Identifying the ${\mathrm{\Xi }}_b(6227)$ and ${\mathrm{\Sigma }}_b(6097)$ as $P$-wave bottom baryons of $J^P=3/2^{-}$

We use the method of QCD sum rules within the framework of heavy quark effective theory to study the mass spectrum of the ${\mathrm{\Sigma }}_b(6097{)}^{\pm }$ and ${\mathrm{\Xi }}_b(6227{)}^{-}$, and use the method of light cone sum rules still within the heavy quark effective theory to study their decay properties. Our results suggest that they can be well interpreted as $P$-wave bottom baryons with the spin-parity $J^P=3/2^{-}$. They belong to the baryon doublet $[{\mathbf{6}}_F,2,1,\lambda ]$, where the total and spin angular momenta of the light degree of freedom are $j_l=2$ and $s_l=1$, and the orbital angular momentum is between the bottom quark and the two-light-quark system ($\lambda$-type). This doublet contains six bottom baryons, and we predict masses (mass differences) and decay widths of the other four states to be $M_{{\mathrm{\Omega }}_b(3/2^{-})}=6.46\pm 0.12\mathrm{GeV}$, ${\mathrm{\Gamma }}_{{\mathrm{\Omega }}_b(3/2^{-})}={58}_{-33}^{+65}\mathrm{MeV}$, $M_{{\mathrm{\Sigma }}_b(5/2^{-})}-M_{{\mathrm{\Sigma }}_b(3/2^{-})}=13\pm 5\mathrm{MeV}$, $M_{{\mathrm{\Xi }}_b^{\prime }(5/2^{-})}-M_{{\mathrm{\Xi }}_b^{\prime }(3/2^{-})}=12\pm 5\mathrm{MeV}$, and $M_{{\mathrm{\Omega }}_b(5/2^{-})}-M_{{\mathrm{\Omega }}_b(3/2^{-})}=11\pm 5\mathrm{MeV}$. We propose to search for them in further LHCb experiments.

Figure 1

Categorization of $P$-wave bottom baryons.

Figure 2

The $S$-wave decay coupling constants (a) $g_{{\mathrm{\Sigma }}_b^{-}[{\frac{1}{2}}^{-}]\to {\mathrm{\Sigma }}_b^0{\pi }^{-}}$, (b) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_b^{\prime 0}{\pi }^{-}}$, (c) $g_{{\mathrm{\Sigma }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_b^{*0}{\pi }^{-}}$, (d) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^{*0}{\pi }^{-}}$, (e) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_b^{*0}{K}^{-}}$, and (f) $g_{{\mathrm{\Omega }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^{*0}{K}^{-}}$ as functions of the Borel mass $T$. Here the excited baryons ${\mathrm{\Sigma }}_b^{-}$, ${\mathrm{\Xi }}_b^{\prime -}$, and ${\mathrm{\Omega }}_b^{-}$ belong to the baryon doublet $[{\mathbf{6}}_F,1,0,\rho ]$.

Figure 3

The $S$-wave decay coupling constants (a) $g_{{\mathrm{\Sigma }}_b^{-}[{\frac{1}{2}}^{-}]\to {\mathrm{\Lambda }}_b^0{\pi }^{-}}$, (b) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_b^0{\pi }^{-}}$, (c) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{1}{2}}^{-}]\to {\mathrm{\Lambda }}_b^0{K}^{-}}$, and (d) $g_{{\mathrm{\Omega }}_b^{-}[{\frac{1}{2}}^{-}]\to {\mathrm{\Xi }}_b^0{K}^{-}}$ as functions of the Borel mass $T$. Here the excited baryons ${\mathrm{\Sigma }}_b^{-}$, ${\mathrm{\Xi }}_b^{\prime -}$, and ${\mathrm{\Omega }}_b^{-}$ belong to the baryon singlet $[{\mathbf{6}}_F,0,1,\lambda ]$.

Figure 4

The $S$-wave decay coupling constants (a) $g_{{\mathrm{\Sigma }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_b^{*0}{\pi }^{-}}$, (b) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^{*0}{\pi }^{-}}$, (c) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Sigma }}_b^{*0}{K}^{-}}$, and (d) $g_{{\mathrm{\Omega }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^{*0}{K}^{-}}$ as functions of the Borel mass $T$. Here the excited baryons ${\mathrm{\Sigma }}_b^{-}$, ${\mathrm{\Xi }}_b^{\prime -}$, and ${\mathrm{\Omega }}_b^{-}$ belong to the baryon doublet $[{\mathbf{6}}_F,2,1,\lambda ]$.

Figure 5

The $D$-wave decay coupling constants (a) $g_{{\mathrm{\Sigma }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Lambda }}_b^0{\pi }^{-}}$, (b) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^0{\pi }^{-}}$, (c) $g_{{\mathrm{\Xi }}_b^{\prime -}[{\frac{3}{2}}^{-}]\to {\mathrm{\Lambda }}_b^0{K}^{-}}$, and (d) $g_{{\mathrm{\Omega }}_b^{-}[{\frac{3}{2}}^{-}]\to {\mathrm{\Xi }}_b^0{K}^{-}}$ as functions of the Borel mass $T$. Here the excited baryons ${\mathrm{\Sigma }}_b^{-}$, ${\mathrm{\Xi }}_b^{\prime -}$, and ${\mathrm{\Omega }}_b^{-}$ belong to the baryon doublet $[{\mathbf{6}}_F,2,1,\lambda ]$.