Exploring a nonperturbative method for calculation of the anomalous magnetic moment of the electron

The electron's anomalous magnetic moment is computed in a light-cone Hamiltonian approach, with Pauli-Villars (PV) particles as UV regulators. The eigenstate is obtained by diagonalizing a matrix that represents the discretization of 48 coupled integral equations for the one-photon/one-electron wave functions. This generalizes earlier work on a one-photon truncation and extends the eigenstate expansion to two photons. In addition to the physical particles, one PV electron flavor and two PV photon flavors are included in the basis. The second PV photon allows the solution to have a very smooth, slowly varying dependence on the PV electron mass. This in turn allows the numerical approximation to use smaller mass ratios, which reduces round-off errors. An intermediate calculation that retains the one-photon contribution and the two-photon self-energy contributions yields a much improved result. Where the older, one-photon calculations of the anomalous moment by S.J. Brodsky et al. differed by 14% from the correct value, inclusion of the self-energy contribution reduces the discrepancy to less than 2%.