Magnetic moment of $\Lambda(1405)$ as a S-shell pentaquark

\def \mate<#1|#2|#3>{\mbox{$\langle {#1}|\,{#2}\,|{#3}\rangle$}} Many theoretical interpretations have been given for exotic baryons, $\Theta^+$ and $\Xi^{--}$ in various scenarios: chiral quark soliton, hadron bound state, valence pentaquark and so on. The simplest pentaquark model is the S-shell pentaquarks where all quarks and an anti-quark are in the ground S-wave state. There is an experimental indication of the $\Theta^+$ being iso- scalar. If we take this indication into S-shell pentaquarks, the $\Theta^+$ become a member of flavor SU(3) anti-decuplet with $J^P = 1/2^-$ and $3/2^-$. In this model, there are also accompanying flavor SU(3) octets with $J^P = 1/2^-$ and $3/2^-$. These octets include one $\Lambda$ hyperon as the ground state octet. The structure of observed $\Lambda(1405)$ with $J^P=1/2^-$ have been given in scenarios: p-wave excited 3-quark, meson-baryon quasi-bound state and so on. Now, we have one another scenario: a S-shell pentaquark. In this paper, we study $\Lambda(1405)$ in this scenario, especially its magnetic moment. Magnetic moment of the $\Lambda$ pentaquark is given by $\mu_{\Lambda} = \sum_{i=1}^{5} \mate<\Lambda| \hat{\mu}_i Q_i \sigma_i^3 |\Lambda>$ because all valence particles are in the ground state S-wave orbit. Using the fit to ground state baryons, we obtain $\mu_{\Lambda (1405)} = 0.427 \mu_N$. This prediction is in contrast with that of p-wave excited 3- quark model: $\mu_{\Lambda(1405)} = -0.13 \mu_N$. It is interesting that the present result agree with the prediction $\mu_{\Lambda(1405)} = +0.25 \sim 0.45 \mu_N$ in the meson-baryon resonance approach. It seems natural because both two approaches share five-quark valence contents for the hyperon. Further discussions will be given at the conference.