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Hyperfine Mixing and the Semileptonic Decays of Double-Heavy Baryons in a Quark Model

The semileptonic decays of the lowest-lying double-heavy baryons is treated in a quark model. For the $Ξ_{bb}$, hyperfine mixing in the spin wave function leaves the total rate for decay into the lowest lying daughter baryons essentially unchanged, but changes the relative rates into the $Ξ_{bc}$ and $Ξ_{bc}^\prime$. The same pattern is obtained in the decays of the $Ω_{bb}$. For the $Ξ_{bc}$, this mixing leads to factor of about 17 suppression in the decay rate to the $Ξ_{cc}^*$, and a factor of two suppression in the total decay rate. For the $Ω_{bc}$, the decay to the $Ω_{cc}^*$ is suppressed by a factor of more than 30 from the unmixed case, and the total decay rate is decreased to about 40% of the decay rate obtained when mixing is ignored.