Muonic Hydrogen and Dark Forces

The measurement of the Lamb shift in the muonic hydrogen has echoed on blogs and elsewhere. Briefly, an experiment at the Paul Scherrer Institute (PSI) measured the energy difference between 2S(1/2) and 2P(3/2) energy levels of an atom consisting of a muon orbiting a proton. Originally, this excercise was intended as a precise determination of the charge radius (that is the size) of the proton: in the muonic hydrogen the finite proton size effect can shift certain energy levels by order one percent, much more than in the ordinary hydrogen, while other contributions to the energy levels are quite precisely known from theory. Indeed, the PSI measurement of the proton charge radius is 10 times more precise than previous measurements based on the Lamb shift in the ordinary hydrogen and on low-energy electron-proton scattering data. Intriguingly, the new result is inconsistent with the previous average at the 5 sigma level.

As usual, when an experimental result is inconsistent with the standard model prediction the most likely explanation is an experimental error or a wrong theoretical calculation. In this particular case the previous experimental data on the proton charge radius do not seem to be rock-solid, at least to a casual observer. For example, if the charge radius is extracted from electron–proton scattering the discrepancy with the PSI measurement becomes only 3.1 sigma;
the PSI paper also quotes another recent measurement that is completely consistent with their result within error bars.

In any case, whenever a discrepancy with the standard model pops up, particle theorists cannot help thinking about new physics explanations. Our folk is notorious for ambulance chasing, but actually this is one of these cases when the ambulance is coming straight at us. Recently the particle community has invested a lot of interest in studies of light, hidden particles very weakly coupled to the ordinary matter. One example is the so-called dark photon: an MeV-GeV mass particle with milli-charge couplings to electrons and muons. This idea is pretty old, but in the past 2 years the interest in dark photons was boosted because their existence could explain certain astrophysical anomalies (Pamela). The signals of dark photons and other hidden particles are now being searched for at the Tevatron, LHC, B-factories, and in dedicated experiments such as ALPS at DESY, or APEX that is just kicking off at JLAB. No signal has been found in these experiments yet, but there is still a lot of room for the dark photon as long as its coupling to electrons and muons is $\epsilon \leq 10^{-3}$ smaller than that of the ordinary photon, see the picture borrowed from this paper. The news of the muonic Lamb shift came somewhat unexpectedly...but not to everyone: here is a passage from a 2-years old paper:

For example, the dark photon contribution to the electron-proton scattering amplitude at low momenta is equivalent to the $6 \epsilon^2 /m_A^2$ correction to the proton charge radius (...) It remains to be seen whether other precision QED tests (e.g. involving muonic atoms) would be able to improve on the current constraints.

So here we are. In the coming weeks we should see whether there exist concrete models capable of fitting all data. In any case, a new front in the battle against dark forces has just been opened. Now, could someone make us a muonium?