The Lamb shift in muonic hydrogen and the proton radius from effective field theories

We comprehensively analyse the theoretical prediction for the Lamb shift in muonic hydrogen, and the associated determination of the proton radius. We use effective field theories. This allows us to relate the proton radius with well-defined objects in quantum field theory, eliminating unnecessary model dependence. The use of effective field theories also helps us to organize the computation so that we can clearly state the parametric accuracy of the result. In this paper we review all (and check several of) the contributions to the energy shift of order $\alpha^5$, as well as those that scale like $\alpha^6\times$logarithms in the context of non-relativistic effective field theories of QED.