The two-loop self-energy: diagrams in the coordinate-momentum representation

TL;DR

This paper introduces a new technique for evaluating Feynman diagrams in mixed coordinate-momentum space, improving numerical accuracy in calculating two-loop self-energy corrections for hydrogen-like ions and comparing results with analytical predictions.

Contribution

The paper develops a novel method for evaluating Feynman diagrams in mixed space, enabling more precise calculations of two-loop self-energy corrections in hydrogen-like ions.

Findings

Numerical accuracy of self-energy calculations is significantly improved.

Extrapolated results for hydrogen are consistent with analytical perturbative results.

Higher-order remainder functions are estimated and compared across different Z values.

Abstract

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Z\alpha) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.