The LPM effect in sequential bremsstrahlung 2: factorization

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. In this paper, we continue analysis of 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), avoiding soft-gluon approximations. In particular, this paper analyzes the subtle problem of how to precisely separate overlapping double splitting (e.g. overlapping double bremsstrahlung) from the case of consecutive, independent bremsstrahlung (which is the case that would be implemented in a Monte Carlo simulation based solely on single splitting rates). As an example of the method, we consider the rate of real double gluon bremsstrahlung from an initial gluon with various simplifying assumptions (thick media;q approximation; large N c ; and neglect for the moment of processes involving 4-gluon vertices) and explicitly compute the correction ∆ dΓ/dx dy due to overlapping formation times.

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

“…Eqs. (5.11) exactly match the two color routings used in previous large-N work on overlapping formation times [10] for the contribution of diagrams like fig. 6.…”

“…[where q 1 and q 2 are two-dimensional vectors as made explicit in (4.4)]. Initial conditions would be set by either (i) appropriately normalized delta functions δ(q 1 −q ′ 1 ) δ(q 2 −q ′ 2 ) or, perhaps more usefully, (ii) the functions the propagator is ultimately convolved with in the application [9,10] (see below).…”

“…We will now generalize the preceding results from SU(3) to SU(N), with the goal of studying how the (simpler) large-N formalism for earlier calculations [9][10][11][12] of overlapping formation time effects is recovered as N→∞. From here on, we refer to the number of colors N c as simply N to make formulas more compact and easy to read.…”

“…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.…”

Groomed jets in heavy-ion collisions: sensitivity to medium-induced bremsstrahlung

“…In the opposite, incoherent case, the colour correlation of the constituents is broken. See also [48,49] for similar conclusions in the context of the two-gluon emission spectrum. These findings imply that energy loss should be applied only to substructures of the jet that are resolved by the medium [50].…”