Coupling strength of the $N^*(1535)S_{11}$ to the $K^+\Lambda$ channel

The $N^*(1535)S_{11}$ coupling strength to the $K^+\Lambda$ channel, $g_{N^*(1535)\Lambda K^+}$, is extracted from the latest and largest $K^+\Lambda$ photoproduction database by using an isobar model. It is found that the coupling is small. In term of the coupling ratio the best result is $R\equiv |g_{N^*(1535)\Lambda K^+}/g_{N^*(1535)\eta p}|=0.460\pm 0.172$, much smaller than that obtained from the isobar analysis of the $J/\psi$ decays, i.e., $1.3\pm 0.3$, but consistent with the results of the unitary chiral approach of the same decay processes as well as the partial wave analysis of kaon photoproduction, i.e., $R=0.5\sim 0.7$. The different results of $R$ found here and in literature to date suggest that a more solid definition of the coupling constant, especially in the case of $N^*(1535)S_{11}$ state, is urgently required, before a fair comparison can be made.