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We have examined the existence of the $N^*(1685)$ resonance, which isrecently listed by the Particle Data Group as a one-star nucleon resonance, byusing a covariant isobar model for kaon photoproduction and assuming that theresonance has $J^p=1/2^+$, in accordance with our previous finding. After theinclusion of this resonance the changes in the total $\chi^2$ show two clearminima at $M_{N^*}=1650$ and 1696 MeV, which correspond to two differentresonance states. The former corresponds to the narrow nucleon resonance foundin our previous investigation, whereas the latter corresponds to a newresonance found as we increase the resonance width. From the latter we derivethe mass and width relation of the $N^*(1685)$ resonance. We observe that theproperties of both the $N^*(1685)$ and $N^*(1710)P_{11}$ resonances arestrongly 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 inprevious investigations suggests that $\Gamma_{N^*}\lesssim 35$ MeV, which,according to the mass and width relation, corresponds to $M_{N^*}\lesssim 1680$MeV.

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