Constraining the mass and width of the $N^{*}\mathbf{(}1685\mathbf{)}$ 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 $M_{N^{*}}=1696\mathrm{MeV}$ and ${\Gamma }_{N^{*}}=76\mathrm{MeV}$, the apparently small $N^{*}(1710)P_{11}$ coupling constant to the $K^{+}\Lambda$ channel found in previous investigations suggests that ${\Gamma }_{N^{*}}\lesssim 35\mathrm{MeV}$, which, according to the mass and width relation, corresponds to $M_{N^{*}}\lesssim 1680\mathrm{MeV}$.

Figure 1

Effects of the inclusion of $P_{11}$, $S_{11}$, and $P_{13}$ resonances on the total cross section of the $\gamma +p\to K^{+}+\Lambda$ process in our previous calculation [1]. Note that the $P_{13}(1680)$ effect was not reported in Ref. 1. Experimental data are from the SAPHIR [14] and CLAS [15] Collaborations.

Figure 2

Changes of the ${\chi }^2$ in the fit of the kaon photoproduction data due to the inclusion of the $N^{*}(1685)P_{11}$ resonance with the corresponding mass and width scanned from 1620 to 1730 MeV and 1 to 100 MeV, respectively.

Figure 3

Total cross sections obtained by the model calculations with (solid red line) and without (dashed blue line) the $N^{*}(1685)P_{11}$ resonance compared with experimental data [15]. In the former, the total cross section is calculated by using the best fit result, i.e., with $M_{N^{*}}=1696\mathrm{MeV}$ and ${\Gamma }_{N^{*}}=76\mathrm{MeV}$. The dash-dotted black line exhibits the $N^{*}(1685)P_{11}$ resonance contribution.

Figure 4

(a) Mass and width relation of the $N^{*}(1685)P_{11}$ resonance extracted from Fig. 2 (solid red line). The uncertainty of this relation is indicated by the dotted (blue) area. (b) ${\chi }_{\min }^2$ per number of degrees of freedom ($N_{\mathrm{d}.\mathrm{o}.\mathrm{f}.}$) obtained for each of the ${\Gamma }_{N^{*}}$ values. The vertical dotted line locates the position of the minimum value of the ${\chi }_{\min }^2/N_{\mathrm{d}.\mathrm{o}.\mathrm{f}.}$. (c) Coupling constants of the dominant resonances that contribute to the first peak of the $\gamma p\to K^{+}\Lambda$ total cross section (see Fig. 3). Notation of the coupling constants can be found in Ref. 7.