Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma

International audienceThe transverse momentum broadening coefficient $\hat{q}$ receives both soft, classical and radiative, quantum corrections. The former are responsible for a large O(g) correction, whereas the latter enter at relative order $\alpha_s$, but are enhanced by a double logarithm of the length of the medium over the thermal wavelength. We analyze radiative corrections for a weakly-coupled quark-gluon plasma. We find that a thermal population of dynamical gluons changes the boundaries and reduces the size of the double-logarithmic phase space. It also provides new subdominant logarithmic corrections. We also show how the quantum, double-logarithmic and classical, soft phase spaces are smoothly connected once the radiated gluon becomes soft enough. Finally, we discuss a pathway to a determination of radiative corrections beyond the harmonic-oscillator approximation