Restoration of the chiral limit in Pauli-Villars-regulated light-front QED

TL;DR

This paper computes the dressed-electron state in light-front QED with Pauli-Villars regulation, revealing the necessity of two PV photons for the correct chiral limit and analyzing the electron's anomalous moment.

Contribution

It demonstrates that two PV photons are required for the proper chiral limit in light-front QED, refining previous assumptions and analyzing renormalization and covariance.

Findings

Two PV photons are necessary for the correct chiral limit.

The electron's anomalous moment is computed using the plus component of the current.

Dependence on regulator masses is mild when two PV photons are used.

Abstract

The dressed-electron eigenstate of Feynman-gauge QED is computed in light-front quantization with a Fock-space truncation to include at most the one-photon/one-electron sector. The theory is regulated by the inclusion of three massive Pauli-Villars (PV) particles, one PV electron and two PV photons. In particular, the chiral limit is investigated, and the correct limit is found to require two PV photons, not just one as previously thought. The renormalization and covariance of the electron current are also analyzed. We find that the plus component is well behaved and use its spin-flip matrix element to compute the electron's anomalous moment. The dependence of the moment on the regulator masses is shown to be slowly varying when the second PV photon is used to guarantee the correct chiral limit.