Medium-induced gluon radiation and colour decoherence beyond the soft approximation

Understand

We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons.

• Results are computed for finite formation times, including interference with vacuum amplitudes.
• By rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation.
• This factorisation allows us to present a simple physical picture of the medium-induced radiation for any value of the formation time, that is of interest for a probabilistic implementation of the modified parton shower.