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.

59 pages, 8 figures [main change from v1: addition of the new appendix B summarizing more about use of the i*epsilon prescription in earlier work]

References in corpus (1)

• The LPM effect in sequential bremsstrahlung 2: factorization

Cited by in corpus (17)

• The LPM effect in sequential bremsstrahlung 2: factorization
• Radiative energy loss of neighboring subjets
• Quantum Field Theory, Feynman-, Wheeler Propagators, Dimensional Regularization in Configuration Space and Convolution of Lorentz Invariant Tempered Distributions
• 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
• In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers
• The LPM effect in sequential bremsstrahlung: 4-gluon vertices
• 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
• Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat{q}$
• The LPM Effect in sequential bremsstrahlung: $1/N_c^2$ corrections
• Jet evolution in a dense QCD medium
• The LPM effect in sequential bremsstrahlung: incorporation of "instantaneous'' interactions for QCD
• Jet substructure observables for jet quenching in Quark Gluon Plasma: a Machine Learning driven analysis
• Two Gluon Emission from MHV: Two Particle Correlations and the Deviation from Poisson
• Partonic transport model application to heavy flavor