Accuracy of traditional Legendre estimators of quadrupole ratios for theN→Δtransition

Abstract

We evaluate the accuracy of traditional estimators often used to extract $N\ensuremath{\rightarrow}\ensuremath{\Delta}$ quadrupole ratios from cross-section angular distributions for pion electroproduction. We find that neither ${M}_{1+}$ dominance nor $\ensuremath{\ell}\ensuremath{\le}1$ truncation is sufficiently accurate for this purpose. Truncation errors are especially large for ${R}_{\mathrm{EM}}$, for which it is also essential to perform Rosenbluth separation. The accuracy of similar truncated Legendre analyses for ${E}_{0+},{S}_{0+}$, and especially ${M}_{1\ensuremath{-}}$ is even worse.