Proton radius puzzle

The radius of the proton is defined by a formula which can be calculated by quantum electrodynamics and be derived from either atomic spectroscopy or by electron–proton scattering. The formula involves a form-factor related to the two-dimensional parton diameter of the proton. == Problem ==

Prior to 2010, the proton charge radius was measured using one of two methods: one relying on spectroscopy, and one relying on nuclear scattering. Spectroscopy method The spectroscopy method compares the energy levels of spherically symmetric 2s orbitals to asymmetric 2p orbitals of hydrogen, a difference known as the Lamb shift. The exact values of the energy levels are sensitive to the distribution of charge in the nucleus since the 2s levels overlap more with the nucleus. Measurements of hydrogen's energy levels are now so precise that the accuracy of the proton radius is the limiting factor when comparing experimental results to theoretical calculations. This method produces a proton radius of about , with approximately 1% relative uncertainty. The resulting angular distribution of the electron and proton are analyzed to produce a value for the proton charge radius. Consistent with the spectroscopy method, this produces a proton radius of about . 2010 experiment In 2010, Pohl et al. published the results of an experiment relying on muonic hydrogen as opposed to normal hydrogen. Conceptually, this is similar to the spectroscopy method. However, the much higher mass of a muon causes it to orbit 207 times closer than an electron to the hydrogen nucleus, where it is consequently much more sensitive to the size of the proton. The resulting radius was recorded as , 5 standard deviations (5σ) smaller than the prior measurements. A follow-up experiment by Pohl et al. in August 2016 used a deuterium atom to create muonic deuterium and measured the deuteron radius. This experiment allowed the measurements to be 2.7 times more accurate, but also found a discrepancy of 7.5 standard deviations smaller than the expected value. == Proposed resolutions ==

New physics The uncertain nature of the experimental evidence did not stop theorists from attempting to explain the conflicting results. Among the postulated explanations were a three-body force, interactions between gravity and the weak force, or a flavour-dependent interaction, higher dimension gravity, a new boson, and the quasi-free hypothesis. Measurement artefact Randolf Pohl, the original investigator of the puzzle, stated that while it would be "fantastic" if the puzzle led to a discovery, the most likely explanation is not new physics but some measurement artefact. His personal assumption is that past measurements have misgauged the Rydberg constant and that the current official proton size is inaccurate. Quantum chromodynamic calculation In a paper by Belushkin et al. (2007), Proton radius extrapolation Papers from 2016 suggested that the problem was with the extrapolations that had typically been used to extract the proton radius from the electron scattering data though these explanation would require that there was also a problem with the atomic Lamb shift measurements. Data analysis method In one of the attempts to resolve the puzzle without new physics, Alarcón et al. (2018) Effectively, this approach attributes the cause of the proton radius puzzle to a failure to use a theoretically motivated function for the extraction of the proton charge radius from the experimental data. Another recent paper has pointed out how a simple, yet theory-motivated change to previous fits will also give the smaller radius. More recent spectroscopic measurements In 2017 a new approach using a cryogenic hydrogen and Doppler-free laser excitation to prepare the source for spectroscopic measurements; this gave results ~5% smaller than the previously accepted spectroscopic values with much smaller statistical errors. Their results support the smaller proton charge radius, but do not explain why the results before 2010 came out larger. 2022 analysis A re-analysis of experimental data, published in February 2022, found a result consistent with the smaller value of approximately 0.84 fm. 2026 atomic spectral results High precision measurements of the 2s-6p electronic transition in atomic hydrogen reported in 2026 give a proton radius value of 0.8406(15) fm in excellent agreement with predictions from the standard model. == References ==