Restoring the Bloch-Nordsieck theorem in the electroweak sector of the standard model

TL;DR

This paper demonstrates that incorporating gauge-invariant states via the Fröhlich-Morchio-Strocchi mechanism restores the Bloch-Nordsieck theorem in electroweak processes, impacting high-energy collider predictions.

Contribution

It introduces a non-perturbative gauge-invariant framework that reinstates the Bloch-Nordsieck theorem in the electroweak sector of the standard model.

Findings

Restores Bloch-Nordsieck theorem in electroweak processes

Negligible effects at low energies, significant at high energies

Provides an alternative PDF-based implementation for hadron colliders

Abstract

The electroweak gauge symmetry cannot be broken in a literal sense due to Elitzur's theorem. Thus, asymptotic states need to be manifestly and non-perturbatively gauge-invariant with respect to the electroweak symmetry. To take this suitably into account perturbation theory augmented by the Fr\"ohlich-Morchio-Strocchi mechanism can be used. We show that this restores the Bloch-Nordsieck theorem in electroweak processes in the standard model. This has potentially substantial impact at, e.g., future lepton colliders, but has only negligible effects at lower energies. We also demonstrate an alternative implementation using PDFs, which allows an approach with manifest electroweak Bloch-Nordsieck theorem also at hadron colliders.