Study of singly heavy baryon lifetimes

We study the inclusive decay widths of singly heavy baryons with the improved bag model in which the unwanted center-of-mass motion is removed. Additional insight is gained by comparing the charmed and bottom baryons. We discuss the running of the baryon matrix elements and compare the results with the non-relativistic quark model (NRQM). While the calculated two-quark operator elements are compatible with the literature, those of the four-quark ones deviate largely. In particular, the heavy quark limit holds reasonably well in the bag model for four-quark operator matrix elements but is badly broken in the NRQM. We predict $1-\tau(\Omega_b)/ \tau(\Lambda_b^0) = (8.34\pm2.22)\%$ in accordance with the current experimental value of $(11.5^{+12.2}_{-11.6})\%$ and compatible with $(13.2\pm 4.7)\%$ obtained in the NRQM. We find an excellent agreement between theory and experiment for the lifetimes of bottom baryons. We confirm that $\Omega_c^0$ could live longer than $\Lambda_c^+$ after the dimension-7 four-quark operators are taken into account. We recommend to measure some semileptonic inclusive branching fractions in the forthcoming experiments to discern different approaches. For example, we obtain ${\cal BF} (\Xi_c^+ \to X e^+ \nu_e) = (8.57\pm 0.49)\% $ and ${\cal BF} (\Omega_c^0 \to X e^+ \nu_e) = (1.88\pm 1.69)\% $ in sharp contrast to ${\cal BF} (\Xi_c^+ \to X e^+ \nu_e) = (12.74^{+2.54}_{-2.45})\% $ and ${\cal BF} (\Omega_c^0 \to X e^+ \nu_e) = (7.59^{+2.49}_{-2.24})\% $ found in the NRQM.