The Proton Radius Puzzle

Editorial

Occasionally,“revolutions” are caused in physics when new measurement techniques becomeavailable and cause us to rethink what we thought we knew. This has recently happenedin the field of proton structure physics, where researchers have had to revisitfundamental assumptions used in their determinations of the proton's meanelectric charge radius.

Until 2010, ourknowledge of the proton's electric charge radius came exclusively fromelectron-proton interactions. One method is to scatter an electron beam ofenergy <1 GeV from a liquid hydrogen target and measure the epelastic scattering differential cross section, dσ/dΩ. By combining aseries of measurements at different electron beam energies and scatteringangles, a “Rosenbluth separation” can be performed which allows the electricand magnetic form factors of the proton to be determined at low four-momentumtransfer Q². Therate of decrease of the electric and magnetic form factors at Q² = 0 are directlyproportional to the rms electric and magnetic radii. For an example of adetailed study using this technique, see Bernauer et al. (2014).

Precisionmeasurements of hydrogen atomic spectra can also be used to determine theproton's electric charge radius. In this case, the hyperfine 1S Lamb shift of atomic hydrogen issensitive to the proton's finite charge radius since there is a small (butnonzero) probability that the electron's orbit will be inside the proton. Sincethe effect is small, a careful bound-state QED calculation of the manyradiative effects must be performed to yield the proton charge radius (Melnikovand van Ritbergen, 2000). The accuracy of the proton form factor measurementsin ep elastic scattering ultimately limits the precision of the radiusdetermination from atomic spectroscopy, but the two methods give electriccharge radius values in good agreement within respective uncertainties of about1% (Particle Data Group, 2012).

Thus, it came as a considerable surprise when a very precisedetermination of the proton's charge radius via Lamb shift measurements onmuonic hydrogen gave results that differed from the accepted value by more thanfive standard deviations (Pohl et al.,2010). When a proton is orbited by a negative muon, its much smaller Bohrradius compared to ordinary atomic hydrogen causes an enhancement of effectsrelated to the finite proton size. The μp Lamb shift between the 2S½and 2P½ states is affected by as much as 2%, which is dramaticallylarger than the equivalent shift in ordinary hydrogen. This measurement wasonly recently made possible through advancements in laser technology and muonbeams and is a real tour-de-force experimentally.

Notsurprisingly, this pioneering muonic Lamb shift measurement caused intensespeculation in the proton structure field and many prior assumptions wereinvestigated. Were the fields of atomic and nuclear physics using the samedefinition of proton charge radius? Is the modeling of muonic hydrogen sufficientlyaccurate? Was there any systematic uncertainty in any of these measurements that was significantlyunderestimated? For a recent review of these investigations, see Pohl et al. (2013). None of theseinvestigations have yielded anything obviously wrong and after the most recentmuonic hydrogen measurements the discrepancy has in fact increased from five toseven standard deviations (Antognini etal., 2013).

As a result, the urgency to find a solution to the protonradius puzzle has only increased and even more fundamental assumptions are nowunder investigation. For example, the possibility that the proton radius puzzlemight be caused by a difference between the muon-proton and electron-protoninteractions has generated much interest because such an effect is notanticipated in the Standard Model of particle physics. A fundamental tenet ofthe Standard Model is lepton universality, which states that after onecorrects for the obvious mass differences between the electron, muon and tauleptons, their interactions should in every other manner be identical. Leptonuniversality has been tested to the sub-percent level by comparing the decayrates of τ and μ leptons to electrons (Martin and Shaw, 2008). However,the interactions between electrons and protons and muons and protons, havenever been directly compared with precision. This will be tested for the firsttime in 2016-17 with the MUSE experiment (MUSE Collaboration, 2014), which willscatter a mixed beam of electrons and muons from liquid hydrogen andsimultaneously compare their scattering cross sections.

To me, it appears that a fundamental flaw of the electronscattering method to determine the proton charge radius is that it invariablyinvolves an extrapolation to Q² = 0 whose polynomial form is notpreviously determined by theory. A recent investigation indicates that thechoice of extrapolation function has a potentially significant impact (Lorenzand Meissner, 2014). Another issue is the 4 standard deviation differencebetween the average of the spectroscopic measurements in ordinary hydrogen andthose in muonic hydrogen. To resolve this, further spectroscopic measurementsin ordinary hydrogen are also underway (Beyer et al., 2013).

The bottom line is that physical systems that were commonlythought to be reasonably well understood can always yield considerablesurprises when technical developments thrust revolutions upon the scientificcommunity. Just as at the beginning of the 20^th century, we shouldpray for continuing innovations and future “revolutions” to force us to rethinkour fundamental assumptions and cause further advancements in our knowledge ofphysics.