Dynamical coupled-channels model of $K^{-}p$ reactions. II. Extraction of ${\mathrm{\Lambda }}^{*}$ and ${\mathrm{\Sigma }}^{*}$ hyperon resonances

Resonance parameters (pole masses and residues) associated with the excited states of hyperons, ${\mathrm{\Lambda }}^{*}$ and ${\mathrm{\Sigma }}^{*}$, are extracted within a dynamical coupled-channels model developed recently by us [Phys. Rev. C 90, 065204 (2014)] through a comprehensive partial-wave analysis of the $K^{-}p\to \overline{K}N,\pi \mathrm{\Sigma },\pi \mathrm{\Lambda },\eta \mathrm{\Lambda },K\mathrm{\Xi }$ data up to invariant mass $W=2.1$ GeV. We confirm the existence of resonances corresponding to most, if not all, of the four-star resonances rated by the Particle Data Group. We also find several new resonances, and in particular propose a possible existence of a new narrow $J^P=3/2^{+}\mathrm{\Lambda }$ resonance that couples strongly to the $\eta \mathrm{\Lambda }$ channel. The $J^P=1/2^{-}\mathrm{\Lambda }$ resonances located below the $\overline{K}N$ threshold are also discussed. Comparing our extracted pole masses with the ones from a recent analysis by the Kent State University group, some significant differences in the extracted resonance parameters are found, suggesting the need of more extensive and accurate data of $K^{-}p$ reactions including polarization observables to eliminate such an analysis dependence of the resonance parameters. In addition, the determined large branching ratios of the decays of high-mass resonances to the $\pi {\mathrm{\Sigma }}^{*}$ and ${\overline{K}}^{*}N$ channels also suggest the importance of the data of $2\to 3$ reactions such as $K^{-}p\to \pi \pi \mathrm{\Lambda }$ and $K^{-}p\to \pi \overline{K}N$. Experiments on measuring cross sections and polarization observables of these fundamental reactions are highly desirable at hadron beam facilities such as J-PARC for establishing the ${\mathrm{\Lambda }}^{*}$ and ${\mathrm{\Sigma }}^{*}$ spectrum.

Figure 1

Mass spectrum of ${\mathrm{\Lambda }}^{*}$ resonances above the $\overline{K}N$ threshold. For each ${\mathrm{\Lambda }}^{*},\mathrm{Re}\left(M_R\right)$ together with the $\mathrm{Re}\left(M_R\right)\pm [-\mathrm{Im}\left(M_R\right)]$ band is plotted, where the length of the band, $-2\mathrm{Im}\left(M_R\right)$, corresponds to the total width of the resonance. The spin and parity of the resonances are denoted as $J^P$ with $P=\pm$, and also specified by the quantum number ($l_{I2J}$) of the associated $\overline{K}N$ partial-wave amplitudes. The horizontal dotted lines represent the $\overline{K}N$ threshold. The results from Models A and B constructed in Ref. [4] are compared with the ones from the KSU analysis [3]. The so-called Breit-Wigner masses and widths of the four- and three-star resonances rated by PDG [21] are also presented.

Figure 2

Mass spectrum of ${\mathrm{\Sigma }}^{*}$ resonances above the $\overline{K}N$ threshold. See the caption of Fig. 1 for the description of the figure.

Figure 3

The $K^{-}p\to K^{-}p$ and $K^{-}p\to {\overline{K}}^{0}n$ total cross sections at the energies near $W\sim 1.67$ GeV. Red solid (blue dashed) curves are the full results from Model A (Model B), while red dotted (blue dashed-dotted) curves are the results for which the $S_{01}$ resonance contributions are turned off.

Figure 4

Total cross section near the threshold (upper panels) and differential cross section at $W=1672$ MeV (lower panels) for the $K^{-}p\to \eta \mathrm{\Lambda }$ reaction. Left panels (right panels) are the results from Model A (Model B). Solid curves are the full results, while the dashed curves are the contribution from the $S_{01}$ partial wave only. For Model B, the difference between the solid and dashed curves almost comes from the $P_{03}$ partial wave dominated by the new narrow $J^P=3/2^{+}\mathrm{\Lambda }$ resonance with $M_R={1671}_{-8}^{+2}-i\left(5_{-2}^{+11}\right)$ MeV.

Figure 5

Graphical comparison of $R_{\overline{K}N,\overline{K}N}$ between Models A and B for the well-established resonances (see text for the details).

Figure 6

Graphical representation of the branching ratios for decays of ${\mathrm{\Lambda }}^{*}$ and ${\mathrm{\Sigma }}^{*}$ resonances found from Model A. Equations (23, 24, 25, 26) are used for evaluating the ratios.

Figure 7

Graphical representation of the branching ratios for decays of ${\mathrm{\Lambda }}^{*}$ and ${\mathrm{\Sigma }}^{*}$ resonances found from Model B. Equations (23, 24, 25, 26) are used for evaluating the ratios.

Figure 8

$S$-wave $\left(J^P=1/2^{-}\right)\mathrm{\Lambda }$ resonances in the $\overline{K}N$ subthreshold region. Red triangles (blue diamonds) are resonance poles found from Model A (Model B).