The proton is the primary building block of the visible Universe, but many of its properties-such as its charge radius and its anomalous magnetic moment-are not well understood. The root-mean-square charge radius, r(p), has been determined with an accuracy of 2 per cent (at best) by electron-proton scattering experiments. The present most accurate value of r(p) (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of r(p) as deduced from electron-proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant). An attractive means to improve the accuracy in the measurement of r(p) is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift (the energy difference between the 2S(1/2) and 2P(1/2) states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find r(p) = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by -110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

Proton Still Too Small Despite a proton's tiny size, it is possible to measure its radius based on its charge or magnetization distributions. Traditional measurements of proton radius were based on the scattering between protons and electrons. Recently, a precision measurement of a line in the spectrum of muonium—an atom consisting of a proton and a muon, instead of an electron—revealed a radius inconsistent with that deduced from scattering studies. Antognini et al. (p. 417 ; see the Perspective by Margolis ) examined a different spectral line of muonium, with results less dependent on theoretical analyses, yet still inconsistent with the scattering result; in fact, the discrepancy increased.

The 7σ discrepancy between the proton rms charge radius from muonic hydrogen and the CODATA-2010 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S-2P transition frequencies measured in muonic hydrogen [1,2]. * Electronic address: aldo@phys.ethz.ch

The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ(-). We measured three 2S-2P transitions in μd and obtain r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The μd value is also 3.5σ smaller than the r(d) value from electronic deuterium spectroscopy. The smaller r(d), when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

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