transport coefficients have got special significance in studying the time evolution of the created matter. We have adopted color string percolation approach for the estimation of thermal conductivity ($κ$), electrical conductivity ($σ_{el}$) and their ratio, which is popularly known as Wiedemann-Franz law in condensed matter physics. The ratio $κ/σ_{el}T$, which is also known as Lorenz number ($\mathbb{L}$) is studied as a function of temperature and is compared with various theoretical calculations. We observe that the thermal conductivity for hot QCD medium is almost temperature independent in the present formalism and matches with the results obtained in ideal equation of state (EOS) for quark-gluon plasma with fixed coupling constant ($α_s$). The obtained Lorenz number is compared with the Stefan-Boltzmann limit for an ideal gas. We observe that a hot QCD medium with color degrees of freedom behaves like a free electron gas.

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arXiv2019

Effect of Hagedorn States on Isothermal Compressibility of Hadronic Matter formed in Heavy-Ion Collisions: From NICA to LHC Energies

In this work, we have studied the isothermal compressibility ($κ_T$) as a function of temperature, baryon chemical potential and centre-of-mass energy ($\sqrt{s_{NN}}$) using hadron resonance gas (HRG) and excluded-volume hadron resonance gas (EV-HRG) models. A mass cut-off dependence of isothermal compressibility has been studied for a physical resonance gas. Further, we study the effect of heavier resonances ($>$ 2 GeV) on the isothermal compressibility by considering the Hagedorn mass spectrum, $ρ(m)\sim{\exp(bm)}/{(m^2+m_0^2)^{5/4}}$. Here, the parameters, $b$ and $m_0$ are extracted after comparing the results of recent lattice QCD simulations at finite baryonic chemical potential. We find a significant difference between the results obtained in EV-HRG and HRG models at a higher temperatures and higher baryochemical potentials. The inclusion of the Hagedorn mass spectrum in the partition function for hadron gas has a large effect at a higher temperature. A higher mass cut-off in the Hagedorn mass spectrum takes the isothermal compressibility to a minimum value, which occurs near the Hagedorn temperature ($T_H$). We show explicitly that at the future low energy accelerator facilities like FAIR (CBM), Darmstadt and NICA, Dubna the created matter would be incompressible compared to the high energy facilities like RHIC and LHC.

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arXiv2019

Limiting fragmentation in high-energy nuclear collisions at the CERN Large Hadron Collider

The hypothesis of limiting fragmentation (LF) or it is called otherwise recently, as extended longitudinal scaling, is an interesting phenomena in high energy multiparticle production process. This paper discusses about different regions of phase space and their importance in hadron production, giving special emphasis on the fragmentation region. Although it was conjectured as a universal phenomenon in high energy physics, with the advent of higher center-of-mass energies, it has become prudent to analyse and understand the validity of such hypothesis in view of the increasing inelastic nucleon-nucleon cross-section ($σ_{\rm in}$). In this work, we revisit the phenomenon of limiting fragmentation for nucleus-nucleus (A+A) collisions in the pseudorapidity distribution of charged particles at various energies. We use energy dependent $σ_{\rm in}$ to transform the charged particle pseudorapidity distributions ($dN^{\rm AA}_{ch}/dη$) into differential cross-section per unit pseudorapidity ($dσ^{\rm AA}/dη$) of charged particles and study the phenomenon of LF. We find that in $dσ^{\rm AA}/dη$ LF seems to be violated at LHC energies while considering the energy dependent $σ_{\rm in}$. We also perform a similar study using A Multi-Phase Transport (AMPT) Model with string melting scenario and also find that LF is violated at LHC energies.

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arXiv2019

Thermodynamic and transport properties in Au + Au collisions at RHIC energies from the clustering of color strings

In this work, we have extracted the initial tempearture from the transverse momentum spectra of charged particles in $Au+Au$ collisions using STAR data at RHIC energies from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV. The initial energy density ($\varepsilon$), shear viscosity to entropy density ratio ($η/s$), trace anomaly ($Δ$), the squared speed of sound ($C_s^2$), entropy density, and bulk viscosity to entropy density ratio ($ζ/s$) are obtained and compared with the lattice QCD calculations for (2+1) flavor. The initial temperatures obtained are compared with various hadronization and chemical freeze-out temperatures. The analysis of the data shows that the deconfinement to confinement transition possibly takes place between $\sqrt{s_{NN}}$ = 11.5 and 19.6 GeV.

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arXiv2019

Radial Flow and Differential Freeze-out in Proton-Proton Collisions at $\sqrt{s}= 7$ TeV at the LHC

We analyse the transverse momentum ($p_{\rm T}$)-spectra as a function of charged-particle multiplicity at midrapidity ($|y| < 0.5$) for various identified particles such as $π^{\pm}$, $K^{\pm}$, $K_S^0$, $p+\overline{p}$, $ϕ$, $K^{*0} + \overline {K^{*0}}$, and $Λ$ + $\barΛ$ in proton-proton collisions at $\sqrt{s}$ = 7 TeV using Boltzmann-Gibbs Blast Wave (BGBW) model and thermodynamically consistent Tsallis distribution function. We obtain the multiplicity dependent kinetic freeze-out temperature ($T_{\rm kin}$) and radial flow ($β$) of various particles after fitting the $p_{\rm T}$-distribution with BGBW model. Here, $T_{\rm kin}$ exhibits mild dependence on multiplicity class while $β$ shows almost independent behaviour. The information regarding Tsallis temperature and the non-extensivity parameter ($q$) are drawn by fitting the $p_{\rm T}$-spectra with Tsallis distribution function. The extracted parameters of these particles are studied as a function of charged particle multiplicity density ($dN_{ch}/dη$). In addition to this, we also study these parameters as a function of particle mass to observe any possible mass ordering. All the identified hadrons show a mass ordering in temperature, non-extensive parameter and also a strong dependence on multiplicity classes, except the lighter particles. It is observed that as the particle multiplicity increases, the $q$-parameter approaches to Boltzmann-Gibbs value, hence a conclusion can be drawn that system tends to thermal equilibrium. The observations are consistent with a differential freeze-out scenario of the produced particles.

