Cancelling Juttner Distributions for Space-like Freeze-out.pdf

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Cancelling Juttner Distributions for Space-like Freeze-out.pdf

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Cancelling Juttner Distributions for Space-like Freeze-out

a r X i v : h e p - p h / 0 4 0 3 1 7 9 v 1 1 6 M a r 2 0 0 4 Cancelling Ju?ttner Distributions for Space-like Freeze-out K. Tamos?iu?nas1, ? and L. P. Csernai1, 2, ? 1Theoretical and Computational Physics Section, Department of Physics, University of Bergen, Allegaten 55, 5007 Bergen, Norway 2MTA-KFKI, Research Inst. for Particle and Nuclear Physics, 1525 Budapest 114, P.O. Box 49, Hungary (Dated: February 1, 2008) We study freeze out process of particles across a three dimensional space-time hypersurface with space-like normal. The problem of negative contribution is discussed with respect to conservation laws, and a simple and practical new one-particle distribution for the post FO side is introduced, the Cancelling Ju?ttner (CJ) distribution. PACS numbers: 25.75.-q, 25.75.Ld, 24.85.+p I. INTRODUCTION Relativistic heavy ion collisions are non-equilibrium relativistic many body systems that can be described by different models, often based on the kinetic theory. The kinetic theory establishes relationship between macro- scopic and microscopic matter properties mostly by us- ing a one-particle distribution function. Kinetic theories are able to describe dilute weakly interacting systems, thus expanding systems where the constituent particles gradually loose contact. Here to simplify such a process we will assume a freeze out (FO) hypersurface in space- time, which can have either space- or time-like normal vector. We will use conservation laws of fluid dynamics to conserve energy, momentum and particle flow across FO hypersurface. We assume thermal equilibrium in pre FO side where the matter is (or can be) in quark gluon plasma (QGP) phase. For the pre FO side the Bag Model equation of state will be used which allows for supercool- ing and rapid hadronization afterwards. For the frozen out matter (post FO side) newly formed hadrons are con- sidered, which are non interacting with each other, and they are described by a one-particle distribution func- tion. The