Baryon chiral perturbation theory with explicit $\Delta (1232)$ degrees of freedom is considered. The most general interactions of pions, nucleons, and Δ consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon σ term, and the pole of the Δ propagator.

• Received 24 May 2005

DOI:https://doi.org/10.1103/PhysRevC.72.055203