Parameter sets |$\Lambda $|, |$\Sigma $|, |$\Xi $|, and Fit, and properties of the neutral |$\Xi (1690)$| state. The regularization scale is |$\mu _{\rm reg} = 630\,\hbox {MeV}$| in all channels. We also show the |$\chi ^{2}$| value for the |$\bar {K}^{0} \Lambda $| and |$K^{-} \Sigma ^{+}$| mass spectra divided by the number of degrees of freedom, |$\chi ^{2} / N_{\rm d.o.f.}$|, and the ratio of the two branching fractions |$R$| defined in Eq. (11).
| . | Set |$\Lambda $| . | Set |$\Sigma $| . | Set |$\Xi $| . | Fit . |
|---|---|---|---|---|
| |$a_{\bar {K} \Sigma }$| | |$-$|2.30 | |$-$|2.23 | |$-$|2.10 | |$-$|1.98 |
| |$a_{\bar {K} \Lambda }$| | |$-$|2.15 | |$-$|2.07 | |$-$|1.91 | |$-$|2.07 |
| |$a_{\pi \Xi }$| | |$-$|2.08 | |$-$|1.99 | |$-$|1.77 | |$-$|0.75 |
| |$a_{\eta \Xi }$| | |$-$|2.57 | |$-$|2.52 | |$-$|2.43 | |$-$|3.31 |
| |$\chi ^{2} / N_{\rm d.o.f.}$| | 65.3/57 | 66.6/57 | 81.2/57 | 59.0/57 |
| |$R$| | 1.32 | 3.04 | 6.07 | 1.06 |
| |$w_{\rm pole}$| | |$1682.6 - 0.8 i\,\hbox {MeV}$| | No |$\Xi (1690)$| pole | No |$\Xi (1690)$| pole | |$1684.3 - 0.5 i\,\hbox {MeV}$| |
| |$g_{K^{-} \Sigma ^{+}}$| | |$1.00 + 0.22 i$| | |$1.02 + 0.60 i$| | ||
| |$g_{\bar {K}^{0} \Sigma ^{0}}$| | |$-0.73 - 0.15 i$| | |$-0.76 - 0.41 i$| | ||
| |$g_{\bar {K}^{0} \Lambda }$| | |$0.24 - 0.04 i$| | |$0.38 + 0.20 i$| | ||
| |$g_{\pi ^{+} \Xi ^{-}}$| | |$0.04 + 0.08 i$| | |$0.06 - 0.05 i$| | ||
| |$g_{\pi ^{0} \Xi ^{0}}$| | |$-0.05 - 0.05 i$| | |$-0.09 + 0.05 i$| | ||
| |$g_{\eta \Xi ^{0}}$| | |$-0.76 - 0.17 i$| | |$-0.66 - 0.48 i$| | ||
| |$X_{K^{-} \Sigma ^{+}}$| | |$0.77 - 0.10 i$| | |$0.83 - 0.31 i$| | ||
| |$X_{\bar {K}^{0} \Sigma ^{0}}$| | |$0.12 + 0.04 i$| | |$0.12 + 0.17 i$| | ||
| |$X_{\bar {K}^{0} \Lambda }$| | |$0.00 + 0.00 i$| | |$-0.02 + 0.00 i$| | ||
| |$X_{\pi ^{+} \Xi ^{-}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\pi ^{0} \Xi ^{0}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\eta \Xi ^{0}}$| | |$0.02 + 0.01 i$| | |$0.01 + 0.02 i$| | ||
| |$Z$| | |$0.08 + 0.04 i$| | |$0.06 + 0.11 i$| |
| . | Set |$\Lambda $| . | Set |$\Sigma $| . | Set |$\Xi $| . | Fit . |
|---|---|---|---|---|
| |$a_{\bar {K} \Sigma }$| | |$-$|2.30 | |$-$|2.23 | |$-$|2.10 | |$-$|1.98 |
| |$a_{\bar {K} \Lambda }$| | |$-$|2.15 | |$-$|2.07 | |$-$|1.91 | |$-$|2.07 |
| |$a_{\pi \Xi }$| | |$-$|2.08 | |$-$|1.99 | |$-$|1.77 | |$-$|0.75 |
| |$a_{\eta \Xi }$| | |$-$|2.57 | |$-$|2.52 | |$-$|2.43 | |$-$|3.31 |
