Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED

Abstract

High-energy partons (E ≫ T ) traveling through a quark-gluon plasma lose energy by splitting via bremsstrahlung and pair production. Regardless of whether or not the quark-gluon plasma itself is strongly coupled, an important question lying at the heart of philosophically different approaches to energy loss is whether the high-energy partons of an in-medium shower can be thought of as a collection of individual particles, or whether their coupling to each other is also so strong that a description as high-energy "particles" is inappropriate. We discuss some possible theorists' tests of this question for simple situations (e.g. an infinite, non-expanding plasma) using thought experiments and first-principles quantum field theory calculations (with some simplifying approximations). The physics of in-medium showers is substantially affected by the Landau-Pomeranchuk-Midgal (LPM) effect, and our proposed tests require use of what might be called "next-to-leading order" LPM results, which account for quantum interference between consecutive splittings. The complete set of such results is not yet available for QCD but is already available for the theory of large-N f QED. We therefore use large-N f QED as an example, presenting numerical results as a function of N f α, where α is the strength of the coupling at the relevant high-energy scale characterizing splittings of the high-energy particles. Contents

Multiparticle potentials from lightlike Wilson lines in quark-gluon plasmas: A generalized relation of in-medium splitting rates to jet-quenching parameters q^

“…8, which can be estimated from free gluon diffusion 15 as ∆B ⊥ ∼ (∆t)/ω. In the limiting case 14 I've assumed that L is large compared to all other distance scales in (4.4). For readers who may find these ranges more familiar or understandable in terms of other variables, here is a translation.…”

Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N=3 via the SU(Arnold1 2019Phys. Rev. DSelf Cite120100View full textAdd to dashboardCite

“…Moreover, to make use of the rates to calculate the development of showers, one also needs x and y integrals involving dΓ/dx dy (see ref. [14], for example). So, if the propagator is found numerically using (7.1), that numerical result would ultimately need to be used inside a numeric integration over (B, B ′ , ∆t, x, y).…”

“…Similarly, the t-channel basis diagonalizesq 13 , and the u-channel basis diagonalizesq 14 . In order to express the potential (2.3) explicitly in a single choice of basis, we need to know how to convert between these bases choices.…”

“…But the redundancy is useful for seeing a simple relation between charges in different channels: Consider ABCD → ACBD, which changes s-channel to t-channel, and similarly ABCD → ADBC for s-channel to u-channel. Their actions on (2.11) give 14 then imply that the 4-particle potential (2.3) block diagonalizes into 5×5 and 3×3 blocks corresponding to the first five rows and last three rows of table II. We will now see that our application lies within the 5×5 block, and so we may ignore the 3×3 block.…”

“…They treat the medium as a set of static scattering centers, and the cross-section for scattering from those scattering centers is determined by single gluon exchange. 16 In contrast, we have focused on theq approximation, 14 The convention for labeling the four gluons in ref. [9] is slightly different than our convention here of fig.…”