Mixing-angle sensitivity of inclusive $Ξ_{bc} $ and $Ω_{bc}$ lifetimes

Abstract

We study the inclusive lifetimes of $Ξ_{bc}^{+}$, $Ξ_{bc}^{0}$, and $Ω_{bc}^{0}$, with emphasis on the mixing between the spin-zero and spin-one $bc$-diquark configurations. The relevant hadronic matrix elements are evaluated in both the homogeneous bag model (HBM) and the nonrelativistic quark model (NRQM). At the benchmark mixing angles of $-23.0^\circ$ for $Ξ_{bc}$ and $-23.5^\circ$ for $Ω_{bc}$, the corresponding lifetime triplets are $\left(τ_{Ξ_{bc}^{+}},τ_{Ξ_{bc}^{0}},τ_{Ω_{bc}^{0}}\right)=\left(0.421^{+0.093}_{-0.093},0.075^{+0.035}_{-0.010},0.223^{+0.074}_{-0.043}\right)\,\mathrm{ps}$ in the HBM and $\left(τ_{Ξ_{bc}^{+}},τ_{Ξ_{bc}^{0}},τ_{Ω_{bc}^{0}}\right)=\left(0.367^{+0.076}_{-0.070},0.100^{+0.032}_{-0.014},0.229^{+0.066}_{-0.042}\right)\,\mathrm{ps}$ in the NRQM. Relative to the unmixed spin-one reference points, the $Ξ_{bc}^{0}$ and $Ω_{bc}^{0}$ lifetimes decrease by approximately $17\%$-$19\%$. Neither the minimum nor the maximum of the central lifetime curves occurs at a pure $S_{bc}=0$ or $S_{bc}=1$ configuration; the extrema instead lie at mixed angles with $\left|ϕ_{\mathcal{B}}\right|\simeq27^\circ$-$63^\circ$. The two pure-spin limits alone are therefore insufficient to characterize the full mixing-angle dependence.