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 dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order , to be combined with the divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for , , and 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 -expansion. We compare the results obtained to the existing literature.
- Received 1 January 2024
- Accepted 9 March 2024
DOI:https://doi.org/10.1103/PhysRevD.109.096020
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society