Two-boson truncation of Pauli-Villars-regulated Yukawa theory

Abstract

We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3+1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion in order to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson--one-fermion equations for eigenstates with J_z=1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.

arXiv comment32 pages, 17 figures; requires elsart.cls

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• Nonperturbative light-front Hamiltonian methods
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• Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
• Discrete Symmetries on the Light Front and a General Relation Connecting Nucleon Electric Dipole and Anomalous Magnetic Moments
• Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model
• On the nonperturbative solution of Pauli--Villars-regulated light-front QED: A comparison of the sector-dependent and standard parameterizations
• A nonperturbative calculation of the electron's magnetic moment with truncation extended to two photons
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• Nonperturbative Pauli-Villars regularization of vacuum polarization in light-front QED
• A first nonperturbative calculation in light-front QED for an arbitrary covariant gauge
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• The box diagram in Yukawa theory
• Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory
• Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory
• Ambiguities in Pauli-Villars regularization
• Covariant analysis of electromagnetic current on the light cone: exposition with scalar Yukawa theory