System of evolution equations for quark and gluon jet quenching with broadening

We propose a system of evolution equations that describe in-medium time-evolution of transverse-momentum-dependent quark and gluon fragmentation functions. Furthermore, we solve this system of equations using Monte Carlo methods. We then quantify the obtained solutions in terms of a few characteristic features, namely the average transverse momentum $\langle |k|\rangle$ and energy contained in a cone, which allow us to see different behaviour of quark and gluon initiated final-state radiation. In particular, the later allows us to conclude that in the gluon-initiated processes there is less energy in a cone, so that the quark jet is more collimated.