Thermal-nonthermal transition of the charged particle production in pp collisions

Abstract

We determine the internal energy of charged particle production in minimum bias pp collisions using a thermostatistical approach by analyzing the $p_{\text{T}}$ spectrum reported by the ALICE Collaboration across LHC energies. To do this, we define temperature as the slope of the $p_{\text{T}}$ spectrum at low $p_{\text{T}}$ values and Shannon's entropy as the system's entropy, calculated considering the normalized $p_{\text{T}}$ spectrum. We found that the internal energy for the Hagedorn and Tricomi functions behaves linearly with temperature at low temperatures but becomes nonlinear at LHC energies, showing a thermal-nonthermal transition in the production of charged particles in pp collisions. Our estimation of the transition center of mass energy is $\sqrt{s^{\ast }}=27(11)\text{ keV}$ at baryon chemical potential ${\mu }_B=0$, which explains why the production of high $p_{\text{T}}$ hadrons has always been observed, even in earlier experiments, which may also encompass other experiments colliding e${}^{-}$p or e${}^{+}$e${}^{-}$.

Comments: 15 pages, 4 figures,