Relations between nucleon, $\Delta$ and nucleon-$\Delta$ 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 $(M_\Delta-M_N)/m_\pi <<1$. The E2/M1 ratio for the nucleon-$\Delta$ transition is shown to scale as $\epsilon^{ -1}$ (with $\epsilon\sim 1/N_c$, $\epsilon \sim m_\pi/\Lambda $ with $\Lambda$ 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.
Categories: hep-ph
