Exploring the initial stage of high multiplicity proton-proton collisions by determining the initial temperature of the quark-gluon plasma

We have analyzed identified particle transverse momentum spectra in high multiplicity events in $pp$ collisions at LHC energies $\sqrt{s}=0.9--13\text{ }\text{ }\mathrm{TeV}$ published by the CMS Collaboration using the color string percolation model (CSPM). In CSPM color strings are formed after the collision, which decay into new strings through color neutral $q\ensuremath{-}\overline{q}$ pairs production. With the increase in the $pp$ collisions energy number of strings grow and randomly statistically overlap producing higher string tension of the composite strings. The net color in the overlap string area is a vector sum of the randomly oriented strings. The Schwinger color string breaking mechanism produces these color neutral $q\ensuremath{-}\overline{q}$ pairs at time $\ensuremath{\sim}1\text{ }\text{ }\mathrm{fm}$/c, which subsequently hadronize. The initial temperature is extracted both in low and high multiplicity events.The shear viscosity to entropy density ratios $\ensuremath{\eta}/s$ are obtained as a function of temperature. For the higher multiplicity events at $\sqrt{s}=7$ and 13 TeV the initial temperature is above the universal hadronization temperature and is consistent with the creation of deconfined matter. The $\ensuremath{\eta}/s$ is similar to that in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=200\text{ }\text{ }\mathrm{GeV}$. The small value of $\ensuremath{\eta}/s$ above the universal hadronization temperature suggested that the matter is a strongly coupled quark gluon plasma. In these small systems it can be argued that the thermalization is a consequence of the quantum tunneling through the event horizon introduced by the quarks confined in the colliding nucleons and their deceleration due to string formation, in analogy to the Hawking-Unruh radiation which provides a stochastic approach to equilibrium. The disk areas cluster on the nucleon transverse collision area. At the $2D$ percolation threshold a macroscopic spanning cluster suddenly occurs at the temperature ${T}_{i}={T}_{h}$, representing a small connected droplet of $q\ensuremath{-}\overline{q}$ pairs, the quark-gluon plasma (QGP). ${T}_{h}$ is the universal hadronization temperature $\ensuremath{\sim}167.7\text{ }\text{ }\mathrm{MeV}$. The collision energy dependent buildup of the 2D percolation clusters defines the temperature range $159\ifmmode\pm\else\textpm\fi{}9\text{ }\text{ }\mathrm{MeV}$ of the crossover transition between hadrons to the QGP in reasonable agreement with the lattice quantum chromodynamics (LQCD) pseudocritical temperature value of $155\ifmmode\pm\else\textpm\fi{}9\text{ }\text{ }\mathrm{MeV}$. Color string percolation model is the new initial stage paradigm for the study of the high density matter produced in $pp$ and $A+A$ collisions. With CSPM we can directly explore the thermodynamics of the QGP above the universal hadronization temperature.

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