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

Steven

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

Article Date: 11 February 2026
Article URL: https://www.nature.com/articles/s41586-026-10124-3
Article Image:
Figure 1: Proton rms charge radius r_p

Summary

The authors report an ultra-precise laser-spectroscopy measurement of the 2S–6P transitions in atomic hydrogen performed on a cryogenic atomic beam. By controlling and modelling subtle systematic effects (notably light-force shifts from the spectroscopy standing wave, quantum‑interference distortions, dc‑Stark shifts and Doppler contributions) they extract Doppler-free transition frequencies with sub-part-per-trillion precision.

Combining the new 2S–6P fine-structure centroid with the well-known 1S–2S frequency yields a proton RMS charge radius r_p = 0.8406(15) fm — in excellent agreement with muonic-hydrogen results and 5.5σ away from the larger CODATA 2014 value. Using the muonic r_p as input, the Standard Model prediction for the 2S–6P centroid matches the measurement to 0.7 parts per trillion, providing a stringent test of bound-state QED (0.5 ppm for the 1S Lamb shift) and improving the determination of the Rydberg constant.

Key Points

  • Record-precision Doppler-free one-photon spectroscopy of the 2S–6P transitions in atomic hydrogen using a cryogenic atomic beam and an active fibre-based retroreflector.
  • Careful modelling and experimental characterisation of light-force shifts (matter-wave diffraction on the standing wave), quantum-interference (QI) line-shape distortions and dc‑Stark effects were essential to reach sub-pptr precision.
  • Measured transition frequencies: ν(2S–6P1/2)=730,690,111,486.30(69) kHz and ν(2S–6P3/2)=730,690,516,650.91(66) kHz; centroid ν(2S–6P)=730,690,248,610.79(48) kHz (0.66 ppt).
  • Derived proton radius r_p = 0.8406(15) fm from atomic hydrogen — agrees with muonic hydrogen (resolving the proton-radius puzzle in favour of the smaller radius) and disagrees with CODATA 2014 by 5.5σ.
  • Direct test of the Standard Model and bound-state QED: experimental vs SM prediction agrees to 0.7 ppt (SM) and 0.5 ppm (1S Lamb shift); Rydberg constant extracted with improved precision (≈0.75 ppt).
  • Data and analysis code are publicly available (Zenodo dataset and corresponding author for code), enabling independent checks and reuse.

Why should I read this?

Short answer: because this is precision physics at its finest. These folks measured hydrogen transitions so precisely they can weigh in on the long-running proton-radius row and double-check bound-state QED at a jaw-dropping level. If you want to know whether atomic hydrogen still agrees with muonic hydrogen and the Standard Model — and why tiny experimental niggles like standing-wave matter-wave diffraction matter — this paper gives the answers and the how-to. We’ve saved you the lab-bench slog: the result backs the muonic radius and delivers a top-tier test of QED.

Context and relevance

The proton-radius puzzle — a previously significant discrepancy between muonic-hydrogen spectroscopy and earlier atomic/spectroscopic or scattering determinations — has driven intense experimental and theoretical work for more than a decade. This new measurement provides an independent, high-precision atomic-hydrogen determination of r_p that matches the muonic value and is substantially more precise than prior atomic results.

Beyond settling r_p, the work tightens the experimental constraints on bound-state QED corrections (reaching sensitivities comparable with the most precise tests of the electron magnetic moment) and improves the Rydberg constant estimate. The techniques (velocity-resolved detection, active retroreflection, detailed LFS and QI simulation, in-situ stray-field characterisation) are broadly applicable to future hydrogen and deuterium spectroscopy and to spectroscopic bounds on light new physics (for example, keV-scale weakly interacting bosons). For metrology and fundamental-constants communities this is a must-read; for wider physics audiences it is a clear demonstration of how careful systematic control pushes tests of the Standard Model to new precision frontiers.

Source

Source: https://www.nature.com/articles/s41586-026-10124-3

Article meta

Authors: Lothar Maisenbacher et al. — Max-Planck-Institut für Quantenoptik and collaborators.
Data: Zenodo dataset available as referenced in the paper. Open Access (CC BY 4.0).