Why $\mathrm{\Xi }(1690)$ and $\mathrm{\Xi }(2120)$ are so narrow

The $\mathrm{\Xi }$ baryons are expected to be naturally narrower as compared to their nonstrange and strange counterparts since they have only one light quark and, thus, their decay involves producing either a light meson and doubly strange baryon or both meson and baryon with strangeness which involves, relatively, more energy. In fact, some $\mathrm{\Xi }$’s have full widths of the order of even 10–20 MeV when, in principle, they have a large phase space to decay to some open channels. Such is the case of $\mathrm{\Xi }(1690)$, for which the width has been found to be of the order of 10 MeV in the latest BABAR and BELLE data. In this manuscript we study why some $\mathrm{\Xi }$’s are so narrow. Based on a coupled channel calculation of the pseudoscalar meson-baryon and vector meson-baryon systems with chiral and hidden local symmetry Lagrangians, we find that the answer lies in the intricate hadron dynamics. We find that the known mass, width, spin-parity, and branching ratios of $\mathrm{\Xi }(1690)$ can be naturally explained in terms of coupled channel meson-baryon dynamics. We find another narrow resonance which can be related to $\mathrm{\Xi }(2120)$. We also look for exotic states ${\mathrm{\Xi }}^{+}$ and ${\mathrm{\Xi }}^{--}$ but find none. In addition we provide the cross sections for $\overline{K}\mathrm{\Lambda },\overline{K}\mathrm{\Sigma }\to \pi \mathrm{\Xi }$ which can be useful for understanding the enhanced yield of $\mathrm{\Xi }$ reported in recent studies of heavy ion collisions.

Figure 1

Decay of a $\mathrm{\Xi }$ resonance to a meson ($q\overline{q}/s\overline{q}$)-baryon ($qss/qqs$) channel.

Figure 2

A comparison of the lowest order $\rho \mathrm{\Xi }$ and ${\overline{K}}^{*}\mathrm{\Sigma }$ amplitudes [Eq. (2)] for different spin-isospin configurations.

Figure 3

Squared amplitudes for the total isospin and spin $1/2$. The vertical dashed lines indicate the thresholds as summarized in Table 2.

Figure 4

Squared amplitudes for the $\overline{K}\mathrm{\Sigma }$ channel, in the complex plane, with total isospin and spin $1/2$.

Figure 5

${\overline{K}}^0\mathrm{\Lambda }$ invariant mass spectra for the process ${\mathrm{\Lambda }}_c\to K^{+}{\overline{K}}^0{\mathrm{\Lambda }}^0$. The data is taken from Ref. [5].

Figure 6

$K^{-}{\mathrm{\Sigma }}^{+}$ invariant mass spectra for the process ${\mathrm{\Lambda }}_c\to K^{+}{K}^{-}{\mathrm{\Sigma }}^{+}$. The data is taken from Ref. [5].

Figure 7

The $\pi \mathrm{\Xi }$ mass spectrum in the process ${\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{K}^{+}$ obtained by summing a Breit-Wigner distribution for the $\mathrm{\Xi }(1530)$ resonance to the s-wave $t$-matrix obtained in the present work. It is possible to notice the presence of a structure around 1690 MeV and a $K\mathrm{\Lambda }$ cusp around 1612 MeV.

Figure 8

Squared amplitudes for total isospin $1/2$ and spin $3/2$. The vertical dashed lines indicate the thresholds as summarized in Table 2.

Figure 9

Squared amplitude of the ${\overline{K}}^{*}\mathrm{\Sigma }$ channel, in the complex plane, calculated by neglecting the widths of the vector mesons.

Figure 10

Possible decay mechanism of a $\mathrm{\Xi }$ with mass around 2050 MeV to the $\overline{K}\mathrm{\Lambda }$ channel.

Figure 11

Variations in the isospin-spin $1/2$ squared amplitude of $\overline{K}\mathrm{\Sigma }$ channel as a function of the cutoff $\mathrm{\Lambda }$ used in Eq. (27). The peak is associated to $\mathrm{\Xi }(1690)$.

Figure 12

Same as Fig. 11 but for ${\overline{K}}^{*}\mathrm{\Sigma }$ in the isospin $1/2$, spin $3/2$ configuration. The peak seen in this plot is related to $\mathrm{\Xi }(2120)$.

Figure 13

Cross sections for the $\pi \mathrm{\Xi }\leftrightarrow \overline{K}\mathrm{\Lambda }$, $\pi \mathrm{\Xi }\leftrightarrow \overline{K}\mathrm{\Sigma }$ processes. The horizontal axis corresponds to the total energy above the respective threshold of each process. We have used isospin $1/2$, spin $1/2$ amplitudes to obtain these cross sections.

Figure 14

Squared amplitudes for the total isospin and spin $1/2$. The solid (dashed) curves show the results of the calculations done with relativistic (nonrelativistic) lowest order amplitudes obtained with cutoff $\mathrm{\Lambda }=800\mathrm{MeV}$. The vertical dashed lines indicate the thresholds summarized in Table 2.

Figure 15

Squared amplitudes for the total isospin $1/2$ and spin $3/2$. The solid (dashed) curves show the results of the calculations done with relativistic (nonrelativistic) lowest order amplitudes obtained with cut-off $\mathrm{\Lambda }=800\mathrm{MeV}$. Notice that the dashed curves have been multiplied by an extra factor 2 for the sake of comparison.