Multiplicity Dependencies of Midrapidity Transverse Momentum Distributions of Identified Charged Particles in Proton-Proton Collisions at (<i>s</i>)^1/2 = 7 TeV at the LHC

Dependencies of midrapidity pt distributions of the charged pions and kaons, protons and antiprotons on charged-particle multiplicity density (dNch/dη>) in inelastic proton-proton collisions at (s)1/2 = 7 TeV at the LHC, measured by ALICE Collaboration, are investigated. The simultaneous minimum χ2 fits with the Tsallis function with thermodynamical consistence and the Hagedorn function with included transverse flow have well-described the pt spectra of the particle species in the ten studied groups of charged-particle multiplicity density. The effective temperatures, T, of the Tsallis function with thermodynamical consistence have shown a steady rise with increasing the charged-particle multiplicity in proton-proton collisions at (s)1/2 = 7 TeV, in agreement with the similar result obtained recently in proton-proton collisions at (s)1/2 = 13 TeV at the LHC. The respective T versus dNch/dη> dependence in proton-proton collisions at (s)1/2 = 7 TeV is reproduced quite well by the simple power function with the same value (≈ 1/3) of the exponent parameter as that extracted in proton-proton collisions at (s)1/2 = 13 TeV. The identical power dependence T~ε1/3 between the initial energy density and effective temperature of the system has been observed in proton-proton collisions at (s)1/2 = 7 and 13 TeV. We have observed that the transverse radial flow emerges at dNch/dη> ≈ 6 and then increases, becoming substantial at larger multiplicity events in proton-proton collisions at (s)1/2 = 7 TeV. We have estimated, analyzing T0 and ⟨βt⟩ versus dNch/dη> dependencies, that the possible onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 TeV occurs at dNch/dη> ≈ 6.1 ± 0.3, which is close to the corresponding recent estimate (dNch/dη> ≈ 7.1 ± 0.2) in proton-proton collisions at (s)1/2 = 13 TeV. The corresponding critical energy densities for probable onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 and 13 TeV at the LHC have been estimated to be 0.67 ± 0.03 and 0.76 ± 0.02 GeV/fm3, respectively

Multiplicity dependencies of midrapidity transverse momentum spectra of identified charged particles in p+pp+p collisions at (s)1/2(s)^{1/2} = 13 TeV at LHC

Multiplicity dependencies of midrapidity $p_t$ spectra of identified charged particles in inelastic $p+p$ collisions at $(s)^{1/2} =$13 TeV at the Large Hadron Collider (LHC), measured by ALICE Collaboration, have been analyzed. The combined minimum $χ^2$ fits with thermodynamically consistent Tsallis function as well as Hagedorn function with the embedded transverse flow describe quite satisfactorily the $p_t$ spectra of particles in the studied 10 different classes of charged-particle multiplicity in inelastic $p+p$ collisions at $(s)^{1/2} =$13 TeV. The obtained effective temperatures $T$ of thermodynamically consistent Tsallis function demonstrate a consistent growth with an increase in multiplicity of charged particles in inelastic $p+p$ collisions at $(s)^{1/2} =$13 TeV, and the corresponding $T$ versus the average charged-particle (pseudorapidity) multiplicity density $(〈dN_{ch}/dη〉)$ dependence is described very well by the simple power function with exponent parameter ≈ (1/3) in the whole analyzed range $〈dN_{ch}/dη〉 > 4$. It is found that the transverse (radial) flow becomes significant at higher multiplicity events in $p+p$ collisions at $(s)^{1/2} =$13 TeV, reaching the maximum value $〈β_t〉 = 0.28 ± 0.02$ at the largest studied multiplicity density $〈dN_{ch}/dη〉 = 26.02 ± 0.35$. It is estimated from analysis of $T_0$ and $〈β_t〉$ versus $〈dN_{ch}/dη〉$ dependencies, obtained using Hagedorn function with the embedded transverse flow, that the probable onset of deconfinement phase transition in inelastic $p+p$ collisions at $(s)^{1/2} = 13$ TeV occurs at $〈dN_{ch}/dη〉$ $\approx 7.1 \pm 0.2$

Analysis of Midrapidity <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-italic">p</mi><mi mathvariant="bold-italic">T</mi></msub></mrow></semantics></math></inline-formula> Distributions of Identified Charged Particles in Pb + Pb Collisions at <inline-formula><math display="inline"><semantics><mrow><msqrt><mrow><msub><mi mathvariant="bold-italic">s</mi><mrow><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">n</mi></mrow></msub></mrow></msqrt></mrow></semantics></math></inline-formula> = 5.02 TeV Using Tsallis Distribution with Embedded Transverse Flow

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at snn  = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ2 fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at snn = 5.02 TeV with the average number of participant nucleons ⟨Npart⟩ > 160. The obtained significantly different growth rates of transverse flow velocity, ⟨βT⟩, in regions ⟨Npart⟩ ⟨Npart⟩ > 71 ± 7 with the temperature parameter T0 remaining constant within uncertainties in region ⟨Npart⟩ > 71 ± 7 probably indicates that ⟨Npart⟩ ≈ 71 ± 7 (corresponding to ⟨dNch/dη⟩ ≈ 251 ± 20) is a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Pb + Pb collisions at snn = 5.02 TeV. The threshold border value for transverse flow velocity ⟨βT⟩ ≈ 0.46 ± 0.03 (corresponding to ⟨Npart⟩ ≈ 71 ± 7), estimated by us in Pb + Pb collisions at snn = 5.02 TeV, agrees well with the corresponding border value ⟨βT⟩ ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at snn = 5.44 TeV, and with almost constant ⟨βT⟩ values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the snn = 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T0 and ⟨βT⟩ parameters are found to be greatly different in regions ⟨βT⟩ ⟨βT⟩ > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at snn = 5.02 TeV