The Greisen Equation Explained and Improved

Details The Greisen Equation Explained and Improved The Greisen Equation Explained and Improved

2006-07-22

arxiv.org/abs/hep-ph/0607248v2

Phys.Rev. D75 (2007) 016005

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, 7 figures, revised version, accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.75.016005

Analytic description of the evolution of cosmic ray showers is dominated by the Greisen equation nearly five decades old. We present an alternative approach with several advantages. Among the new features are a prediction of the differential distribution, replacing Greisen's form which fails to be positive definite. Explicit comparison with Monte Carlo simulations shows excellent agreement after a few radiation lengths of development. We find a clear connection between Monte Carlo adjustment of Greisen's form and underlying physics, and present a concise derivation with all steps explicit. We also reconstruct the steps needed to reproduce Greisen's approximate formula, which appears not to have been published previously.

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