Decay widths of the excited ${\mathrm{\Omega }}_b$ baryons

The LHCb Collaboration recently observed five narrow ${\mathrm{\Omega }}_c^0$ resonances and measured their masses and widths through the decays ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^{+}{K}^{-}$. Motivated by this discovery, and also by the fact that the ground-state bottom baryon ${\mathrm{\Omega }}_b^{-}$ with spin $1/2$ was already found experimentally, we perform a theoretical investigation of the spin-$1/2$ and spin-$3/2$, ${\mathrm{\Omega }}_b$, baryons by calculating the decay width of their first orbitally and radially excited states to ${\mathrm{\Xi }}_b^0{K}^{-}$. For this purpose, we employ the QCD sum rule method on the light cone by including in the analysis the $K$-meson distribution amplitudes up to twist 4. Obtained analytical expressions are utilized to extract parameters of these decay processes, which may be useful for forthcoming experimental studies of bottom baryons.

Figure 1

Contributions to ${\mathrm{\Pi }}^{\mathrm{OPE}}(p,q)$ determined by two-particle (a) and three-particle (b) and (c) distribution amplitudes of the $K$ meson.

Figure 2

Diagrams with gluon (a), quark (b), and mixed (c) vacuum condensates.

Figure 3

The dependence of the pole contribution to $g_{{\tilde{\mathrm{\Omega }}}_b^{\star }{\mathrm{\Xi }}_{b}K}$ on the Borel parameter $M^2$ (left panel) and on the continuum threshold $s_0$ (right panel).

Figure 4

The perturbative and nonperturbative contributions to the coupling $g_{{\tilde{\mathrm{\Omega }}}_b^{\star }{\mathrm{\Xi }}_{b}K}$ as functions of the Borel parameter $M^2$ (left panel) and of the continuum threshold $s_0$ (right panel).

Figure 5

The nonperturbative contributions to the strong coupling $g_{{\tilde{\mathrm{\Omega }}}_b^{\star }{\mathrm{\Xi }}_{b}K}$ as functions of the Borel parameter $M^2$ (at $s_0=46.25{\mathrm{GeV}}^2$, left panel) and of the continuum threshold $s_0$ ($M^2=8{\mathrm{GeV}}^2$, right panel).

Figure 6

The dependence of the strong coupling $g_{{\mathrm{\Omega }}_b^{\prime }{\mathrm{\Xi }}_{b}K}$ on the Borel parameter $M^2$ at fixed $s_0$ (left panel) and on the continuum threshold $s_0$ for chosen $M^2$ (right panel).

Figure 7

The strong coupling $g_{{\tilde{\mathrm{\Omega }}}_b^{\star }{\mathrm{\Xi }}_{b}K}$ vs the Borel parameter $M^2$ (left panel) and vs continuum threshold $s_0$ (right panel).

Figure 8

The strong coupling of the radially excited ${\mathrm{\Omega }}_b^{\star \prime }$ baryon with ${\mathrm{\Xi }}_{b}K$ as a function of the Borel parameter $M^2$ at fixed $s_0$ (left panel) and as a function of the continuum threshold $s_0$ at different $M^2$ (right panel).