Electromagnetic corrections in hadronic processes

In many applications of chiral perturbation theory, one has to purify physical matrix elements from electromagnetic effects. On the other hand, the splitting of the Hamiltonian into a strong and an electromagnetic part cannot be performed in a unique manner, because photon loops generate ultraviolet divergences. In the present article, we propose a convention for disentangling the two effects: one matches the parameters of two theories - with and without electromagnetic interactions - at a given scale mu(1), referred to as the matching scale. This method enables one to analyse the separation of strong and electromagnetic contributions in a transparent manner. We first study in a Yukawa-type model the dependence of strong and electromagnetic contributions on the matching scale. In a second step, we investigate this splitting in the linear sigma model at one-loop order, and consider in some detail the construction of the corresponding low-energy effective Lagrangian, which exactly implements the splitting of electromagnetic and strong interactions carried out in the underlying theory. We expect these model studies to be useful in the interpretation of the standard low-energy effective theory of hadrons, leptons and photons.