A unified picture of medium-induced radiation

Abstract

We revisit the picture of jets propagating in the quark-gluon plasma. In addition to vacuum radiation, partons scatter on the medium constituents resulting in induced emissions. Analytical approaches to including these interactions have traditionally dealt separately with multiple, soft, or rare, hard scatterings. A full description has so far only been available using numerical methods. We achieve full analytical control of the relevant scales and map out the dominant physical processes in the full phase space. To this aim, we extend existing expansion schemes for the medium-induced spectrum to the Bethe-Heitler regime. This covers the whole phase space from early to late times, and from hard splittings to emissions below the thermal scale. Based on the separation of scales, a space-time picture naturally emerges: at early times, induced emissions start to build from rare scatterings with the medium. At a later stage, induced emissions due to multiple soft scatterings result in a turbulent cascade that rapidly degrades energy down to, and including, the Bethe-Heitler regime. We quantify the impact of such an improved picture, compared to the current state-of-the-art factorization that includes only soft scatterings, by both analytical and numerical methods for the medium-induced energy distribution function. Our work serves to improve our understanding of jet quenching from small to large systems and for future upgrades of Monte Carlo generators.

Jet medium modifications

“…Notably, the computation of this particular splitting at large N c is slightly less complicated compared to other 1 → 2 splittings, as it does not involve the calculation of 4-point correlators of Wilson lines (quadrupole). The other case is the γ → q q splitting obtained in [41], which already involves the calculation of the quadrupole at large N c . In this large-N c limit and under the harmonic oscillator approximation, the quadrupole can be analytically obtained.…”

“…In this large-N c limit and under the harmonic oscillator approximation, the quadrupole can be analytically obtained. More interestingly, the authors in [41] have developed a numerical method based on solving a system of coupled Schrödinger equations, which allows for the calculation of the quadrupole for finite numbers of colors. This recipe could potentially be applied to the q → qg and g → gg processes as well, providing an opportunity to evaluate the accuracy of the commonly used approximations to obtain the double-differential spectrum for these emissions, including the semi-hard approximation.…”

“…This recipe could potentially be applied to the q → qg and g → gg processes as well, providing an opportunity to evaluate the accuracy of the commonly used approximations to obtain the double-differential spectrum for these emissions, including the semi-hard approximation. It is worth noting, however, that the computational complexity of the approach in [41] would considerably increase for these particular splittings.…”

Medium-induced radiation with vacuum propagation in the pre-hydrodynamics phase

“…Most analytical calculations of in-medium radiation, including recent efforts [17][18][19][20][21][22][23][24][25], assume that the initial hard particle is created inside the medium, hence allowing it to immediately interact with the QGP. In practice, this implies that the particle is set to be produced after the medium forms, thus ignoring the initial part of its propagation.…”

Precise description of medium-induced emissions

“…This is true whether the spectra are differential in both the longitudinal momentum splitting variable z and the relative transverse momentum dI/[dz d 2 p], or simply dI/dz. The full problem can be tackled by numerical [32][33][34][35][36][37] or analytical techniques [38][39][40][41][42][43].…”