The origin of the proton radius puzzle

The dimension of the proton, the basic building block of matter, is still object of controversy. The most precise electron-proton scattering data at low transferred momenta are re-analyzed and the extraction of the proton radius is discussed. A recent experiment from the JLAB-CLAS collaboration gives a small value for the radius (The symbol $$R_E^\alpha $$ R E α stands for the root-mean-square charge radius of the proton $$\sqrt{\langle r_E^2\rangle }$$ ⟨ r E 2 ⟩ , obtained by the experimental or theoretical Collaboration $$\alpha $$ α .) $$R_E^\mathrm{CLAS}= (0.831\pm 0.007_\mathrm{stat}\pm 0.012_\mathrm{syst})$$ R E CLAS = ( 0.831 ± 0 . 007 stat ± 0 . 012 syst ) fm (Xiong et al. in Nature 575:147, 2019), in contrast with previous electron scattering experiments, in particular with the MAINZ experiment (Bernauer et al. (A1 Collaboration), Phys. Rev. C 90:015206, 2014) that concluded $$R_E^\mathrm{MAINZ}= (0.879\pm 0.005_\mathrm{stat}\pm 0.004_\mathrm{syst}\pm 0.002_\mathrm{model}\pm 0.004_\mathrm{group})$$ R E MAINZ = ( 0.879 ± 0 . 005 stat ± 0 . 004 syst ± 0 . 002 model ± 0 . 004 group ) fm. The experimental results are re-analyzed in terms of different fits of the cross section and of its discrete derivative with analyticity constraints. The uncertainty on the derivative is two orders of magnitude larger than the error on the measured observable, i.e., the cross section. The systematic error associated with the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions, and the range of the data sample.

Two-photon frequency comb spectroscopy of atomic hydrogen

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R∞ = 10,973,731.568226(38) per meter] and the proton charge radius [rp = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

The proton radius puzzle – 9 years later

High-precision measurements of the proton radius via scattering, electric hydrogen spectroscopy and muonic hydrogen spectroscopy do not agree on the level of more than 5 σ. This proton radius puzzle persists now for almost a decade. This paper gives a short summary over the progress in the solution of the puzzle as well as an overview over the planned experiments to finally solve this puzzle at the interface of atomic and nuclear physics.

A measurement of the atomic hydrogen Lamb shift and the proton charge radius

The surprising discrepancy between results from different methods for measuring the proton charge radius is referred to as the proton radius puzzle. In particular, measurements using electrons seem to lead to a different radius compared with those using muons. Here, a direct measurement of the n = 2 Lamb shift of atomic hydrogen is presented. Our measurement determines the proton radius to be rp = 0.833 femtometers, with an uncertainty of ±0.010 femtometers. This electron-based measurement of rp agrees with that obtained from the analogous muon-based Lamb shift measurement but is not consistent with the larger radius that was obtained from the averaging of previous electron-based measurements.