Inclusive weak-annihilation decays and lifetimes of beauty-charmed baryons

Abstract

Imbalanced beauty-charmed baryons $ Ξ_{bc}^{+,0} $ are of great significance to the development of heavy flavor physics. In this work, we study the inclusive weak-annihilation decays of $Ξ_{bc}^{+,0}$ and their contributions to the $Ξ_{bc}^{+,0}$ lifetimes. For the calculation of the inclusive $Ξ_{bc}^{+,0}\to X_{cs}$ decay width where $X_{cs}$ stands for the sum of the final states with charm number +1 and strange number -1, we work in the heavy diquark effective theory which provides us with a convenient technical tool to construct the operator product expansion. The $Ξ_{bc}^{+,0}$ is considered to be a superposition of two states with one containing a spin-0 $bc$ diquark and the other one containing a spin-1 $bc$ diquark. It is found that both the $Ξ_{bc}^{+,0}$ lifetimes and the $Ξ_{bc}^{+,0}\to X_{cs}$ branching ratios are very sensitive to the $bc$ spin in $Ξ_{bc}^{+,0}$. The $Ξ_{bc}^{+,0}\to X_{cd}$ results are also presented. As $Ξ_{bc}^+$ has a longer lifetime than $Ξ_{bc}^{0}$ and bigger branching ratios of similar decay channels, the exclusive decays $Ξ_{bc}^+\to D^{(*)+}Λ$, $Ξ_{bc}^+\to Λ_c^+\bar{K}^{(*)0}$, $Ξ_{bc}^+\to D^{(*)+}K^-p$, and $Ξ_{bc}^+\to D^{0}\bar{K}^{(*)0}p$ are more promising for experimental searches of $Ξ_{bc}^{+,0}$ at the LHC comparing with exclusive decay $Ξ_{b c} ^{0} \to D^0pK^-$.