Electromagnetic corrections in hadronic processes

In quantum field theory, the splitting of the Hamiltonian into a strong and an electromagnetic part cannot be performed in a unique manner. In the present article, we propose a convention for disentangling these two effects: one matches the parameters of two theories – with and without electromagnetic interactions – at a given scale μ1, referred to as the matching scale. This method enables one to analyze the separation of strong and electromagnetic contributions in a transparent manner. We first study in a Yukawa model – supplemented with electromagnetic interactions – the dependence of strong and electromagnetic contributions on the matching scale. In a second step, we investigate this splitting in the linear sigma model (in the presence of virtual photons) 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. Pacs: 11.10.Hi, 11.30.Rd, 12.39.Fe,13.40.Dk,13.40.Ks