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 transition ${\Xi }_{bc}\to H_{cc}+X$, which has been proposed as a useful channel for searching for beauty-charmed baryons. Starting from the inclusive heavy-diquark framework, we include 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 transition model, and for a benchmark scalar-channel normalization of order unity at zero recoil, we find that the interference between the scalar and axial components is large in the separate spin sectors but cancels after summing over the two members of the adopted ground-state $ccq$ spin multiplet, ${\Gamma }_{AS}^{1/2}=-{\Gamma }_{AS}^{3/2}$. Consequently, the spin-summed inclusive rate is less sensitive to hyperfine mixing than the direct ground-state contribution, provided feed-down from the spin-excited ${\Xi }_{cc}^{\ast }$ partner is experimentally unresolved. For a scalar-channel normalization of order unity, the direct contribution can be 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 test this pattern for several convention-matched literature admixtures and for a separately labeled decay-interference diagnostic angle, together with the dependence on the scalar-to-axial normalization and recoil-shape choice. The cancellation of the spin-summed interference is a consequence of baryon spin recoupling within the spectator and common-multiplet assumptions, whereas the magnitude of the spin selectivity is conditional on the magnitude and relative phase of the scalar-to-axial transition.