Abstract
We develop techniques to calculate the four $\ensuremath{\Delta}$ electromagnetic form factors using lattice QCD, with particular emphasis on the subdominant electric quadrupole form factor that probes deformation of the $\ensuremath{\Delta}$. Results are presented for pion masses down to approximately 350 MeV for three cases: quenched QCD, two flavors of dynamical Wilson quarks, and three flavors of quarks described by a mixed action combining domain-wall valence quarks and dynamical staggered sea quarks. The magnetic moment of the $\ensuremath{\Delta}$ is compared with chiral effective field theory calculations and the $\ensuremath{\Delta}$ charge density distributions are discussed.
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