Muonic Hydrogen Size Still Smaller Than Expected

Muonic hydrogen protons still appear smaller than ordinary hydrogen protons.

In 2010, scientists published the results of an experiment showing that "the size of the proton (to be precise, its charge radius), measured in exotic hydrogen, in which the electron orbiting the nucleus is replaced by a negatively charged muon, yielded a value significantly smaller than the one from previous investigations of regular hydrogen or electron-proton-scattering. A new measurement published this year by the same team confirms the value of the electric charge radius" by a different method that is 1.7 times more precise than the previous measurement and that can ultimately be made even more precise. (The pre-print of the ultimate source is here).

The standard value of the electric charge proton radius determined from ordinary hydrogen was 0.862(12) fm, as of 1999 based on a 1980 measurement, about two and a half percent larger than the most recent measurement just announced for the electric charge proton radius in muonic hydrogen which is 0.84087(39) fm. 

While the measured magnetic radius is closer to the old ordinary hydrogen measurement, it is so imprecise that it is currently irrelevant to resolving the true size of the proton. "The new measurement also allows a determination of the magnetic radius of the proton for the first time by laser spectroscopy of muonic hydrogen. This results in a value of 0.87(6) femtometres, in agreement with all previous measurements."  The magnetic radius measurement, however, is sufficiently imprecise that it is consistent with both the old canonic ordinary hydrogen measurement and the new muonic hydrogen measurement - both results are less than half of a standard deviation away from the new magnetic radius measurment. 

The muon hydrogen experiment involved medium budget experiments as opposed to super-expensive experiments like the Large Hadron Collider that requires a cast of thousands of scientists and billions of dollars of hardware to conduct. 

This makes it a remarkable value because it is an independent tool that could point to possible beyond the Standard Model physics. 

Alternately, this experiment could confirm the Standard Model and dramatically increase the experimental accuracy of a constant that can be used to add precision to other QCD measurements such as the value of the strong force coupling constant. The strong force coupling constant is the least accurately known of the Standard Model coupling constants by many orders of magnitude (the uncertainty is about 0.6%) and the uncertainty in this experimentally measured constant accounts for a large share of the uncertainty, for example, in the theoretically predicted value of the proton mass from QCD first principles (which is about 1%).

What could explain the result?

Nothing in the Standard Model explains how a lepton orbiting a proton could change the size of the proton it orbits.

In the Standard Model, the orbits of both the electron and the muon around a single proton are governed exclusively by quantum electrodynamics, which has the most accurately determined theoretical calculations and most precisely determined experimental constants, and the electric charge radius of the proton.  Each of the relevant physical constants (other than the electric charge radius of the proton) is known to a one part per ten million accuracy or more.

Hydrogen consists of a single positively charged proton orbited by a negatively charged electron, a model whose success in explaining spectroscopy data dates back to its proposal by Bohr in 1913. The energy levels of this simplest of atoms can be predicted with excellent precision from the theory of quantum electrodynamics. However, the calculations have to take into account that -- in contrast to the point-like electron -- the proton is an extended object with a finite size, made of three quarks bound by so-call 'gluons'. Therefore, the electric charge as well as the magnetism of the proton is distributed over a certain volume. The extended nature of the proton causes a shift of the energy levels in hydrogen. Hence the electric and the magnetic charge radii can be deduced from a measurement of the level shifts. . . .

Muons behave a lot like electrons, except for their mass: muons are 200 times heavier than electrons. The atomic orbit of the muon is therefore much closer to the proton than the electron's orbit in a regular hydrogen atom. This results in a much larger sensitivity of the muon's energy level to the proton size and hence to a stronger shift of the energy levels.

So, what could be going on?  As the article linked above explains:

Physicists around the world are actively seeking a solution to the proton size puzzle. Previous measurements in regular hydrogen and by electron-proton-scattering are being reanalyzed and even repeated. Theorists of various disciplines suggested ways to explain the discrepancy. Very interesting proposals explain the discrepancies by physics beyond the standard model. Other explanations suggest a proton structure of higher complexity than assumed today which only reveals itself under the influence of the heavy muon.

