We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the ∆(1232) in a systematic formalism which we call the "small scale expansion".

We study the low energy expansion of the nucleon's electroweak form factors in the framework of an effective chiral Lagrangian including pions, nucleons and the $Delta (1232)$. We work to third order in the so-called small scale expansion and compare the results with the ones previously obtained in the chiral expansion. In addition, these calculations serve as a first exploratory study of renormalization and decoupling within the small scale expansion.Comment: 21 pp, RevTeX, uses epsf, 4 figs, minor corrections, accepted for publication in Nucl.Phys.

We present a projector formalism which allows to define dynamical polarizabilities of the nucleon from a multipole expansion of the nucleon Compton amplitudes. We give predictions for the energy dependence of these dynamical polarizabilities both from dispersion theory and from leading-one-loop chiral effective field theory. Based on the good agreement between the two theoretical frameworks, we conclude that the energy dependence of the dynamical polarizabilities is dominated by chiral dynamics, except in those multipole channels where the first nucleon resonance ∆(1232) can be excited. Both the dispersion theory framework and a chiral effective field theory with explicit ∆(1232) degrees of freedom lead to a very good description of the available low energy proton Compton data. We discuss the sensitivity of the proton Compton cross section to dynamical polarizabilities of different multipole content and present a fit of the static electric and magnetic dipole polarizabilities from low-energy Compton data up to ω ∼ 170 MeV, findingᾱ E = (11.04 ± 1.36) · 10 −4 fm 3 ,β M = (2.76 ∓ 1.36) · 10 −4 fm 3 .