Abstract
We complete the physical picture for the evolution of a high-energy jet propagating through a weakly-coupled quark-gluon plasma by investigating the thermalization of the soft components of the jet. We argue that the following scenario should hold: the leading particle emits a significant number of mini-jets which promptly evolve via quasi-democratic branchings and thus degrade into a myriad of soft gluons, with energies of the order of the medium temperature T. Via elastic collisions with the medium constituents, these soft gluons relax to local thermal equilibrium with the plasma over a time scale which is considerably shorter than the typical lifetime of the mini-jet. The thermalized gluons form a tail which lags behind the hard components of the jet. We support this scenario, first, via parametric arguments and, next, by studying a simplified kinetic equation, which describes the jet dynamics in longitudinal phase-space. We solve the kinetic equation using both (semi-)analytical and numerical methods. In particular, we obtain the first exact, analytic, solutions to the ultrarelativistic Fokker-Planck equation in one-dimensional phase-space. Our results confirm the physical picture aforementioned and demonstrate the quenching of the jet via multiple branching followed by the thermalization of the soft gluons in the cascades.
Highlights
Qualitatively, within the pQCD picture for medium-induced radiation, which predicts the formation of well-developed gluon cascades, or ‘mini-jets’, via multiple branching [27,28,29,30,31,32,33,34,35]
We argue that the following scenario should hold: the leading particle emits a significant number of mini-jets which promptly evolve via quasidemocratic branchings and degrade into a myriad of soft gluons, with energies of the order of the medium temperature T
The theoretical description of medium-induced multiple branching started being developed only recently and in its current formulation it leaves unanswered a number of important questions, among which: what is the physical mechanism which stops the medium-induced cascades, and at which energy scale? How does this mechanism influence the dynamics of the branchings at higher energy scales? What is the fate of the softest quanta, as produced at the low-energy end of the cascade? What is the precise mechanism for energy transfer from the jet to the medium and what are the imprints of this transfer on the medium itself?
Summary
We summarize the physical picture underlying the in-medium evolution of a jet generated by a high-energy parton propagating through a weakly-coupled quark-gluon plasma. This picture largely reflects the current understanding of this problem, as presented in the literature, but includes some additional arguments which are physically motivated and which will be later on confirmed by the new analysis in this work. We start with a brief review of recent studies of the medium-induced gluon cascade [27,28,29,30], which recognized the importance of multiple branchings, but did not address the important problem of the thermalization of the soft components of the jet. We discuss the interplay between multiple branching and the elastic collisions responsible for thermalization
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