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

Abstract

Imbalanced beauty-charmed baryons ${\Xi }_{bc}^{+,0}$ are of great significance to the development of heavy flavor physics. In this work, we study the inclusive weak-annihilation decays of ${\Xi }_{bc}^{+,0}$ and their contributions to the ${\Xi }_{bc}^{+,0}$ lifetimes. For the calculation of the inclusive ${\Xi }_{bc}^{+,0}\to X_{cs}$ 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 ${\Xi }_{bc}^{+,0}$ 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 ${\Xi }_{bc}^{+,0}$ lifetimes and the ${\Xi }_{bc}^{+,0}\to X_{cs}$ branching ratios are very sensitive to the $bc$ spin in ${\Xi }_{bc}^{+,0}$. The ${\Xi }_{bc}^{+,0}\to X_{cd}$ results are also presented. As ${\Xi }_{bc}^{+}$ has a longer lifetime than ${\Xi }_{bc}^0$ and bigger branching ratios of similar decay channels, the exclusive decays ${\Xi }_{bc}^{+}\to D^{(\ast )+}\Lambda$, ${\Xi }_{bc}^{+}\to {\Lambda }_c^{+}{\bar{K}}^{(\ast )0}$, ${\Xi }_{bc}^{+}\to D^{(\ast )+}{K}^{-}p$, and ${\Xi }_{bc}^{+}\to D^0{\bar{K}}^{(\ast )0}p$ are more promising for experimental searches of ${\Xi }_{bc}^{+,0}$ at the LHC comparing with exclusive decay ${\Xi }_{bc}^0\to D^{0}p{K}^{-}$.

Comments: 7 pages, 4 figures