Landau Hydrodynamics Reexamined

Abstract

We review the formulation of Landau hydrodynamics and find that the rapidity distribution of produced particles in the center-of-mass system should be more appropriately modified as dN/dy \exp[\sqrt{y_b^2-y^2}], where y_b=\ln[\sqrt{s_{NN}}/m_p] is the beam nucleon rapidity, instead of Landau's original distribution, dN/dy(Landau) \exp[\sqrt{L^2-y^2}], where L=\ln[\sqrt{s_{NN}}/2m_p]. The modified distribution agrees better with experimental dN/dy data than the original Landau distribution and can be represented well by the Gaussian distribution, dN/dy(Gaussian) \exp[-y^2/2L]. Past successes of the Gaussian distribution in explaining experimental rapidity data can be understood, not because it is an approximation of the original Landau distribution, but because it is in fact a close representation of the modified distribution. Predictions for pp and AA collisions at LHC energies in Landau hydrodynamics are presented.