José A. M. Lopes

The size of the proton

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, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments. The present most accurate value of rp (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 rp 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 rp 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 2S1/2 and 2P1/2 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 rp = 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 Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen

Proton Still Too Small Despite a protons 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. A precision spectroscopic measurement of the proton radius indicates a growing discrepancy with respect to scattering results. [Also see Perspective by Margolis] Accurate knowledge of the charge and Zemach radii of the proton is essential, not only for understanding its structure but also as input for tests of bound-state quantum electrodynamics and its predictions for the energy levels of hydrogen. These radii may be extracted from the laser spectroscopy of muonic hydrogen (μp, that is, a proton orbited by a muon). We measured the 2S1/2F=0-2P3/2F=1 transition frequency in μp to be 54611.16(1.05) gigahertz (numbers in parentheses indicate one standard deviation of uncertainty) and reevaluated the 2S1/2F=1-2P3/2F=2 transition frequency, yielding 49881.35(65) gigahertz. From the measurements, we determined the Zemach radius, rZ = 1.082(37) femtometers, and the magnetic radius, rM = 0.87(6) femtometer, of the proton. We also extracted the charge radius, rE = 0.84087(39) femtometer, with an order of magnitude more precision than the 2010-CODATA value and at 7σ variance with respect to it, thus reinforcing the proton radius puzzle.

Laser spectroscopy of muonic deuterium

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science, this issue p. 669 The charge radius of the deuteron is several standard deviations smaller than the previously accepted value. 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 rd = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value rd = 2.1424(21) fm. The μd value is also 3.5σ smaller than the rd value from electronic deuterium spectroscopy. The smaller rd, when combined with the electronic isotope shift, yields a “small” proton radius rp, similar to the one from muonic hydrogen, amplifying the proton radius puzzle.

The size of the proton and the deuteron

We have recently measured the 2S1/2F=1 − 2P3/2F = 2 energy splitting in the muonic hydrogen atom μp to be 49881.88 (76) GHz. Using recent QED calculations of the fine-, hyperfine, QED and finite size contributions we obtain a root-mean-square proton charge radius of rp = 0.84184 (67) fm. This value is ten times more precise, but 5 standard deviations smaller, than the 2006 CODATA value of rp = 0.8768 (69) fm. The source of this discrepancy is unknown. Using the precise measurements of the 1S-2S transition in regular hydrogen and deuterium and our value of rp we obtain improved values of the Rydberg constant, R∞ = 10973731.568160 (16) m−1and the rms charge radius of the deuteron rd = 2.12809 (31) fm.

Lifetime and population of the 2S state in muonic hydrogen and deuterium

Radiative deexcitation (RD) of the metastable 2S state of muonic protium and deuterium atoms has been observed. In muonic protium, we improve the precision on lifetime and population (formation probability) values for the short-lived {\mu}p(2S) component, and give an upper limit for RD of long-lived {\mu}p(2S) atoms. In muonic deuterium at 1 hPa, 3.1 +-0.3 % of all stopped muons form {\mu}d(2S) atoms. The short-lived 2S component has a population of 1.35 +0.57 -0.33 % and a lifetime of {\tau}_short({\mu}d) = 138 +32 -34 ns. We see evidence for RD of long-lived {\mu}d(2S) with a lifetime of {\tau}_long({\mu}d) = 1.15 +0.75 -0.53 {\mu}s. This is interpreted as formation and decay of excited muonic molecules.

Muonic hydrogen spectroscopy: the proton radius puzzle

By means of pulsed laser spectroscopy applied to muonic hydrogen (μ¯p) we havemeasured the 2S (F=1)/(1/2) - 2P(F=2)/(3/2) transition frequency to be 49881.88(76)GHz.1 By comparing this measurement with its theoretical prediction 2-7 based on bound-state QED we have determined a proton radius value of rP =0.84184(67) fm. This new value differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm,8 and 3 standard deviation from the e-p scattering results of 0.897(18) fm.9 The observed discrepancy may arise from a computational mistake of the energy levels in μp or H, or a fundamental problem in bound-state QED, an unknown effect related to the proton or the muon, or an experimental error.