| |$\chi ^{2} / N_{\rm d.o.f.}$| | 65.3/57 | 66.6/57 | 81.2/57 | 59.0/57 |
| |$R$| | 1.32 | 3.04 | 6.07 | 1.06 |
| |$w_{\rm pole}$| | |$1682.6 - 0.8 i\,\hbox {MeV}$| | No |$\Xi (1690)$| pole | No |$\Xi (1690)$| pole | |$1684.3 - 0.5 i\,\hbox {MeV}$| |
| |$g_{K^{-} \Sigma ^{+}}$| | |$1.00 + 0.22 i$| | |$1.02 + 0.60 i$| | ||
| |$g_{\bar {K}^{0} \Sigma ^{0}}$| | |$-0.73 - 0.15 i$| | |$-0.76 - 0.41 i$| | ||
| |$g_{\bar {K}^{0} \Lambda }$| | |$0.24 - 0.04 i$| | |$0.38 + 0.20 i$| | ||
| |$g_{\pi ^{+} \Xi ^{-}}$| | |$0.04 + 0.08 i$| | |$0.06 - 0.05 i$| | ||
| |$g_{\pi ^{0} \Xi ^{0}}$| | |$-0.05 - 0.05 i$| | |$-0.09 + 0.05 i$| | ||
| |$g_{\eta \Xi ^{0}}$| | |$-0.76 - 0.17 i$| | |$-0.66 - 0.48 i$| | ||
| |$X_{K^{-} \Sigma ^{+}}$| | |$0.77 - 0.10 i$| | |$0.83 - 0.31 i$| | ||
| |$X_{\bar {K}^{0} \Sigma ^{0}}$| | |$0.12 + 0.04 i$| | |$0.12 + 0.17 i$| | ||
| |$X_{\bar {K}^{0} \Lambda }$| | |$0.00 + 0.00 i$| | |$-0.02 + 0.00 i$| | ||
| |$X_{\pi ^{+} \Xi ^{-}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\pi ^{0} \Xi ^{0}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\eta \Xi ^{0}}$| | |$0.02 + 0.01 i$| | |$0.01 + 0.02 i$| | ||
| |$Z$| | |$0.08 + 0.04 i$| | |$0.06 + 0.11 i$| |
Parameter sets |$\Lambda $|, |$\Sigma $|, |$\Xi $|, and Fit, and properties of the neutral |$\Xi (1690)$| state. The regularization scale is |$\mu _{\rm reg} = 630\,\hbox {MeV}$| in all channels. We also show the |$\chi ^{2}$| value for the |$\bar {K}^{0} \Lambda $| and |$K^{-} \Sigma ^{+}$| mass spectra divided by the number of degrees of freedom, |$\chi ^{2} / N_{\rm d.o.f.}$|, and the ratio of the two branching fractions |$R$| defined in Eq. (11).
| . | Set |$\Lambda $| . | Set |$\Sigma $| . | Set |$\Xi $| . | Fit . |
|---|---|---|---|---|
| |$a_{\bar {K} \Sigma }$| | |$-$|2.30 | |$-$|2.23 | |$-$|2.10 | |$-$|1.98 |
| |$a_{\bar {K} \Lambda }$| | |$-$|2.15 | |$-$|2.07 | |$-$|1.91 | |$-$|2.07 |
| |$a_{\pi \Xi }$| | |$-$|2.08 | |$-$|1.99 | |$-$|1.77 | |$-$|0.75 |
| |$a_{\eta \Xi }$| | |$-$|2.57 | |$-$|2.52 | |$-$|2.43 | |$-$|3.31 |
| |$\chi ^{2} / N_{\rm d.o.f.}$| | 65.3/57 | 66.6/57 | 81.2/57 | 59.0/57 |
| |$R$| | 1.32 | 3.04 | 6.07 | 1.06 |
| |$w_{\rm pole}$| | |$1682.6 - 0.8 i\,\hbox {MeV}$| | No |$\Xi (1690)$| pole | No |$\Xi (1690)$| pole | |$1684.3 - 0.5 i\,\hbox {MeV}$| |
| |$g_{K^{-} \Sigma ^{+}}$| | |$1.00 + 0.22 i$| | |$1.02 + 0.60 i$| | ||
| |$g_{\bar {K}^{0} \Sigma ^{0}}$| | |$-0.73 - 0.15 i$| | |$-0.76 - 0.41 i$| | ||
