From soft to hard radiation: the role of multiple scatterings in medium-induced gluon emissions

Abstract

A proper understanding of the physics of medium-induced gluon emissions is known to be of critical importance to describe the properties of strongly interacting matter under extreme conditions. In this regard, many theoretical efforts have been directed towards obtaining analytical calculations which might help us discerning the underlying physical picture and the dominant dynamics for different regimes. These analytical approaches rely on approximations whose validity is analyzed here by comparing their results with a recently developed numerical evaluation which includes all-order resummation of multiple scatterings. More specifically, by quantitatively comparing the energy spectrum and rates, we observe that three different regimes — each with its corresponding physical picture — emerge naturally from the equations: the high-energy regime where the emission process is dominated by a single hard scattering, the intermediate-energy regime where coherence effects among multiple scatterings become fundamental, and the low-energy regime where the dynamics is again dominated by a single scattering but where one must include the suppression factor due to the probability of not having any further scatterings (which is obtained through the resummation of virtual terms).

Quenching effects in the cumulative jet spectrum

“…A discussion of the regions of validity of these approaches was recently addressed in refs. [24][25][26]41]. In the soft scattering regime, the formation time of emissions t f = 2ω/k 2 becomes modified due to Gaussian broadening, i.e.…”

“…It follows that emissions with ω > ω c cannot be produced by soft collisions and Gaussian broadening, and are dominated by a single, hard scattering with the medium constituents. Similarly, at short formation times of the order of the medium mean free path t ∼ λ L, or ω ∼ qλ 2 /2 = ω BH ω c , the spectrum is again dominated by single scattering [40,41]. Since this latter regime gives a small contribution to energy loss, we will not discuss it further here.…”

“…(2.29) (for more details, see the next subsection). Finally, the grey band in figure 1 corresponds to emissions with ω ∼ ω BH , which are given by the Bethe-Heitler spectrum [40,41]. In what follows, we will neglect such emissions since these emissions do not contribute significantly to jet energy loss at high-p T [27,28].…”

Medium-induced radiative kernel with the Improved Opacity Expansion

“…These limitations in the analytic front have motivated the investigation of the radiative spectrum numerically [28][29][30][31][32][33][34]. However, the proposed approaches are in general less transparent and potentially more computationally costly as compared to their analytic counterparts for computing jet observables where multiple gluon radiation is to be resummed to all orders [35], for applications to jet suppression [36,37], or as a building block for Monte Carlo event generators [38][39][40][41][42][43][44][45][46][47][48].…”

A modified in-medium evolution equation with color coherence

“…See[25][26][27][28][29] for recent efforts 2. See the discussion on the multiple soft emission region conducted in[9,11].…”