Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

TL;DR

This paper presents a nonperturbative calculation of the anomalous magnetic moment in the Yukawa model using truncated light-front Fock space, employing numerical methods and systematic renormalization.

Contribution

It introduces a systematic nonperturbative approach within light-front dynamics to compute physical observables in the Yukawa model with Fock space truncation.

Findings

Numerical calculation of the three-body Fock sector contributions.

Regularization using Pauli-Villars fields ensures finite results.

First nonperturbative estimate of the anomalous magnetic moment in this framework.

Abstract

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.