# Masses and electric charges: gauge anomalies and anomalous thresholds

## TL;DR

This paper investigates collinear divergences in gauge theories with massless charges, revealing new divergences linked to gauge anomalies and deriving a gravitational bound on the lightest charged fermion's mass.

## Contribution

It demonstrates that certain collinear divergences can only be canceled through quantum interference involving gauge anomalies, challenging the consistency of anomaly-free massless charge theories.

## Key findings

- Discovery of new collinear divergences related to gauge anomalies
- Link between anomalous thresholds and gravitational bounds on fermion masses
- Implication that anomaly cancellation is incompatible with massless long-range charges

## Abstract

We work out in the forward limit and up to order $e^6$ in perturbation theory the collinear divergences. In this kinematical regime we discover new collinear divergences that we argue can be only cancelled using quantum interference with processes contributing to the gauge anomaly. This rules out the possibility of a quantum consistent and anomaly free theory with massless charges and long range interactions. We use the anomalous threshold singularities to derive a gravitational lower bound on the mass of the lightest charged fermion.