Including the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1232</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>resonance in baryon chiral perturbation theory

Baryon chiral perturbation theory with explicit $\ensuremath{\Delta}(1232)$ degrees of freedom is considered. The most general interactions of pions, nucleons, and \ensuremath{\Delta} 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 \ensuremath{\sigma} term, and the pole of the \ensuremath{\Delta} propagator.

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