Decay properties of $N(1535)$ in the holographic QCD

We study one pion emission decay of the first excited state of the nucleon with negative parity $N(1535)\equiv N^{*}$ in the holographic model of QCD. The excited state is described as a vibrational mode along the extra $z$ direction in the five-dimensional space-time of the model. We have obtained an analytic formula for the axial coupling of $g_A^{N{N}^{*}}$. The off diagonal axial coupling is obtained at the decaying pion momentum $|\mathit{k}|=448\mathrm{MeV}$ as $g_A^{N{N}^{*}}\sim 0.32$ and hence, a partial decay width ${\mathrm{\Gamma }}_{N^{*}\to \pi N}\sim 30\mathrm{MeV}$, which is smaller than but reasonably compared to the experimental data.

Figure 1

The emitted pion momentum $\mathit{k}$ dependance of the form factor $F_A({\mathit{k}}^2)$.