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arXiv · 2509.14175

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

J. Alonso Tlali·D. Rosales Herrera·J. R. Alvarado García·A. Fernández Téllez·C. Pajares·J. E. Ramírez
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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 $\sqrt{s^*}=27(11)\text{ keV}$ 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$^-$.

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J. Alonso Tlali, D. Rosales Herrera, J. R. Alvarado García, A. Fernández Téllez, C. Pajares, J. E. Ramírez. 2025-09-17. Thermal-nonthermal transition of the charged particle production in pp collisions. https://arxiv.org/abs/2509.14175

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