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Itay Yavin on the New Size of the Proton

July 22, 2013

[Recent research has determined the size of the proton to be smaller than previously thought and has prompted much discussion among scientists. Itay Yavin of the Department of Physics and Astronomy is among the contributors to the field and offers his thoughts on the situation.]

A simple question one might ask is "How big is the proton"?

The proton is a positively charged particle that make up the nucleus of hydrogen and other atoms (together with the neutron). The proton has a finite size, but it is much much smaller than the atom itself. If the atom was the size of a human, the proton would be a little less than the width of human hair. So, how can you measure the size of something so incredibly small?

Two methods are commonly used [1]. The first method extracts the proton radius from a careful measurement of the energy levels of hydrogen. Hydrogen, which is made of a bound state of a proton and an electron, has discrete energy levels whose precise value is determined by quantum electrodynamics, the theory that governs electromagnetic interactions at the quantum level. The finite size of the proton means that its charge is spread over some finite volume and hence the force it exerts on the electron is somewhat diminished. This minuscule effect can be measured through a precise determination of the different in energy levels of normal hydrogen.

The second method commonly used is to scatter free electrons on free protons. One then measures how the electrons deflect following the scattering. The distance scales the electrons can probe in this way are determined by their quantum wavelength (their de-Broglie wavelength), which is controlled by their energy. By observing the scattering process at higher and higher energies, one can probe very short distances. This way, it is possible to observe the structure of the proton's charge distribution and in particular its charge radius.

For a long while, these two methods of extractions have yielded comparable results consistent within the experimental uncertainty. Then in 2010 a group at PSI, Switzerland lead by Randolf Pohl announced a new measurement of the proton radius using muonic hydrogen which differed by six standard deviations from the world average obtained with the old methods [2]. This was very surprising and unexpected and indicated a statistically significant discrepancy between the new measurement and the old ones. But, what on earth is muonic hydrogen?

Muonic hydrogen is basically normal hydrogen, but where the electron is replaced by a muon. Muons are unstable elementary particles that carry the same charge as the electron, but are 200 times heavier and are unstable. Muonic hydrogen is a bound system since the proton and muon attract and so it has discretized energy levels similar to hydrogen. But, because the muon is 200 times heavier than the electron, its orbit is 200 times smaller than that of the electron in normal hydrogen. It can feel the charge distribution of the proton much more sensitively because it orbits a lot closer. Therefore, the effects of the finite size of the proton on the energy levels of muonic hydrogen are much more noticeable as compared to normal hydrogen. The hope was that this measurement will yield a more precise determination of the proton radius. This hope was realized, but with a twist. The more precise value turned out to be in disagreement with previous measurements!

So, what gives? How can these conflicting measurements be reconciled? There have been several attempts at a resolution, but no convincing explanation has emerged so far. One of these attempts was made in 2011 when, together with David Tucker-Smith, I published a short paper showing that this discrepancy can be the result of a new force of nature that results in a slightly stronger attraction between muons and protons [3]. Interestingly, this new force could also explain the long-standing discrepancy in the measurement of the muon's gyromagnetic ratio. Both anomalies might be the result of a new, very weak force that perturbs muons. This proposal is not without its problems. Most importantly, it is not clear how to reconcile this new force with the other forces and symmetries of the Standard Model of particle physics.

As it stands the situation is still very confusing. It will take more experiments and more thought before we have a clearer picture of what is behind the discrepancy between the different ways of measuring the proton's radius. This story of the proton radius' puzzle was recently featured in an article in the popular science magazine New Scientist [4].

[1] R. Pohl et al, Annu. Rev. Nucl. Part. Sci. Vol 63 (2013)
[2] R. Pohl et al, Nature 466:213 (2010)
[3] D. Tucker-Smith and I. Yavin, Phys. Rev. D83:101702 (2011)
[4] J. Cartwright, ``Honey, I shrunk the proton,'' New Scientist, 2926 (2013)