According to the paper's authors the main possibilities that could cause the observed discrepencies are that:

* The electronic hydrogen experiments are almost, but not quite, as accurate as stated,
* The QED calculations are almost, but not quite, as accurate as stated,
* The two photon exchange term that depends on proton polarizability has not been correctly evaluated [this involves an intersection between QED and QCD effect: "The computer effect of this term is proportional to the lepton mass to the fourth power, and so is capable of being relevant for muonic atoms, but irrelevant for electronic atoms.], and/or
* The electron and muon really do have different interactions with the proton, so that there is physics beyond the Standard Model.

None of these possibilities seem very likely, but all must be pursued.
 

Any combination of the first three answers, of course, is boring, but collectively, those possibilities are much more likely than the last one.  The first two possiblities are entirely boring, the third is of interest only to true physics junkies, and the last could profoundly change the course of physics for decades to come.

Experimental Error In The Proton Radius Measured In Ordinary Hydrogen

One boring possibility is that measurements of the proton radius in an ordinary hydrogen atom are simply old, are far less precise than those with muonic hydrogen (something inherent in the lower mass of the electron), have understated error bars, and are slightly inaccurate.  If so, more accurately remeasured proton radius in ordinary hydrogen atoms conducted with state of the art modern equipment and QED calculations will match the muonic hydrogen result.

The central value of the canonical measurement of the electric charge radius of protons in ordinary hydrogen is 54 sigma different from the muonic hydrogen radius, a clearly inconsistent result.  But,  the central value of the muonic hydrogen based estimate of the proton radius is only about 1.75 sigma from the central value of the measurement made in 1980 which were still the best available as of 1999  (and even as of 2005).  Thus, the possibility that the difference is simply due to experimental error in the inherently less accurate measurement of the proton radius in ordinary hydrogen is very plausible. 

After all, the whole point of measuring the proton radius with muonic hydrogen was to get getter precision in this measurement relative to the ordinary hydrogen based measurement which was known to be not very precise.  Only no one had expected the ordinary hydrogen results to be so far off.

A review of the source data for the canonical ordinary hydrogen proton radius measurement in the new paper using the latest data available in 2013 from hydrogen spectroscopy, which includes eight new post-1980 data points developed from 2003 through 2011, states that:

From Fig. 2 one can observe that all rpvalues from H favor a larger rp around 0.88 fm. Still, half of the individual rp values agree with the muonic hydrogen value of 0.84 fm on the level of 1 sigma. In fact, only the 2S-8D5/2 transition disagrees with the muonic rp value on the level of 3 sigma. The discrepancy between the combined value from H, as obtained in the elaborate CODATA adjustment of the fundamental constants, and the muonic hydrogen value, is about 4.4 sigma.

The new paper summarizes also ordinary hydrogen proton radius estimates from another indepedent method (electron-proton scattering) from the results summarized in the blockquote above at:

rp = 0.879 fm +/- 0.005stat +/- 0.004syst +/- 0.002model +/- 0.004group,

adding up the errors in quadrature, the combined error estimate is about +/- 0.0078 fm, which is about 4.6 sigma away from the muonic hydrogen measurement.

There is currently one experiment in the works (scheduled for 2014-2015) to make a more precise measurement based on electron-proton scattering called Jefferson Lab E12-11-106, but it will have to be conducted with technical virtuosity just barely within the capabilities of the relevant equipment to produce a sufficiently precise result to improve on the results from the experiments done from 2003 to 2011.  Six new experiments are in progress to make more precision measurments of proton size in ordinary hydrogen using spectroscopy.

A muon-proton scattering experiment called MUSE at PSI is also in the works.  This experiment could be conducted by 2016 is the necessary $2 million of funding can be secured.

These two kinds of scattering experiments are particularly helpful in evaluating whether the proton polarizability term in the calculation of the proton electric charge radius from spectroscopy measurements have been correctly evaluated, thus, either implicating or ruling out on of the four most plausible explanations for the discrepency in proton size measurements between ordinary hydrogen and muonic hydrogen.

