Mixing-angle sensitivity of inclusive ${\Xi }_{bc}$ and ${\Omega }_{bc}$ lifetimes

Abstract

We study the inclusive lifetimes of ${\Xi }_{bc}^{+}$, ${\Xi }_{bc}^0$, and ${\Omega }_{bc}^0$, 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 ${\Xi }_{bc}$ and $-23.5^{\circ }$ for ${\Omega }_{bc}$, the corresponding lifetime triplets are $\left({\tau }_{{\Xi }_{bc}^{+}},{\tau }_{{\Xi }_{bc}^0},{\tau }_{{\Omega }_{bc}^0}\right)=\left(0.421_{-0.093}^{+0.093},0.075_{-0.010}^{+0.035},0.223_{-0.043}^{+0.074}\right)\mathrm{ps}$ in the HBM and $\left({\tau }_{{\Xi }_{bc}^{+}},{\tau }_{{\Xi }_{bc}^0},{\tau }_{{\Omega }_{bc}^0}\right)=\left(0.367_{-0.070}^{+0.076},0.100_{-0.014}^{+0.032},0.229_{-0.042}^{+0.066}\right)\mathrm{ps}$ in the NRQM. Relative to the unmixed spin-one reference points, the ${\Xi }_{bc}^0$ and ${\Omega }_{bc}^0$ 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 $\left|{\varphi }_{\mathcal{B}}\right|\simeq 27^{\circ }$-$63^{\circ }$. The two pure-spin limits alone are therefore insufficient to characterize the full mixing-angle dependence.

Comments: 20 pages, 5 figures