The $\mathrm{\Delta }(1232)$ as an Effective Degree of Freedom in Chiral Perturbation Theory

Heavy baryon chiral perturbation theory including spin 3/2 delta resonances as effective degrees of freedom is reviewed. The theory admits a systematic expansion in the small scale $ϵ$, where $ϵ$ collectively denotes soft momenta, the pion mass or the delta-nucleon mass difference. Renormalization is discussed in some detail on the example of the scalar sector of one-nucleon processes, and a reformulation of the principle of resonance saturation for counterterms of the HBChPT lagrangian is sketched. As an application, the polarizabilities of the nucleon are discussed at order ${ϵ}^3$.