Ultra-High Energy Quenching of the LPM Effect: Implications for   GZK-Violating Events
  Cosmic rays in the regime of 10^19-10^20 eV should not exist, according to the GZK bound. Conflicts between data and the bound have led to suggestions that laws of physics must be modified. We find that physical processes neglected in the early history terminate the LPM effect, important in calibrating the energy of electromagnetic and hadronic showers in the GZK energy regime. The processes neglected are the direct losses of electrons and positrons, overlooked by LPM and greatly augmented by ultra-high energy circumstances. We present an exact formula for direct energy losses of e^+e^- pairs in electromagnetic showers. Numerical integration in current hadronic models shows that actual energy losses are always substantially larger than LPM estimates, but the energy at which crossover occurs depends on models. 
John P. Ralston, Soebur Razzaque and Pankaj Jain