Chiral structure of the Lamb shift and the definition of the proton radius

The standard definition of the electromagnetic radius of a charged particle (in particular the proton) is ambiguous once electromagnetic corrections are considered. We argue that a natural definition can be given within an effective field theory framework in terms of a matching coefficient. The definition of the neutron radius is also discussed. We elaborate on the effective field theory relevant for hydrogen and muonic hydrogen, especially for the latter. We compute the hadronic corrections to the Lamb shift (for the polarizability effects only with logarithmic accuracy) within heavy-baryon effective theory. We find that they diverge in the inverse of the pion mass in the chiral limit.