Mass-operator calculation of the electrongfactor

Abstract

We report on a mass-operator calculation of sixth-order contributions to the electron magnetic moment. We consider contributions with zeroth-order photon Green's functions and use an expansion of the mass operator equivalent to a perturbation series in the bound interaction picture. The method for isolating magnetic moment contributions in the mass operator is described using symmetric integration techniques on integrals with noncommuting momenta. Particular attention is given to the subtraction of both ultraviolet and infrared singularities in the numerical calculation. Our result ($2\sigma$ uncertainty in parentheses) is a contribution of $0.75\left(11\right)\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^3$ that gives a total sixth-order contribution of $1.02\left(11\right)\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^3$. Systematic and random errors are discussed.