Electromagnetic Properties of the Delta in the Large N and Chiral Limits

Relations between nucleon, $\mathrm{\Delta }$ and nucleon-$\mathrm{\Delta }$ electromagnetic properties associated with chiral physics which have been derived in a pure large-$N_c$ limit are greatly modified in a combined large $N_c$ and chiral limits; the large $N_c$ relations are valid for $(M_{\mathrm{\Delta }}-M_N)\mathrm{/}{m}_{\pi }<<1$. The E2/M1 ratio for the nucleon-$\mathrm{\Delta }$ transition is shown to scale as ${ϵ}^{-1}$ (with $ϵ\sim 1\mathrm{/}{N}_c$, $ϵ\sim m_{\pi }\mathrm{/}\mathrm{\Lambda }$ with $\mathrm{\Lambda }$ a typical hadronic scale) in the combined large $N_c$ and chiral expansions as opposed to $N_c^{-2}$ in the pure large $N_c$ expansion.