N-to-ΔElectromagnetic-Transition Form Factors from Lattice QCD

The magnetic dipole (M1), the electric quadrupole (E2), and the Coulomb quadrupole (C2) amplitudes for $\gamma N\to \Delta$ are calculated in quenched lattice QCD. Using a new method, which combines an optimal choice of interpolating fields for the $\Delta$ and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios $R_{\mathrm{E}\mathrm{M}}=\mathrm{E}2/\mathrm{M}1$ and $R_{\mathrm{S}\mathrm{M}}=\mathrm{C}2/\mathrm{M}1$, up to momentum transfer squared $1.5{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. We show for the first time, using lattice QCD, that both $R_{\mathrm{E}\mathrm{M}}$ and $R_{\mathrm{S}\mathrm{M}}$ are nonzero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the $N/\Delta$ system.