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

Abstract: We study the inclusive lifetimes of $Ξ<em>{bc}<sup>{+}$, $Ξ</em>{bc}<sup>{0}$, and $Ω<em>{bc}<sup>{0}$, 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 $-23.0<sup>\circ$ for $Ξ</em>{bc}$ and $-23.5<sup>\circ$ for $Ω<em>{bc}$, the corresponding lifetime triplets are $$\left(τ</em>{Ξ<em>{bc}^{+}},τ</em>{Ξ<em>{bc}^{0}},τ</em>{Ω<em>{bc}^{{0}}\right)=\left(0.421^{+0.093}}</em>{-0.093},0.075<sup>{+0.035}<em>{-0.010},0.223^{+0.074}</em>{-0.043}\right)\,\mathrm{ps}$$ in the HBM and $$\left(τ<em>{Ξ</em>{bc}<sup>{+}},τ<em>{Ξ</em>{bc}<sup>{0}},τ<em>{Ω</em>{bc}<sup>{0}}\right)=\left(0.367<sup>{+0.076}<em>{-0.070},0.100^{+0.032}</em>{-0.014},0.229<sup>{+0.066}_{-0.042}\right)\,\mathrm{ps}$$ in the NRQM. Relative to the unmixed spin-one reference points, the $Ξ<em>{bc}<sup>{0}$ and $Ω</em>{bc}<sup>{0}$ 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 $\left|φ_{\mathcal{B}}\right|\simeq27<sup>\circ$-$63<sup>\circ$. The two pure-spin limits alone are therefore insufficient to characterize the full mixing-angle dependence.