In this case, the research team had some lasers poised to go off, waiting on a trigger provided by a muon detector. As soon as the muonic hydrogen was likely to be present, the lasers fired, allowing spectroscopic measurements of this atom. Because of the muon's (relatively) large mass, these measurements provided very precise values for some of the basic properties of the protons they were orbiting. The researchers also measured two different energy level transitions, allowing them to get a second set of independent values.
Both of them placed the proton's radius at 0.84fm. That may not seem like a huge difference, but the high precision meant that there was very little statistical error. So little, in fact, that the value they calculate is about seven standard deviations (or seven sigma) out from the value obtained by the other methods.
The quantization ratio of the muon is different, and the impedance of light in free space is a ratio of the quant ratios between the electron and the magnetic, it is not a direct property of the vacuum. Fire light at a muon atom and the light couples with the muon quant ratio, the frequency of light will change. In Maxwell, the rate of change of electro to magnetic makes the light move at c. Fire that light into a muon region, the electro couples with the muon quant rate, the impedance of the light rises, the light both changes frequency a bit higher and straightens along the charge wave of the muon.
Our world does not pack magnetic nulls, but the magnetic wave number is still fixed relative to the atom. Hence we get a constant 377 for the impedance of free space. The muonic atom is not the electron atom.
Make the corrections for coupling and the numbers will come out right.
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