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 = 4-2*epsilon dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order epsilon, to be combined with the 1/epsilon 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 Zalpha-expansion. We compare the results obtained to the existing literature.
Keywords
Cite
@article{arxiv.2403.07127,
title = {Dimensional Regularization and Two-Loop Vacuum Polarization Operator: Master Integrals, Analytic Results and Energy Shifts},
author = {S. Laporta and U. D. Jentschura},
journal= {arXiv preprint arXiv:2403.07127},
year = {2024}
}
Comments
17 pages; RevTeX; see Physical Review D for Supplementary Material