Two-loop electron self-energy for low nuclear charges

Abstract

Calculations of the two-loop electron self-energy for the $1S$ Lamb shift are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine structure constant). Our approach allows calculations to be extended to nuclear charges lower than previously possible and improves the numerical accuracy by more than an order of magnitude. Extrapolation of our all-order results to hydrogen yields a result twice as precise as the previously accepted value [E. Tiesinga et al. Rev. Mod. Phys. 93, 025010 (2021)], differing from it by 2.8 standard deviations. The resulting shift in the theoretical prediction for the $1S$-$2S$ transition frequency in hydrogen decreases the value of the Rydberg constant by one standard deviation.

References in corpus (14)

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• Two-Loop Bethe Logarithms
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• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
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• Two-loop QED corrections with closed fermion loops
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• The two-loop self-energy: diagrams in the coordinate-momentum representation

Cited by in corpus (7)

• Sub-part-per-trillion test of the Standard Model with atomic hydrogen
• Two-loop electron self-energy with accelerated partial-wave expansion
• One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge
• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions
• Precision Spectroscopy of 2S-nS Transitions in Atomic Hydrogen: A Determination of the Proton Charge Radius
• A Bayesian Approach for Strong Field QED Tests with He-like Ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation