Running coupling effects in the evolution of jet quenching

Understand

We study the consequences of including the running of the QCD coupling in the equation describing the evolution of the jet quenching parameter $\hat q$ in the double logarithmic approximation.

• To start with, we revisit the case of a fixed coupling, for which we obtain exact solutions valid for generic values of the transverse momentum (above the medium saturation scale) and corresponding to various initial conditions.
• In the case of a running coupling, we construct approximate solutions in the form of truncated series obtained via successive iterations, whose convergence is well under control.
• We thus deduce the dominant asymptotic behavior of the renormalized $\hat q$ in the limit of a large evolution time $Y\equiv\ln(L/\lambda)$, with $L$ the size of the medium and $\lambda$ the typical wavelength of a medium constituent.