Hagedorn Temperature - The Boiling Hadron Matter

The Boiling Hadron Matter

Very high energy collisions generally result in the production of many secondary particles. This was an unexpected feature when it was first observed in cosmic ray interactions. The idea of applying the wide body of knowledge of statistical thermodynamics to such multi-particle production processes naturally comes to mind and prominent physicists like Enrico Fermi and Lev Landau made pioneering contributions. However, difficulties quickly speak for themselves, and this approach did not become the main stream of the study of particle production at first. The question was, what might actually be "thermalized" in a high energy particle collision? Applying straightforward statistical mechanics gave too small a yield of pions. But, even if there was a thermalized system in the first place, why was the apparent temperature constant, shouldn't one expect it to rise with incident beam energy? It is Hagedorn's great credit that he proposed the right model and stayed with his thermal interpretation, solving the mysteries one after the other. His particle production models turned out to be remarkably accurate at predicting yields for the many different types of secondaries which originate from high energy collisions. He understood that the temperature governing particle spectra does not increase, since as more and more energy is poured into the system, new particles are produced. It is the entropy which increases with the collision energy. If the number of particles of given mass (mass spectrum) increases exponentially, the temperature gets stuck to a limiting value. This is the Hagedorn temperature. It is in particle units nearly kT=160 MeV, about 15% above the energy mass of the lightest hadron, the pion. Moreover, since more massive particles fragment into less massive ones, and eventually give the observed secondary particles as the bottom line, this solved the pion yield problem.