Dominant Contributions to Lateral Distribution Functions in Ultra-High   Energy Cosmic Ray Air Showers
  In hadron induced air showers of highest energies (E> 1e18 eV), the lateral distribution functions of electrons and muons are a superposition of many separate electromagnetic sub-showers, initiated by meson decay at different altitudes and energies. The lateral distribution function is the primary tool for reconstructing the energy of the primary in a UHE cosmic ray shower, so understanding it in detail is a prerequisite for having confidence in the energy determination. We analyze in this paper the dominant contributions to the ground level lateral distribution functions, as a function of the altitude and energy at which the sub-showers are initiated. Far from the core, the dominant contribution to the density of electrons comes from sub-showers initiated at low altitudes and low energies (E<100 GeV). The dominant sub-showers are initiated at large radial distance from the core and at a large angle with respect to the main shower axis. This demonstrates the need for careful treatment of low energy hadron physics modeling even for ultrahigh energy primaries. 
Hans-Joachim Drescher and Glennys R. Farrar