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

S. J. Brodsky·J. R. Hiller·G. McCartor
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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.

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S. J. Brodsky, J. R. Hiller, G. McCartor. 2005-08-29. Two-boson truncation of Pauli-Villars-regulated Yukawa theory. https://doi.org/10.1016/j.aop.2005.09.005

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