${\mathit{Q}}^2$ Dependence of Quadrupole Strength in the ${\mathit{\gamma }}^{*}\mathit{p}\to {\mathit{\Delta }}^{+}\left(1232\right)\to \mathit{p}{\mathit{\pi }}^0$ Transition

Models of baryon structure predict a small quadrupole deformation of the nucleon due to residual tensor forces between quarks or distortions from the pion cloud. Sensitivity to quark versus pion degrees of freedom occurs through the $Q^2$ dependence of the magnetic $\left(M_{1+}\right)$, electric $\left(E_{1+}\right)$, and scalar $\left(S_{1+}\right)$ multipoles in the ${\gamma }^{*}p\to {\Delta }^{+}\to p{\pi }^0$ transition. We report new experimental values for the ratios $E_{1+}{/M}_{1+}$ and $S_{1+}{/M}_{1+}$ over the range $Q^2=0.4\mathrm{}–1.8{\mathrm{GeV}}^2$, extracted from precision $p\left({e,e}^{\prime }p\right){\pi }^0$ data using a truncated multipole expansion. Results are best described by recent unitary models in which the pion cloud plays a dominant role.