Dimensional regularization and two-loop vacuum polarization operator: Master integrals, analytic results, and energy shifts

Abstract

We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in D=4−2ε dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order ε, to be combined with the 1/ε divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for 1S, 2S, and 2P states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the Zα-expansion. We compare the results obtained to the existing literature. Published by the American Physical Society 2024