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

Abstract

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.

Four pages

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