On partition temperature of massless particles in high-energy collisions

TL;DR

This paper derives the exact one-particle distribution function for massless particles in high-energy collisions, examining the concept of partition temperature without relying on exponential forms, and discusses implications for observed spectra.

Contribution

It provides a precise derivation of the distribution function for massless particles in a canonical ensemble, challenging the traditional notion of partition temperature in this context.

Findings

Exact phase space integration for massless particles obtained

Distribution function not in exponential form, questioning standard thermodynamic assumptions

Implications for Tsallis distribution in high-energy collision spectra discussed

Abstract

Although partition temperature derived using the Darwin-Fowler method is exact for simple scenarios, the derivation for complex systems might reside on specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed form expression can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed.