An Estimate of the Inclusive Branching Ratio to ${\bar B}_c$ in $\Xi_{bbq}$ Decay

Abstract

We estimate the branching ratio for the inclusive decays $\Xi_{bbq} \rightarrow {\bar B}_c^{(*)}+X_{c,s,q}$ to be approximately 1%. Our estimate is performed using non-relativistic potential quark model methods that are appropriate if the bottom and charm quarks are heavy compared to the strong interaction scale. Here the superscript $(*)$ denotes that we are summing over spin zero ${\bar B}_c$ and spin one ${\bar B}_c^*$ mesons and the subscript $q$ denotes a light quark. Our approach treats the two bottom quarks in the baryon $\Xi_{bbq}$ as a small color anti-triplet. This estimate for the inclusive branching ratio to ${\bar B}_c$ and ${\bar B}^*_c$ mesons also holds for decays of the lowest lying $T_{bb{\bar q}{\bar q}}$ tetraquark states, provided they are stable against strong and electromagnetic decay.