Landau Hydrodynamics Reexamined

TL;DR

This paper revises Landau hydrodynamics by proposing a modified rapidity distribution that aligns better with experimental data, offering improved predictions for high-energy collisions at LHC.

Contribution

It introduces a modified rapidity distribution in Landau hydrodynamics that better fits experimental data and clarifies the Gaussian distribution's effectiveness.

Findings

Modified rapidity distribution fits experimental data better.

Gaussian distribution closely represents the modified distribution.

Predictions for LHC energies in pp and AA collisions are provided.

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.