Δ(1232)and the polarizabilities of the nucleon

Previous calculations of the polarizabilities of the nucleon within the framework of heavy baryon chiral perturbation theory have included the contribution of the $\Delta$(1232) only its effect on various contact terms or have been performed in chiral SU(3) where systematic errors are difficult to control. Herein we perfrom a corresponding calculation in chiral SU(2) wherein $\Delta$(1232) is treated as an explicit degree of freedom and the expansion is taken to third order in soft momenta, the pion mass and the quantity $M_\Delta-M_N$, collectively denoted by $\epsilon$. We present the results of a systematic $O(\epsilon^3)$ calculation of forward Compton scattering off the nucleon, extract the electric polarizability $\bar{\alpha}_E$, the magnetic polarizability $\bar{\beta}_M$ and the spin polarizability $\gamma$ and compare with available information from experiments and from previous calculations. Concluding with a critical discussion of our results, we point out the necessity of a future $O(\epsilon^4)$ calculation.Comment: 36 page standard latex file plus 4 figure