N-to-delta electromagnetic-transition form factors from lattice QCD.

The magnetic dipole (M1), the electric quadrupole (E2), and the Coulomb quadrupole (C2) amplitudes for $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\Delta}$ are calculated in quenched lattice QCD. Using a new method, which combines an optimal choice of interpolating fields for the $\ensuremath{\Delta}$ 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 $1.5\text{ }\text{ }{\mathrm{G}\mathrm{e}\mathrm{V}}^{2}$. 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 $N/\ensuremath{\Delta}$ system.