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

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 continue study 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-emission approximations. In this particular paper, we show (i) how the "instantaneous" interactions of Light-Cone Perturbation Theory must be included in the calculation to account for effects of longitudinally-polarized gauge bosons in intermediate states, and (ii) how to compute virtual corrections to LPM emission rates, which will be necessary in order to make infrared-safe calculations of the characteristics of inmedium QCD showering of high-energy partons. In order to develop these topics in as simple a context as possible, we will focus in the current paper not on QCD but on large-N f QED, where N f is the number of electron flavors. Contents

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 the limit N→3, the 4-gluon singlets |ch "0" constructed from the "0" representation no longer mix in table IV with any of the other singlets and so will completely decouple 13 See our earlier footnote 5. Our table IV corrects for the (non-propagating) misprints in ref.…”

“…Table IV presents the corresponding table of s|t matrix elements, which can be extracted from the work of refs. [20] or [22], 13 and whose computation is also discussed in our appendix A.…”

“…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.…”

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

“…So we are interested in α(Q ⊥ ), with (1.1) giving Q ⊥ ∼ (qE) 1/4 . The above argument that (1.3) is the relevant scale for α is qualitative, but it has been checked by explicit calculation in the case of large-N f QED [13].…”

“…In general, at very high energy, each 3 For a very brief review of formation times in the language of this paper, see section II.A.1 of ref. [13]. The QED formation time essentially goes back to Migdal [15], though he did not use this language.…”