Phys. Rev. C 99, 035202 (2019)

Even though Ernest Rutherford discovered the proton more than a hundred years ago, some of its properties still remain a mystery. The radius of the proton, commonly defined via the proton’s three-dimensional charge density, is one of them. The proton radius measured from hydrogen spectroscopy and electron­–proton scattering experiments is about 0.88 fm, whereas spectroscopy of muonic hydrogen atoms reveals a radius of 0.84 fm. The origin of this small difference of 4% remains unclear.

Now, Gerald Miller has argued that the quarks and gluons inside the proton behave relativistically, and that any measurement of the proton will change the proton’s interior wave function, making the definition of a three-dimensional charge density impossible. Based on a two-dimensional charge density, the proton radius is defined as a measure of the interaction between a photon and one of the charged constituents of the proton. This means that both experiments refer to the same quantity when they measure the proton radius.