Basics

Atoms, muons, and nuclear size

The hydrogen atom is the simplest of all atoms: it consists of a single proton which is orbited by a single electron. Electrons are negatively charged and protons carry postive charge. Opposite charges attract each other, that's why hyrogen atoms exist!

The electron is - as far as we know - a point-like elementary particle. The proton, however, is a compound object made from quarks and gluons. Hence the proton is an extended object - it has a diameter.

In muonic hydrogen, the electron is replaced by its 200 times heavier brother called muon: µ. The 200 times larger mass of the muon causes the muon to orbit a proton about 200 times closer, compared to the electron in regular hydrogen.

Muons and electrons can orbit their proton in different orbits. A special kind of orbit are the so-called S-states. Muons in these S-states actually spend some of their time inside the proton! Inside the proton the muon sees only a reduced electric charge of the proton, which leads to a reduced attraction between a muon in an S-state and it's proton.

And here is the deal:
The larger the proton is, the less bound is the muon.

That's why we use laser spectroscopy to determine the position, i.e. the binding energy of the 2S state in muonic hydrogen (and in muonic deuterium and helium ions, which are all "a positively charged nucleus orbited by a single negative muon").
From this we deduce the proton charge radius. It is 0.84087 +- 0.00039 fm. This is 4% smaller than the previously accepted value from hydrogen spectroscopy and electron-proton scattering. This discrepancy is now called the proton radius puzzle.