Semileptonic decays of doubly charmed baryons with bag model
We study the semileptonic decays of $B_{cc}$ ${\rightarrow}$ $B_c\ell^+ν_\ell$ with the bag model, where $\ell$ = $(e, μ)$, $B_{cc}$ = $(Ξ_{cc}^{++}$, $Ξ_{cc}^+$, $Ω_{cc}^+$), and $ B_c$ are the singly charmed baryons with $J^P= 1/2^+$. We obtain the decay widths of $Γ(Ξ_{cc}^{++}{\rightarrow}Ξ_c^+e^+ν_e, Ξ_c^{\prime+}e^+ν_e, Λ_c^+e^+ν_e, Ω_c^+ e^+ν_e) =(5.1\pm 0.1 , 11\pm 1, 0.34\pm 0.06, 0.76\pm 0.06)\times 10^{-14}$~GeV, $Γ(Ξ_{cc}^+\rightarrow Ξ_c^0e^+ν_e, Ξ_c^{\prime0}e^+ν_e , Σ_c^0e^+ν_e) = (5.1\pm 0.6, 11\pm 1, 1.5\pm 0.1) \times 10^{-14}$~GeV, and $Γ(Ω_{cc}^+\rightarrow Ω_c^0 e^+ν_e, Ξ_c^0e^+ν_e , Ξ_c^{\prime0} e^+ν_e) = (22\pm 2, 0.32 \pm 0.04, 0.77\pm 0.06)\times 10^{-14}$~GeV. We also get that $Γ$($B_{cc}$ ${\rightarrow}$ $B_cμ^+ν_μ$)/$Γ$($B_{cc}$ ${\rightarrow}$ $B_ce^+ν_e$) = $0.97\sim 1.00$. In addition, we discuss the $SU(3)$ flavor breaking effects, classified into three aspects: phase space differences, spectator quarks, and overlappings of the transited quarks. In particular, we show that the breaking effects are dominated by the phase space differences, which can be as large as 25\%. Explicitly, we find that $Γ(Ξ_{cc}^{++} \to Λ_c ^+ e^+ ν_e) V_{cs}^2/Γ(Ξ_{cc}^{++} \to Ξ_c ^+ e^+ ν_e )V_{cd}^2 = 1.24$, which is expected as $1$ under the exact $SU(3)$ flavor symmetry.