Eur. Phys. J. A (2009) 40: 99-108
https://doi.org/10.1140/epja/i2008-10753-8

Regular Article - Theoretical Physics

A potential including the Heaviside function in the 1 + 1 dimensional hydrodynamics by Landau

Its basic properties and application to data at RHIC energies

¹ Toba National College of Maritime Technology, 517-8501, Toba, Japan
² Graduate School of Science and Technology, Shinshu University, 390-8621, Matsumoto, Japan
³ School of General Education, Shinshu University, 390-8621, Matsumoto, Japan

^* e-mail: mizoguti@toba-cmt.ac.jp

Received: 17 October 2008
Revised: 29 December 2008
Accepted: 22 February 2009
Published online: 21 March 2009

Abstract

In the 1 + 1 dimensional hydrodynamics originally proposed by Landau, we derive a new potential and distribution function including the Heaviside function and investigate their mathematical and physical properties. Using the original distribution derived by Landau, a distribution function found by Srivastava et al., our distribution function, and the Gaussian distribution proposed by Carruthers et al., we analyze the data of the rapidity distribution on charged pions and K mesons at RHIC energies ( = 62.4 GeV and 200GeV). Three distributions derived from the hydrodynamics show almost the same chi-squared values provided the CERN MINUIT is used. We know that our calculations of hadron’s distribution do not strongly depend on the range of integration of fluid rapidity, contrary to that of Srivastava et al. Finally, the roles of the Heaviside function in concrete analyses of data are investigated.