Learning hydrodynamics with Yogiro Hama

Abstract

As part of the celebration of his 70th birthday, I review the works done in collaboration with Prof. Yogiro Hama and try to recover the history of some of his ideas concerning the formation of a fluid in high energy hadronic collisions, its expansion and dissociation. I show how these ideas evolved and how they are relevant for understanding the present experimental data.Keywords: Relativistic hydrodynamics; Multiparticle production; High energy hadronic collisions I. THE BEGINING OF THE FIELDA complete history of relativistic hydrodynamics is yet to be written. Some partial accounts can be found in [1,2]. Here, I just want to remember some seminal works which started this field, which might be called hydrodynamics applied to multiparticle production in high energy hadronic collisions. In his pioneering work of 1953 [3] Landau developed several aspects of hydrodynamics and prepaired the formalism for future phenomenological applications. In the following year Khalatnikov [4] found the analytical solution of the one dimensional problem. These brilliant works went forgotten for many years. When remembered, they were regarded with suspition, if not with a frank opposition. About twenty years later, Carruthers used Landau hydrodynamics to study the, at that time, new data from the CERN ISR proton -proton collisions [5]. The phenomenological success of this approach renewed the interest on hydrodynamics and, in particular, motivated the search for the three-dimensional solution of the Landau model. This first success of hydrodynamics found also opponents, for whom this type of collective treatment of a microscopic problem was, at best, a parametrization of data, which was successful only because it was an implementation of energy-momentum conservation applied to a system whose dynamics was dominated by phase space. Still according to these opponents, there was no chance that hydrodynamics would describe a real system because there was no fluid! The number of produced particles was too small and the lifetime of the system was so short that no thermal equilibrium would ever be achieved.It was in this period of phenomenological success but theoretical discredit, that Yogiro got interested in this subject. II. THE FIRST WORKSIn his first contribution to the field, Yogiro [6,7] computed the transverse momentum distribution of charged particles produced in p-p collisions, measured by different collaborations working at CERN [8]. He adopted the simple extension of the one -dimensional solution of the Landau model advanced in [5], assuming that the transverse rapidity of fluid followed a gaussian distribution, in the same way as the (longitudinal) rapidity. He improved the existing formalism introducing an energy dependent width of the transverse rapidity distribution and, most important, taking into account the local thermal motion of the final particles. With his model, Yogiro was able to fit the measured p T spectra up to values considered large, where many people expected to see the effect of the jets arising from parto...