ar X iv : n uc l - ex / 0 70 10 24 v 1 1 6 Ja n 20 07 Accuracy of Extracted Multipoles from γ ∗ N → ∆ Data

This work evaluates the model dependence of the electric and Coulomb quadrupole amplitudes (E2, C2) in the predominantly M1 (magnetic dipole-quark spin flip) γ * N → ∆ transition. Both the model-to-model dependence and the intrinsic model uncertainties are evaluated and found to be comparable to each other and no larger than the experimental errors. It is confirmed that the quadrupole amplitudes have been accurately measured indicating significant non-zero angular momentum components in the proton and ∆. Experimental confirmation of the presence of non-spherical hadron amplitudes (i.e. d states in quark models or p wave π-N states) is fundamental and has been the subject of intense experimental and theoretical interest (for reviews see [1, 2, 3]). This effort has focused on the measurement of the electric and Coulomb quadrupole amplitudes (E2, C2) in the predominantly M1 (magnetic dipole-quark spin flip) γ * N → ∆ transition. Since the proton has spin 1/2, no quadrupole moment can be measured. However, the ∆ has spin 3/2 so the γ * N → ∆ reaction can be studied for quadrupole amplitudes in the nucleon and ∆. Due to spin and parity conservation in the γ * N(J π = 1/2 +) → ∆(J π = 3/2 +) reaction, only three multipoles can contribute to the transition: the magnetic dipole (M1), the electric quadrupole (E2), and the Coulomb quadrupole (C2) photon absorption multipoles. The corresponding resonant pion production multipoles are M