Running coupling effects in the evolution of jet quenching

Abstract

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. We show that the asymptotic expansion is universal with respect to the choice of the initial condition at $Y=0$ and, moreover, it is remarkably similar to the corresponding expansion for the saturation momentum of a shockwave (a large nucleus). As expected, the running of the coupling significantly slows down the increase of $\hat{q}$ with $Y$ in the asymptotic regime at $Y\gg 1$. For the phenomenologically interesting value $Y\simeq 3$, we find an enhancement factor close to 3, independently of the initial condition and for both fixed and running coupling.

25 pages, 5 figures

References in corpus (5)

• The Color Glass Condensate
• Antiangular Ordering of Gluon Radiation in QCD Media
• Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium
• High-energy jet quenching in weakly-coupled quark-gluon plasmas
• Universal behavior of the gluon saturation scale at high energy including full NLL BFKL effects

Cited by in corpus (8)

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• Radiative corrections to the jet quenching parameter in dilute and dense media
• Inconsistencies in, and short pathlength correction to, $R_{AA}(p_T)$ in $\mathrm{A}+\mathrm{A}$ and $\mathrm{p}+\mathrm{A}$ collisions
• Medium-induced jet evolution: wave turbulence and energy loss
• Anomalous dimension of transverse momentum broadening in planar $\mathcal{N}=4$ SYM
• Universality aspects of quantum corrections to transverse momentum broadening in QCD media
• Anomalous diffusion in QCD matter