Quantum Coherence in High Energy Showers: New Developments in the LPM Effect for QCD

Gluon bremsstrahlung is the dominant process through which high energy particles lose their energy in a Quark Gluon plasma. Calculations of bremsstrahlung rate are complicated by interference of different emission terms which give rise to the Landau-Pomeranchuk-Migdal (LPM) effect. Previous authors have analyzed the case where the coherence lengths of two consecutive emissions overlap, but only in limits where at least one of the bremsstrahlung gluons is soft. We have analyzed this problem without using such limits, for general energies of bremsstrahlung gluons. We also show that the differential rate for double gluon bremsstrahlung can be reduced to a 1-dimensional integral which can be solved numerically.