Study on the mixing of $Ξ_c$ and $Ξ'_c$ by the transition $Ξ_{b}\toΞ^{(')}_c$

Abstract

Recently, the LHCb collaboration has observed the decays $Ξ^0_{b}\toΞ^+_{c}D^-_s$ and $Ξ^-_{b}\toΞ^0_{c}D^-_s$. They measured the relative branching fractions times the ratio of beauty-baryon production cross-sections $\mathcal{R}(\frac{Ξ^0_b}{Λ_b})\equiv\frac{σ(Ξ_b^0)}{σ(Λ^0_b)}\times\frac{B(Ξ^0_{b}\toΞ^+_{c}D^-_s)}{B(Λ^0_{b}\toΛ^+_{c}D^-_s)}$ and $\mathcal{R}(\frac{Ξ^-_b}{Λ_b})\equiv\frac{σ(Ξ^-_b)}{σ(Λ^0_b)}\times\frac{B(Ξ^-_{b}\toΞ^0_{c}D^-_s)}{B(Λ^0_{b}\toΛ^+_{c}D^-_s)}$. Once the ratio $\frac{σ(Ξ_b^0)}{σ(Λ^0_b)}$ or $\frac{σ(Ξ_b^-)}{σ(Λ^0_b)}$ is known, one can determine the relative branching fractions which can be used to exam the mixing of $Ξ_c$ and $Ξ'_c$. In previous literature, $Ξ_c$ and $Ξ'_c$ were assumed to belong to SU(3)$_F$ antitriple and sextet, respectively. However, recent experimental measurements such as the ratio $Γ(Ξ_{cc}\toΞ_cπ^+)/Γ(Ξ_{cc}\toΞ'_cπ^+)$ indicate the spin-flavor structures of $Ξ_{c}$ and $Ξ'_{c}$ are a mixture of $Ξ^{\bar 3}_{c}$ and $Ξ^{6}_{c}$. The exact value of mixing angle $θ$ is still under debate. In theoretical models, the mixing angle was fitted to be about $16.27^\circ\pm2.30^\circ$ or $85.54^\circ\pm2.30^\circ$ based on decay channels $Ξ_{cc} \toΞ^{(')}_{cc} $. While in lattice calculation, a small angle ($1.2^\circ\pm0.1^\circ$) is preferred. To address such discrepancy and test the mixing of $Ξ_c$ and $Ξ'_c$, here we propose the analysis of semileptonic and non-leptonic decays of $Ξ_{b}\toΞ_{c}$ and $Ξ_{b}\toΞ^{'}_{c}$. We calculate the decay rate of $Ξ_{b}\toΞ_{c}$ and $Ξ_{b}\toΞ^{'}_{c}$ based on light-front quark model and study the effect of the mixing angle on the ratios of weak decays $Ξ_{b}\toΞ_{c}$ and $Ξ_{b}\toΞ^{'}_{c}$.....