Hyperfine Mixing and Final-Spin Redistribution in Inclusive ${\Xi }_{bc}\to H_{cc}+X$

Abstract

In this work, we study the effect of hyperfine mixing on the inclusive weak decay ${\Xi }_{bc}\to H_{cc}+X$, which has been proposed as a useful channel for searching for the beauty-charmed baryons. Starting from the inclusive heavy-diquark framework, we include the mixing between the scalar and axial-vector $bc$ configurations and decompose the final doubly charmed system into the $J_f=1/2$ and $J_f=3/2$ spin sectors. Within a minimal scalar-to-axial current model, we find that the interference between the scalar and axial components is large in each spin sector but cancels after summing over the two members of the ground-state $ccq$ spin multiplet, ${\Gamma }_{AS}^{1/2}=-{\Gamma }_{AS}^{3/2}$. As a consequence, the inclusive branching fraction remains close to the original estimate when feed-down from the spin-excited ${\Xi }_{cc}^{\ast }$ sector is included. However, the direct ground-state contribution is strongly spin selective: ${\Xi }_{bc}^{(1)}$ dominantly feeds the $J_f=1/2$ ${\Xi }_{cc}$ channel, whereas ${\Xi }_{bc}^{(2)}$ dominantly feeds the $J_f=3/2$ ${\Xi }_{cc}^{\ast }$ sector. We also test the stability of the aforementioned conclusion under variations of the mixing angle, scalar-current normalization, and recoil-shape choice. It is found that hyperfine mixing is hidden in the total inclusive rate, but can be exposed through the final-spin composition.