| |$g_{\bar {K}^{0} \Lambda }$| | |$0.24 - 0.04 i$| | |$0.38 + 0.20 i$| | ||
| |$g_{\pi ^{+} \Xi ^{-}}$| | |$0.04 + 0.08 i$| | |$0.06 - 0.05 i$| | ||
| |$g_{\pi ^{0} \Xi ^{0}}$| | |$-0.05 - 0.05 i$| | |$-0.09 + 0.05 i$| | ||
| |$g_{\eta \Xi ^{0}}$| | |$-0.76 - 0.17 i$| | |$-0.66 - 0.48 i$| | ||
| |$X_{K^{-} \Sigma ^{+}}$| | |$0.77 - 0.10 i$| | |$0.83 - 0.31 i$| | ||
| |$X_{\bar {K}^{0} \Sigma ^{0}}$| | |$0.12 + 0.04 i$| | |$0.12 + 0.17 i$| | ||
| |$X_{\bar {K}^{0} \Lambda }$| | |$0.00 + 0.00 i$| | |$-0.02 + 0.00 i$| | ||
| |$X_{\pi ^{+} \Xi ^{-}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\pi ^{0} \Xi ^{0}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\eta \Xi ^{0}}$| | |$0.02 + 0.01 i$| | |$0.01 + 0.02 i$| | ||
| |$Z$| | |$0.08 + 0.04 i$| | |$0.06 + 0.11 i$| |
| . | Set |$\Lambda $| . | Set |$\Sigma $| . | Set |$\Xi $| . | Fit . |
|---|---|---|---|---|
| |$a_{\bar {K} \Sigma }$| | |$-$|2.30 | |$-$|2.23 | |$-$|2.10 | |$-$|1.98 |
| |$a_{\bar {K} \Lambda }$| | |$-$|2.15 | |$-$|2.07 | |$-$|1.91 | |$-$|2.07 |
| |$a_{\pi \Xi }$| | |$-$|2.08 | |$-$|1.99 | |$-$|1.77 | |$-$|0.75 |
| |$a_{\eta \Xi }$| | |$-$|2.57 | |$-$|2.52 | |$-$|2.43 | |$-$|3.31 |
| |$\chi ^{2} / N_{\rm d.o.f.}$| | 65.3/57 | 66.6/57 | 81.2/57 | 59.0/57 |
| |$R$| | 1.32 | 3.04 | 6.07 | 1.06 |
| |$w_{\rm pole}$| | |$1682.6 - 0.8 i\,\hbox {MeV}$| | No |$\Xi (1690)$| pole | No |$\Xi (1690)$| pole | |$1684.3 - 0.5 i\,\hbox {MeV}$| |
| |$g_{K^{-} \Sigma ^{+}}$| | |$1.00 + 0.22 i$| | |$1.02 + 0.60 i$| | ||
| |$g_{\bar {K}^{0} \Sigma ^{0}}$| | |$-0.73 - 0.15 i$| | |$-0.76 - 0.41 i$| | ||
| |$g_{\bar {K}^{0} \Lambda }$| | |$0.24 - 0.04 i$| | |$0.38 + 0.20 i$| | ||
| |$g_{\pi ^{+} \Xi ^{-}}$| | |$0.04 + 0.08 i$| | |$0.06 - 0.05 i$| | ||
| |$g_{\pi ^{0} \Xi ^{0}}$| | |$-0.05 - 0.05 i$| | |$-0.09 + 0.05 i$| | ||
| |$g_{\eta \Xi ^{0}}$| | |$-0.76 - 0.17 i$| | |$-0.66 - 0.48 i$| | ||
| |$X_{K^{-} \Sigma ^{+}}$| | |$0.77 - 0.10 i$| | |$0.83 - 0.31 i$| | ||
| |$X_{\bar {K}^{0} \Sigma ^{0}}$| | |$0.12 + 0.04 i$| | |$0.12 + 0.17 i$| | ||
| |$X_{\bar {K}^{0} \Lambda }$| | |$0.00 + 0.00 i$| | |$-0.02 + 0.00 i$| | ||
| |$X_{\pi ^{+} \Xi ^{-}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\pi ^{0} \Xi ^{0}}$| | |$0.00 + 0.00 i$| | |$0.00 + 0.00 i$| | ||
| |$X_{\eta \Xi ^{0}}$| | |$0.02 + 0.01 i$| | |$0.01 + 0.02 i$| | ||
| |$Z$| | |$0.08 + 0.04 i$| | |$0.06 + 0.11 i$| |
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