Rolf Hagedorn

Rolf Hagedorn (20 July 1919 – 9 March 2003) was a German theoretical physicist who worked at CERN. He is known for the idea that hadronic matter has a "melting point". The Hagedorn temperature is named in his honor.

Early life
Hagedorn's younger life was deeply marked by the upheavals of World War II in Europe. He graduated from high school in 1937 and was drafted into the German Army. After the war began, he was shipped off into North Africa as an officer in the Rommel Afrika Korps. He was captured in 1943, and spent the rest of the war in an officer prison camp in the United States. Most of the prisoners were young and with nothing to do, Hagedorn and others set up their own 'university' where they taught each other whatever they knew. There, Hagedorn ran into an assistant of David Hilbert, who taught him mathematics.

Becoming a physicist
When Hagedorn came back home in January 1946, most German universities were destroyed. Because of his training in the Crossville, Tennessee prison camp, he was accepted as a fourth-semester student at the University of Göttingen – one of the few remaining universities.

After having completed his studies with the usual diploma (1950) and doctorate (1952), with a thesis under R. Becker on thermal solid-state theory, he was accepted as a postdoc at the Max Planck Institute for Physics (MPI), still at Göttingen at the time. The MPI director was Werner Heisenberg. While he was there, he was among a group of physicists including Bruno Zumino, Harry Lehmann, Wolfhart Zimmermann, Kurt Symanzik, Gerhard Lüders, Reinhard Oehme, Vladimir Glaser, and Carl Friedrich von Weizsäcker.

Life at CERN
In 1954, Hagedorn went to CERN. There, he helped with particle accelerator designs, particularly to calculate non-linear oscillations in particle orbits. The pioneering work on linear orbit theory had just been completed by Gerhard Lüders, who wished to go back to Göttingen. Lüders asked Werner Heisenberg, the then-director of the MPI, to send somebody to replace him. Heisenberg asked Hagedorn if he was interested for a couple of months.

When the CERN theory group came to Geneva from Copenhagen, where it had been located at first, Hagedorn joined the group. Hagedorn brought to the Theory Division (TH) an unusual interdisciplinary background which included particle and nuclear as well as thermal, solid state and accelerator physics. Once at the TH, he exclusively focused on the statistical models of particle production.

Particle production work
Hagedorn's work started when Bruno Ferretti (then-head of the Theory Division), asked him to try to predict particle yields in the high energy collisions of the time. He started with Frans Cerulus. There were few clues to begin with but they made the best of the "fireball concept" which was then supported by cosmic ray studies and used it to make predictions about particle yields (and therefore the secondary beams to be expected from the main beam directed at a target). As a result of his investigations the self-consistency principle was developed.

Many key ingredients brought soon afterward by experiment helped refine the approach. Among them is the limited transverse momentum with which the overwhelming majority of the secondary particles happen to be produced. They show an exponential drop with respect to the transverse mass. There is also the exponential drop of elastic scattering at wide angles as a function of incident energy. Such exponential behaviors strongly suggested a thermal distribution for whatever eventually comes out of the reaction. Based on this, Hagedorn put forth his thermal interpretation and used it to build production models which turned out to be remarkably accurate at predicting yields for the many different types of secondary particles. Many objections were raised at the time, particularly as to what could actually be 'thermalized' in the collisions, applying straightforward statistical mechanics to the produced pions gave the wrong results, and the temperature of the system was apparently constant when it should have risen with the incident energy or with the mass of the excited fireball (according to Boltzmann's Law).

For collision energies above approximately 10 GeV the Hagedorn's predictions fail, since in this case, nonextensive aspects may be present. A Non-extensive self-consistent thermodynamical theory has been proposed which give the correct predictions for fireballs at extremely high energies.

Limiting temperature
Hagedorn interpreted the apparently limiting temperature which could be associated with the transverse mass distribution of the secondary particles as resulting from an exponential spectrum for the many resonant states into which hadrons can be excited. The rise of the temperature is associated with the population of higher and higher energy levels by the elements of a system. If there is an exponentially increasing number of levels offering themselves to be filled, the temperature saturates. It is the entropy which eventually increases linearly with the collision energy but the temperature gets stuck to a limiting value. This is the Hagedorn temperature, which is of the order of ~160 MeV.

The impressive number of states which have now to be considered at the same time leads to a new writing of equations based on statistical physics. The factorial factor, which was plaguing statistical calculation focusing on pions only, and which was introduced to rightfully avoid multiple counting in phase space integrals, had now become unimportant since each one of the many states was unlikely to have a population exceeding 1. This reconciled experimental results and statistical calculations.