Nonextensive Statistical Mechanics

7.1 Physics 223Fig. 7.1 Computational verification with quantum Monte Carlo (left panels), and laboratory verificationwith C s atoms (right panels) of Lutz’s theory (from [461]).7.1.2 High-Energy Physics7.1.2.1 Electron–Positron AnnihilationElectrons and positrons in frontal collisions at high energy typically annihilate andproduce a few hadronic jets. The analysis of the transverse momenta of those jetsprovides interesting physical information related, among others, to the production ofmesons. The process can in principle be described in thermostatistical terms, withoutentering into microscopic details in the realm of Quantum Chromodynamics.Fermi was the pioneer of this type of approach [402], followed by Hagedorn [403].According to Hagedorn, such high-energy collisions produce excited hadron fireballsthat reach some kind of thermal equilibrium. An important consequence ofthis approach would be that increasing the collisional energy would not change theinvolved basic masses (that of mesons that are being produced) but it would onlyincrease their number, such as an increase of heat delivery when one boils waterdoes not modify the phase-transition temperature, but only increases the amountof liquid that becomes gas. A similar statement was made, a few years later, byField and Feynman [404]. The use of the Boltzmann weight in the relativistic limityields [403] a distribution of hadronic transverse momenta which exhibits a reasonablysatisfactory agreement with experimental data at relatively low collisionalenergy, say at 14 Gev (TASSO experiments). But increasing that energy, the temperature(a fitting parameter) did not remain constant, as predicted by the theory.This approach was somewhat discredited and abandoned. The idea was revisited in