Precise Predictions of Charmed-Bottom Hadrons from Lattice QCD

We report the ground state masses of hadrons containing at least one charm and one bottom quark using lattice quantum chromodynamics. These include mesons with spin ($J$) and parity ($P$), ($J^P$): $0^{-}$, $1^{-}$, $1^{+}$, and $0^{+}$ and the spin $1/2$ and $3/2$ baryons. Among these hadrons, only the ground state of $0^{-}$ is known experimentally, and therefore our predictions provide important information for the experimental discovery of all other hadrons with these quark contents.

Figure 1

Ground state mass of the $B_c(0^{-})$ meson at three lattice spacings is shown in terms of energy splittings from the spin-average mass [Eq. (1)]. Continuum extrapolated and experimental values are also shown.

Figure 2

(Top) Hyperfine splitting in $B_c$ mesons at three different lattice spacings and at the continuum limit. (Bottom three) Ratios [as defined in Eq. (5)] of subtracted masses of $1^{-}$, $1^{+}$, and $0^{+}$ mesons to that of the $0^{-}$ $B_c$ meson are plotted at three lattice spacings and at the continuum limit.

Figure 3

(Top) ${\mathrm{\Xi }}_{cb}$ masses as a function of $m_{\pi }^2$. Chiral extrapolation is performed with a linear term in $m_{\pi }^2$. (Bottom three) Chiral extrapolated (as shown above) subtracted masses [as defined in Eq. (1)] of ${\mathrm{\Xi }}_{cb}$, ${\mathrm{\Xi }}_{cb}^{\prime }$, and ${\mathrm{\Xi }}_{cb}^{*}$ baryons at three lattice spacings and at the continuum limit.

Figure 4

Subtracted masses, as defined in Eq. (1), of ${\mathrm{\Omega }}_{cb}$, ${\mathrm{\Omega }}_{cb}^{\prime }$, ${\mathrm{\Omega }}_{cb}^{*}$ (top three), ${\mathrm{\Omega }}_{ccb}$, ${\mathrm{\Omega }}_{ccb}^{*}$ (middle two), and ${\mathrm{\Omega }}_{cbb}$, ${\mathrm{\Omega }}_{cbb}^{*}$ (bottom two) baryons at three lattice spacings and at the continuum limit.

Figure 5

Ground state masses of all $bc$ baryons as predicted in this work.