articleNatureFeb 11, 2026HYBRID OA

Sub-part-per-trillion test of the Standard Model with atomic hydrogen

Max Planck Institute of Quantum Optics · University of California, Berkeley · +3 more institutions

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Abstract

Abstract Quantum electrodynamics (QED), the first relativistic quantum field theory, describes light–matter interactions at a fundamental level and is one of the pillars of the Standard Model (SM). Through the extraordinary precision of QED, the SM predicts the energy levels of simple systems such as the hydrogen atom with up to 13 significant digits 1 , making hydrogen spectroscopy an ideal test bed. The consistency of physical constants extracted from different transitions in hydrogen using QED, such as the proton charge radius r p , constitutes a test of the theory. However, values of r p from recent measurements 2–7 of atomic hydrogen are partly discrepant with each other and with a more precise value from…

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