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 in-medium 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.

43 pages + appendices for 89 pages total; 43 figures. Difference from v4: Missing absolute value signs added to eq. (A29)

References in corpus (7)

• Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium
• High-energy jet quenching in weakly-coupled quark-gluon plasmas
• One-loop corrections to light cone wave functions: the dipole picture DIS cross section
• The non-linear evolution of jet quenching
• Radiative energy loss and radiative p_T-broadening of high-energy partons in QCD matter
• The LPM effect in sequential bremsstrahlung: 4-gluon vertices
• Revisiting the equivalence of light-front and covariant QED in the light-cone gauge

Cited by in corpus (9)

• The LPM effect in sequential bremsstrahlung: nearly complete results for QCD
• Precise description of medium-induced emissions
• Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma
• Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss
• The LPM effect in sequential bremsstrahlung: from large-N QCD to N=3 via the SU(N) analog of Wigner 6-j symbols
• Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED
• The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections
• The LPM effect in sequential bremsstrahlung: incorporation of "instantaneous'' interactions for QCD
• Are Parton Showers in a Quark-Gluon Plasma Strongly Coupled? A Theorist's Test