On the nonperturbative solution of Pauli--Villars-regulated light-front QED: A comparison of the sector-dependent and standard parameterizations

TL;DR

This paper compares sector-dependent and standard parameterizations in light-front QED regulated by Pauli--Villars particles, analyzing their effects on ultraviolet divergences and the anomalous magnetic moment, with implications for nonperturbative solutions of strongly coupled theories.

Contribution

It demonstrates the differences between sector-dependent and standard parameterizations in light-front QED with PV regulation, highlighting their handling of divergences and their impact on physical predictions.

Findings

Neither approach allows all PV masses to go to infinity.

Sector-dependent parameterization suffers from an infrared divergence requiring a nonzero photon mass.

Standard parameterization can match experimental anomalous magnetic moment with two-photon truncation.

Abstract

We consider quantum electrodynamics quantized on the light front in Feynman gauge and regulated in the ultraviolet by the inclusion of massive, negative-metric Pauli--Villars (PV) particles in the Lagrangian. The eigenstate of the electron is approximated by a Fock-state expansion truncated to include one photon. The Fock-state wave functions are computed from the fundamental Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic moment, as a point of comparison. Two approaches are considered: a sector-dependent parameterization, where the bare parameters of the Lagrangian are allowed to depend on the Fock sectors between which the particular Hamiltonian term acts, and the standard choice, where the bare parameters are the same for all sectors. Both methods are shown to require some care with respect to ultraviolet divergences; neither method can allow all PV masses to be taken to infinity. In addition, the sector-dependent approach suffers from an infrared divergence that requires a nonzero photon mass; due to complications associated with this divergence, the standard parameterization is to be preferred. We also show that the self-energy effects obtained from a two-photon truncation are enough to bring the standard-parameterization result for the anomalous moment into agreement with experiment within numerical errors. This continues the development of a method for the nonperturbative solution of strongly coupled theories, in particular quantum chromodynamics.