The LPM effect in sequential bremsstrahlung

Abstract

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We analyze the case when the coherence lengths of two consecutive splitting processes overlap, which is important for understanding corrections to standard treatments of the LPM effect in QCD. Previous authors have analyzed this problem in the case of overlapping double bremsstrahlung where at least one of the bremsstrahlung gluons is soft. Here we show how to generalize to include the case where both splittings are hard. A number of techniques must be developed, and so in this paper we simplify by (i) restricting attention to a subset of the interference effects, which we call the "crossed" diagrams, and (ii) working in the large-N c limit. We first develop some general formulas that could in principle be implemented numerically (with substantial difficulty). To make more analytic progress, we then focus on the case of a thick, homogeneous medium and make the multiple scattering approximation (also known as theq or harmonic approximation) appropriate at high energy. We show that the differential rate dΓ/dx dy for overlapping double bremsstrahlung of gluons with momentum fractions x and y can then be reduced to the calculation of a 1-dimensional integral, which we perform numerically.

Two-gluon emission and interference in a thin QCD medium: insights into jet formation

“…This is a more intricate analysis which we leave for future work. Other analyses of the rate of emission of two gluons of comparable momentum from an on-shell quark propagating in the plasma can be found in [56,57].…”

“…See also [54,55] for related work in next-to-leading order corrections to the medium-induced spectrum. The emission spectrum of two gluons with comparable formation times was analysed for the case of a dense medium in [56]. These approaches, however, consider the gluon transverse momenta to be of the order of the medium scale and therefore do not explicitly study the interplay between emissions of the former kind and genuine vacuum emissions, either short-or long-distance ones, which can take place in the context of high-energy jets.…”

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

“…In section IV, we briefly review that, for this application, ref. [9] showed how to use symmetry to reduce the 4-body evolution problem to an effective 2-body evolution problem. We explicitly construct the corresponding harmonic oscillator Hamiltonian, which we will see has the form (1.2).…”

“…, which (unlike the 4-body potential) has no interesting color structure [9,16]: it is the same for both 3-gluon color singlets and so does not induce any transitions between the two. Which channel the end 4-gluon state is in compared to the initial 4-gluon state depends on the interference diagram.…”

“…1 As we'll discuss, such calculations must generically address a non-trivial problem of how to account for the color dynamics of the high-energy partons as they split while interacting with the medium. This problem has been sidestepped in overlapping formation time calculations to date by taking either (i) the soft bremsstrahlung limit [6][7][8] or (ii) the large-N c limit [9][10][11][12]. In this paper, we show how to avoid these limits by showing how to incorporate the full color dynamics.…”