Entropy and heat capacity of the transverse momentum distribution for collisions at RHIC and LHC energies
D. Rosales Herrera (Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico); J.R. Alvarado García (Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico); A. Fernández Téllez (Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico); J.E. Ramírez (Centro de Agroecología, Instituto de Ciencias, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico); C. Pajares (Departamento de Física de Partículas and Instituto Galego de Física de Altas Enerxías, Universidad de Santiago de Compostela, E-15782 Santiago de Compostela, Spain)
We investigate the transverse momentum distribution (TMD) statistics from three different theoretical approaches. In particular, we explore the framework used for string models, wherein the particle production is given by the Schwinger mechanism. The thermal distribution arises from the Gaussian fluctuations of the string tension. The hard part of the TMD can be reproduced by considering heavy tailed string tension fluctuations, for instance, the Tsallis -Gaussian function, giving rise to a confluent hypergeometric function that fits the entire experimental TMD data. We also discuss the QCD-based Hagerdon function, another family of fitting functions frequently used to describe the spectrum. We analyze the experimental data of minimum bias collisions reported by the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) experiments (from TeV to TeV). We extracted the corresponding temperature by studying the behavior of the spectra at low transverse momentum values. For the three approaches, we compute all moments, highlighting the average, variance, and kurtosis. Finally, we compute the Shannon entropy and the heat capacity through the entropy derivative with respect to the temperature. We found that the -Gaussian string tension fluctuations lead to a monotonically increasing heat capacity as a function of the center-of-mass energy, which is also observed for the Hagedorn fitting function. This behavior is consistent with the experimental observation that the temperature slowly rises with increments of the collision energy.