Abstract
In the context of the recently derived probabilistic picture of in-medium jet evolution, we study radiative corrections which yield potentially large double logarithms, αs ln2 L, for large enough medium length L. We show that these large corrections are universal and can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L2+γ, with γ = , as compared to the standard scaling in L2.
Highlights
A high energy parton propagating through a dense medium, cold nuclear matter, or a high temperature quark-gluon plasma, undergoes multiple interactions with the constituents of the medium
We return to the approximation that we have used in order to identify the radiative correction to the 2-point function as a correction to the jet quenching parameter
We end this paper by discussing several implications of the scale dependence of the jetquenching parameter coming from the radiative corrections
Summary
A high energy parton propagating through a dense medium, cold nuclear matter, or a high temperature quark-gluon plasma, undergoes multiple interactions with the constituents of the medium. That the spectrum (1) depends on the same jet-quenching parameter reflects the basic process at work in medium-induced radiation: the matching between the formation time of a gluon τf ∼ ω/k⊥2 , and the transverse momentum acquired during τf , k⊥2 ∼ qτf , which determines the typical branching time as τf ∼ τbr ≡ ω/q, and the spectrum above, ωdN/dω ∝ L/τbr It follows from this spectrum that the mean energy lost through radiation by a particle going through a Preprint submitted to Elsevier medium is given (parametrically) by ω αsCR qL2. The quantity that we wish to calculate is the probability that the initial gluon acquires a given transverse momentum through its interaction with the medium This is obtained by squaring the amplitude, averaging over the initial color and polarization, summing over final polarization and color, and averaging over the background field. This expression will be referred to later in the discussion
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