Constraining the mass and width of the $N^*(1685)$ resonance

We have examined the existence of the $N^*(1685)$ resonance, which is recently listed by the Particle Data Group as a one-star nucleon resonance, by using a covariant isobar model for kaon photoproduction and assuming that the resonance has $J^p=1/2^+$, in accordance with our previous finding. After the inclusion of this resonance the changes in the total $\chi^2$ show two clear minima at $M_{N^*}=1650$ and 1696 MeV, which correspond to two different resonance states. The former corresponds to the narrow nucleon resonance found in our previous investigation, whereas the latter corresponds to a new resonance found as we increase the resonance width. From the latter we derive the mass and width relation of the $N^*(1685)$ resonance. We observe that the properties of both the $N^*(1685)$ and $N^*(1710)P_{11}$ resonances are strongly correlated. Although the best fit of the present work yields $M_{N^*}=1696$ MeV and $\Gamma_{N^*}=76$ MeV, the apparently small $N^*(1710)P_{11}$ coupling constant to the $K^+\Lambda$ channel found in previous investigations suggests that $\Gamma_{N^*}\lesssim 35$ MeV, which, according to the mass and width relation, corresponds to $M_{N^*}\lesssim 1680$ MeV.