The LPM effect in sequential bremsstrahlung: dimensional regularization

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. Of recent interest is 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). In previous papers, we have developed methods for computing such corrections without making soft-gluon approximations. However, our methods require consistent treatment of canceling ultraviolet (UV) divergences associated with coincident emission times, even for processes with tree-level amplitudes. In this paper, we show how to use dimensional regularization to properly handle the UV contributions. We also present a simple diagnostic test that any consistent UV regularization method for this problem needs to pass.

In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers

“…[4][5][6] in the context of energy loss of highmomentum partons traversing a QCD medium (such as a quark-gluon plasma). Together with Chang, we subsequently developed and implemented field theory formalism needed for the more general case where x and y are arbitrary [7][8][9][10]. We used the formalism to calculate the LPM interference effects on real double gluon bremsstrahlung g → ggg in medium, given by the processes depicted in fig.…”

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

“…Including yet more particles would be needed to study the simultaneous overlap of three or more splittings. To date, calculations of overlap effects have made simplifying assumptions such as soft emission limits [11][12][13] or the large-N c limit [9,[15][16][17]. In this paper, I take a first step toward removing those assumptions by finding the generalization of (1.4) to four or more particles.…”

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

“…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.…”

“…Here we use the notation C ij to help avoid confusion with the Casimir operator C ij for the joint color representation of particles i and j. 11 Eqs. (5.14) of ref.…”

“…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.…”