Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
Jacopo Ghiglieri, Eamonn Weitz
Abstract
A bstract The transverse momentum broadening coefficient $$ \hat{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:math> receives both soft, classical and radiative, quantum corrections. The former are responsible for a large $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( g ) correction, whereas the latter enter at relative order α 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.