Spectroscopy experiments have also been contemplated with exotic synthetic "atoms" such as positronium (hydrogen atoms in which a positron is substituted for the proton), muonium (hydrogen atoms in which an anti-muon is substituted for the proton), muonic deuterium (heavy hydrogen atoms with muons instead of electrons rotating around them), muonic helium-3, and muonic helium-4, muonic lithium ions, muonic berylium ions, and muonic boron ions. Apparently, it is not feasible to conduct tests on tauonic hydrogen because taus (i.e. third generation electrons) are so short lived relative to muons.

Failure To Consider Material But Non-Obvious Factors In The Muonic Hydrogen Experiment 

Another boring possibility is that experimenters doing the theoretical calculations of the electric charge and magnetic charge radius in the muonic hydrogen experiments have overlooked a material adjustment that must be made, for example, for the electro-magnetic fields of neighboring muonic hydrogen atoms or special relativistic effects.

Similar issues gave rise to the only recently resolved Pioneer anomoly that showed an apparent discepency between the law of gravity and this space probe's actual course until adjustments for a previously unaccounted for factor related the thermal effects from the probe's power source were used to adjust the theoretically predicted trajectory.

Beyond The Standard Model Physics Explanations

But, any beyond the Standard Model physics that could emerge from this measurement would be entirely unexpected and point the way towards theoretical directions far removed from the vast majority of theoretical work in the last few decades.  It could, for example, be experimental evidence of quantum gravity effects, unexpected internal structure in quark-gluon model of the proton that could modify QCD, or even some previously unknown force. 

The biggest indicator that there could be non-Standard Model aspects to muon behavior is that the "experimental value of the muon anomalous magnetic moment exceeds the Standard Model expectation by more than three sigma." The discrepency between the theoretically predicted value of the muon anomalous magnetic moment and the experimentaly measured value is still only about one part per fifty million, however, and this could easily arise from something as subtle as some slight overconfidence in estimating margins of error. Data from tau physics experiments favor a smaller discrepency.  (More background discussion can be found here). 

At least five other sets of experimental data, in addition to the muon anomalous magnetic moment constrain modifications of the Standard Model that would given the muon properties other than mass that differ from those of an electron.

The 2013 paper discusses five ideas for beyond the Standard Model physics that could account for the results while not being inconsistent with the experimental data.  But, existing experimental data rule out "plain vanilla" forces mediated by bosons of spin 0 (scalar fields like that of the Higgs boson), spin 1 (vector fields like those of photons, W and Z bosons and gluons), or spin 2 (tensor fields like that of the hypothetical graviton) that couple to muons and nucleons but not to electrons, and which have equal couplings to muoons and to nucleons (both of which have the same electromagnetic charge).  Experimental data also rule out even more elaborate scalar fields.

Among the possible results would be a MeV mass force carrier that couples to both muons and nucleons but has different coupling constants for each.  A 30 MeV mass heavy photon that interacts with right handed neutrinos has been considered but is highly constrained (i.e. basically disfavored) by current experimental results.  Another set of models looks at two extra force carrier particles that are quite different in kind from one another - one that gives rise to an effect even bigger than the anomalous results observed and another which suppresses these effects in circumstances other than the ones in which the anomalous effects are observed.  Yet another possibility is a very short range force that modifies electromagnetic interactions (i.e. Coulomb forces) at short ranges where muons orbit, but not at longer ranges where electrons orbit.

Bottom Line

By far the mostly likely possibility is that the temptest in a teapot within the physics commuity over the different measured sizes of the proton in ordinary hydrogen and in muonic hydrogen respectively, will be resolved by finding in a more careful analysis that physicists measuring the quantity in ordinary hydrogen were overconfident in their estimates and calculations, or made a slight miscalculation of one difficult to evaluate term in their calculation.

But, since this data point and another one related to muons presents a possibility that it could reveal new physics at a tiny fraction of the cost of LHC experiments which currently seem far less likely to do so, this issues deserves the funding necessary to answer the question.