Proton radius puzzle

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The proton radius puzzle is an unanswered problem in physics that relates to several experiments that measured a changed radius of a proton after an electron and electric charge change.


The known and officially recorded radius of a proton is (8.8±0.1)×10−16 m (or 0.88±0.01 fm), for an approximately 1% relative uncertainty. In 2010, Pohl et al. conducted an experiment in order to refine this measurement and obtain a more precise radius. Their study involved forming muonic hydrogen by replacing the electron in the atom with a muon. This was done because the much higher mass of a muon causes it to orbit much closer than an electron to the hydrogen nucleus (a single proton), where it is consequently much more sensitive to the size of the proton. The resulting radius was recorded as 0.842±0.001 fm, more than 5 standard deviations away from the prior measurements. The experiment does not directly measure the physical size of the radius, but rather an energy difference between two separate energy levels of the atom, known as the Lamb shift, which is sensitive to the radius.[1][2] The newly measured radius is 4% smaller than the prior measurements, which were expected to be accurate within 1%. The new uncertainty limit of only 0.1% makes a negligible contribution to this discrepancy.[3]

A followup experiment by Pohl et al. in August 2016 used a deuterium atom to create muonic deuterium and measured the deuteron radius. This experiment allowed the measurements to be 2.7 times more accurate, but also found a discrepancy of 7.5 standard deviations smaller than the expected value.[4]

Proposed resolutions[edit]

In 2012, Karr and Hilico attempted to explain the energy difference in the puzzle using the three-body force, but found through calculations that the ions involved did not bind tightly enough to explain the change in energy.[5]

In 2013, Onofrio suggested that the unknown effect may be the result of quantum gravity based on interactions between gravity and the weak force. This would result in a higher binding energy in the nucleus, decreasing the energy difference within it. Onofrio noted that while the energy difference for atomic hydrogen would be two orders of magnitude smaller, it should still be possible to detect it. Otherwise, the inability to detect the difference may be due to a flavour-dependent interaction.[6][2]

In August 2016, Dahia and Lemos proposed that gravity in higher dimensions is the cause. This relates to models based on brane cosmology where the effects of gravitational potential are amplified across shorter distances far more than in Newtonian physics.[7]

A month later in September, a new boson was proposed by Yu-Sheng, McKeen and Miller to resolve both the proton radius puzzle and the muon's anomalous magnetic dipole moment problem.[8]

Randolf Pohl, the original investigator of the puzzle, stated that while it would be "fantastic" if it led to a new discovery, the "most realistic thing is that it’s not new physics". He stated that his personal assumption is that past measurements have misgauged the Rydberg constant and that the official proton size for hydrogen is inaccurate.[9]


  1. ^ Pohl R, et al. (2010). "The size of the proton". Nature. 466 (7303): 213–216. Bibcode:2010Natur.466..213P. doi:10.1038/nature09250. PMID 20613837. 
  2. ^ a b Zyga, Lisa (November 26, 2013). "Proton radius puzzle may be solved by quantum gravity". Retrieved September 2, 2016. 
  3. ^ Carlson CE (2015). "The proton radius puzzle". Progress in Particle and Nuclear Physics. 82: 59–77. arXiv:1502.05314Freely accessible. Bibcode:2015PrPNP..82...59C. doi:10.1016/j.ppnp.2015.01.002. 
  4. ^ Pohl R, et al. (2016). "Laser spectroscopy of muonic deuterium". Science. 353 (6300): 669–673. Bibcode:2016Sci...353..669P. doi:10.1126/science.aaf2468. 
  5. ^ Karr J, Hilico L (2012). "Why Three-Body Physics Does Not Solve the Proton-Radius Puzzle". Physical Review Letters. 109 (10): 103401. arXiv:1205.0633Freely accessible. Bibcode:2012PhRvL.109j3401K. doi:10.1103/PhysRevLett.109.103401. 
  6. ^ Onofrio R (2013). "Proton radius puzzle and quantum gravity at the Fermi scale". EPL. 104 (2): 20002. arXiv:1312.3469Freely accessible. Bibcode:2013EL....10420002O. doi:10.1209/0295-5075/104/20002. 
  7. ^ Dahia F, Lemos AS (2016). "Is the proton radius puzzle evidence of extra dimensions?". European Physical Journal. 76 (8): 435. arXiv:1509.08735Freely accessible. Bibcode:2016EPJC...76..435D. doi:10.1140/epjc/s10052-016-4266-7. 
  8. ^ Liu Y, McKeen D, Miller GA (2016). "Electrophobic Scalar Boson and Muonic Puzzles". Physical Review Letters. 117 (10): 101801. arXiv:1605.04612Freely accessible. Bibcode:2016PhRvL.117j1801L. doi:10.1103/PhysRevLett.117.101801. 
  9. ^ Wolchover, Natalie (August 11, 2016). "New Measurement Deepens Proton Puzzle". Quanta Magazine. Retrieved September 2, 2016.