Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model

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.

7 pages, 7 figures. Contribution to the proceedings of the Workshop: Light-Cone 2008, "Relativistic Nuclear and Particle Physics", Mulhouse, France, July 7-11, 2008. To be published in the online journal "Proceedings of Science" - PoS