Determination of quadrupole strengths in the ? * p ? ? ( 1232 ) transition at Q 2 = 0.20 ( GeV / c )

We report new precise p$(\vec{e},e^\prime p)\pi^0$ measurements at the peak of the $\Delta^{+}(1232)$ resonance at $Q^2=\unit[0.20](GeV/c)^2$ performed at the Mainz Microtron (MAMI). The new data are sensitive to both the electric quadrupole ($E2$) and the coulomb quadrupole ($C2$) amplitudes of the $\gamma^* N\to\Delta$ transition. They yield precise quadrupole to dipole amplitude ratios CMR $= (-5.09 \pm 0.28_{stat+sys}\pm 0.30_{model})%$ and EMR $= (-1.96 \pm 0.68_{stat+sys} \pm 0.41_{model})%$ for $M^{3/2}_{1+} = (39.57 \pm 0.75_{stat+sys}\pm 0.40_{model})(10^{-3}/m_{\pi^+})$. The new results are in disagreement with Constituent Quark Model predictions and in qualitative agreement with models that account for mesonic contributions, including recent Lattice calculations. They thus give further credence to the conjecture of deformation in hadronic systems favoring the attribution of the origin of deformation to the dominance of mesonic effects.