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A new confirmation of the muonic value of the proton radius

Accurate knowledge of the radius of the proton is essential, not only for understanding its structure. Thus, the study of the hydrogen atom has been at the heart of the development of modern physics.

In 2013, this radius was extracted from the laser spectroscopy of muonic hydrogen (μp). A muonic hydrogen is a proton orbited by a muon which is elementary subatomic particle similar to the electron but 207 times heavier. It was one breakthrough when the result showed a value for the proton charge radius that was significantly smaller, by four standard deviations, than previous determinations using regular hydrogen. This discrepancy and its origin have attracted much attention in the scientific community, with implications for the so-called Standard Model of physics.

Since then, the proton charge radius rp has been under debate because the very accurate value from laser spectroscopy of the exotic muonic hydrogen atom (µp) small. This accuracy of the muonic radius result is enabled by the fact that the muon’s orbit is ~200 times smaller than the electron’s orbit in H, resulting in a seven orders of magnitude larger influence of rp on the energy levels.

The CODATA value is obtained from a combination of 24 transition frequency measurements in H and deuterium and several results from elastic electron scattering.


This year, a new measurement was done on the proton radius using a cryogenic beam of H atoms. The team of Prof. Thomas Udem measured the 2S-4P transition frequency in H, yielding the values of the proton radius rp = 0.8335(95) femtometer. Their value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the muonic value and with the holographic mass solution proposed by Nassim Haramein in 2012.

"Our measurement is almost as precise as all previous measurements on regular hydrogen combined. We are in good agreement with the values from muonic hydrogen, but disagree by 3.3 standard deviations with the hydrogen world data, for both the Rydberg constant and the proton radius. To find the causes of these discrepancies, additional measurements with perhaps even higher precision are needed. After all, one should keep in mind that many new discoveries first showed up as discrepancies."

Prof. Thomas Udem, Max Planck Institute, Germany

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