Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model

TL;DR

This paper nonperturbatively calculates the anomalous magnetic moment in the Yukawa model using light-front dynamics, regularization, and a systematic renormalization scheme, providing preliminary numerical results.

Contribution

It introduces a nonperturbative method for calculating fermion properties in the Yukawa model with Fock space truncation and systematic renormalization.

Findings

Nonperturbative calculation of the anomalous magnetic moment.

Regularization using Pauli-Villars fields.

Preliminary numerical results for the magnetic moment.

Abstract

Within the covariant formulation of light-front dynamics, we calculate the state vector of a fermion coupled to identical scalar bosons (the Yukawa model). The state vector is decomposed in Fock sectors and we consider the first three ones: a single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, and these contributions are calculated with no approximations. The divergences of the amplitudes are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we developed. This renormalization scheme is a necessary condition in order to avoid uncancelled divergences when Fock space is truncated. As an example, we present preliminary numerical results for the anomalous magnetic moment of a fermion in the Yukawa model.