Jet fragmentation in a QCD medium: Universal quark/gluon ration and Wave turbulence

We calculate the evolution of a jet shower due to medium induced splittings in the deep LPM regime. Due to the characteristic energy dependence of the formation time $t_{\rm form}(ω)= \sqrt{ω/\hat{\bar{q}}}$, the radiative break-up process exhibits turbulent characteristics, allowing for analytic predictions of various inclusive properties of the medium induced cascade in an inertial range of energies $T \ll ω\ll E$, where $E$ is the energy of the jet and $T$ is the temperature of the medium.