Chiral effective-field theory with a resonance and heavy fields

Several conceptual points concerning the inclusion of the $Δ$(1232) resonance in the framework of chiral effective-field theory are discussed, with an emphasis on the problem of power counting in the baryon sector in general. I also formulate a new dispersion relation in the pion-mass squared (or, the quark mass) and make a link between the power counting and the analytic properties of chiral expansion. A controversy regarding the determination of the proton's magnetic polarizability from Compton-scattering data is stressed here as well.

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