The proton radius puzzle
Prof. Aldo Antognini (ETH - Zürich)

At the Paul Scherrer Institute, Switzerland, we have recently measured several 2S−2P transition frequencies (Lamb shift) in muonic hydrogen (μp) and deuterium (μd) with 20 ppm precision by means of laser spectroscopy. The Lamb shift in µp is dominated by QED effects (mainly vacuum polarization) and the proton finite size effect is as large as 2% of the total Lamb shift. Therefore, from our measurements we can extract the proton radius value with a relative accuracy of 10−3 . This new value is 10 times more precise than previously obtained. However, it disagrees by 5 standard deviations from the current CODATA value.
The origin of this discrepancy is not yet known. It may come from theory of the muonic hydrogen energy levels (used to deduce the new value), or from problems in hydrogen spectroscopy experiments or hydrogen energy level theory (both used to deduce the CODATA value).
The decrease of the proton radius uncertainties opens the way to compare the pre-,10−12 ...−14 , dictions of hydrogen energy levels with high-precision (ur = measurements in hydrogen to a previously unachievable level of accuracy. This will stimulate progress in the understanding of the simplest atom and its related bound-state QED theory. For example the prediction of the 1SLamb shift can be tested to a relative accuracy of 3×10−7 . Additionally this measurement will improve the Rydberg constant (which is the best know fundamental constant) by a factor of six to a relative accuracy of 1×10−12 . First, however, the origin of the ”proton radius puzzle” must be understood.
Similarly we have improved the deuteron rms charge radius by an order of magnitude. In addition the Zemach radii of both nuclei and the deuteron polarizability will also be determined. The new proton charge radius value is a benchmark for lattice QCD, and the deuteron radius for few-nucleon theories. The impact of muonic atoms spectroscopy on few-nucleon theories will be extended by the planned measurement of the muonic helium Lamb shift. This will improve by an order of magnitude the helion and alpha-particle radius values to a relative accuracy of 3 × 10−4 .
Experimental setup, measurements and results will be presented. Additionally the key issues regarding the observed discrepancy will be given together with the impacts of these measurements on bound-state QED tests and fundamental constants. Moreover the importance and the confrontation with the new Mainz scattering results will be discussed.