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arXiv2018

Dissipative Properties and Isothermal Compressibility of Hot and Dense Hadron Gas using Non-extensive Statistics

We evaluate the transport properties such as shear viscosity ($η$), bulk viscosity ($ζ$) and their ratios over entropy density ($s$) for hadronic matter using relativistic non-extensive Boltzmann transport equation (NBTE) in relaxation time approximation (RTA). In NBTE, we argue that the system far from equilibrium may not reach to an equilibrium described by extensive (Boltzmann-Gibbs (BG)) statistics but to a $q$-equilibrium defined by Tsallis non-extensive statistics after subsequent evolution, where $q$ denotes the degree of non-extensivity. We observe that $η/s$ and $ζ/s$ decrease rapidly with temperature ($T$) for various $q$-values. As $q$ increases, the magnitudes of $η/s$ and $ζ/s$ decrease with $T$. We also show the upper mass cutoff dependence of these ratios for a particular $q$ and find that they decrease with the increase in mass cutoff of hadrons. Further, we present the first estimation of isothermal compressibility ($κ_T$) using non-extensive Tsallis statistics at finite baryon chemical potential ($μ_B$). It is observed that, $κ_T$ changes significantly with the degree of non-extensivity. We also study the squared speed of sound ($c_{s}^{2}$) as a function of temperature at finite baryon chemical potential for various $q$ and upper mass cutoffs. It is noticed that there is a strong impact of $q$ and mass cutoff on the behaviour of $c_{s}^{2}$.

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arXiv2018

Electrical conductivity of Hot and Dense QCD matter at RHIC BES energies: A Color String Percolation Approach

Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($σ_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamical flavours. We find that $σ_{\rm el}$/T in CSPM has a very weak dependence on the temperature. We compare CSPM results with those obtained in Boltzmann Approach to Multi-Parton Scatterings (BAMPS) model. A good agreement is found between CSPM results and predictions of BAMPS with fixed strong coupling constant.

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arXiv2018

Energy and Centrality Dependent Study of Deconfinement Phase Transition in a Color String Percolation Approach at RHIC Energies

We take the experimental data for transverse momentum spectra of identified charged hadrons in different centrality classes for nucleus-nucleus (A+A) collisions at various Relativistic Heavy-Ion Collider (RHIC) energies measured by the STAR collaboration. We analyse these data in the framework of color string percolation model (CSPM) in order to extract various percolation parameters at different centralities at RHIC energies to study the effect of collision geometry and collision energy. We use these parameters to study the centrality dependent behaviour of initial temperature of the percolation cluster, energy density, average transverse momentum, shear viscosity to entropy density ratio ($η/s$) and trace anomaly for different energies at RHIC from $\sqrt{s_{\rm NN}}$ = 19.6 to 200 GeV. These observables are found to strongly depend on centrality at various collision energies. The critical percolation density, which is related to the deconfinement phase transition is achieved in the most central nucleus-nucleus collisions, while it fails in the peripheral collisions. A universal scaling is observed in color suppression factor and initial temperatures when studied as a function of charged particle pseudorapidity distribution scaled by nuclear overlap area at RHIC energies. The minimum of $η/s$ is observed in the most central collisions at $\sqrt{s_{\rm NN}}$ = 130 and 200 GeV.

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arXiv2018

Elliptic Flow in Pb+Pb Collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC Using Boltzmann Transport Equation with Non-extensive Statistics

Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ($p_{\rm T}$) distribution in proton+proton ($p+p$) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate the elliptic flow in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified particles seems to be described quite well in the available $p_{\rm T}$ range. An approach, which combines the non-extensive nature of particle production in $p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.

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arXiv2018

Transverse Energy per Charged Particle in Heavy-Ion Collisions: Role of Collective Flow

The ratio of (pseudo)rapidity density of transverse energy and the (pseudo)rapidity density of charged particles, which is a measure of the mean transverse energy per particle, is an important observable in high energy heavy-ion collisions, which reveals about the mechanism of particle production and the freeze-out criteria. Its collision energy and centrality dependence is exactly like the chemical freeze-out temperature till top RHIC energy. The LHC measurement at $\sqrt{s_{NN}}$ = 2.76 TeV brings up new challenges to rule out the mechanisms of gluon saturation or non-equilibrium phenomena being prevalent at high energies, which could contribute to the above observable. The Statistical Hadron Gas Model (SHGM) with a static fireball approximation has been successful in describing both the centrality and energy dependence till top RHIC energies. However, the SHGM predictions for higher energies are highly underestimated by the LHC data. In order to understand this, we have incorporated radial flow effect in an excluded volume SHGM. The hard-core radius of baryons at lower collision energies plays an important role in the description of a hadronic system. In view of this, in order to make a complete energy dependence study from FAIR to LHC energies, we have considered an excluded volume SHGM. Our studies suggest that the collective flow plays an important role in describing $E_{T}/N_{ch}$ and it could be one of the possible parameters to explain the jump observed in $E_{T}/N_{ch}$ from RHIC to LHC energies. Predictions for the LHC measurements at $\sqrt{s_{NN}}$ = 5.02 TeV are given.

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arXiv2017

Transverse Momentum Spectra and Nuclear Modification Factor using Boltzmann Transport Equation with Flow in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $ϕ$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.

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