The LPM effect in sequential bremsstrahlung: dimensional regularization

TL;DR

This paper advances the theoretical understanding of the LPM effect in high-energy bremsstrahlung by employing dimensional regularization to handle UV divergences in overlapping coherence length regimes, crucial for QCD corrections.

Contribution

It introduces a dimensional regularization approach for UV divergence cancellation in sequential bremsstrahlung calculations, improving the consistency of theoretical predictions.

Findings

Dimensional regularization effectively handles UV divergences.

A diagnostic test for UV regularization consistency is proposed.

Enhanced understanding of overlapping coherence length effects in QCD.

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.