We study the axial amplitudes for the N-∆ transition in models with quarks and chiral mesons. A set of constraints on the pion field is imposed which enforces PCAC and the off-diagonal Goldberger-Treiman relation. The quark contribution to the amplitudes in general strongly underestimates the C A 5 amplitude as well as the πN∆ strong coupling constant. We show that the results are considerably improved in models that, in addition to the pion cloud, incorporate a fluctuating σ field inside the baryon.

The multipole amplitudes for the N-⌬(1232) electromagnetic transition are computed in the framework of the linear model and the chiral chromodielectric model for small and moderate photon virtualities. The models include quark and meson degrees of freedom and the nucleon and the ⌬ are clusters of three valence hedgehog quarks surrounded by meson clouds described by coherent states. Angular momentum and isospin projections are performed to endow model states representing the nucleon and the ⌬ with proper quantum numbers. Recoil corrections involved in the process ␥ v N→⌬ are taken into account by performing linear momentum projection of the initial and final baryon states. The ratios E2/M 1 and C2/M 1 are in good agreement with the data in the two models, but the magnetic amplitude is better reproduced in the linear model. The ratios show little dependence with the model parameters. Both in the linear model and in the chromodielectric model the charged pions are responsible for the nonvanishing quadrupole-electric and -Coulomb amplitudes. The recoil corrections enhance the results obtained for the amplitudes without linear momentum projection, improving the comparison with experimental data. The dependence of the theoretical amplitudes with the choice of the reference frame is also studied.

Abstract. We present a method to calculate directly the K matrix for the pion electro-production processes in the framework of chiral quark models which allows for a clean separation of the resonant amplitudes from the background. The method is applied to the calculation of the multipole amplitudes M1+, E1+, and S1+ in the ∆ channel within the Cloudy Bag Model. A good overall description is found in a broad energy range.