People try to calculate the value of the radius of the regular proton by going through the energies of the transitions within atoms. But it is very difficult to find the transition that is directly related to the radius of the hydrogen electron because it seems that there is no exact theory about it yet.

So would a good theory about quantum gravity explain the radius of a subatomic particle including the radii of the neutron and the proton?

Our preprints on RG consider for example that the small radius of the proton of muonic hydrogen is directly related to the radius of the neutron and not directly related to the radius of the proton.

So when people are working with muonic hydrogen they have to take into consideration that the muon redraws the charge distribution of the regular proton by making it smaller than its natural value. What people then measure is not at all the natural value of the proton radius (eg. 0.8758 fm) but another value much lower (eg. 0.84087 fm).

A small proton radius is, according to our theory, obtained by a redistribution of the regular proton charge making this distribution lower than normal due to the effect of the muon. According to us the muon interferes with the Higgs field. According to us the Higgs field keeps the natural proton charge distribution normal.