Revisiting the transition $Ξ^{+}_{cc}\toΞ^{(')+}_c$ to understand the data from LHCb

Abstract

The LHCb collaboration newly measured the decay rate of doubly charmed baryon $Ξ^{++}_{cc}\toΞ^{'+}π^+$ and a ratio of its branching fraction with respect to that of the decay $Ξ^{++}_{cc}\toΞ^{+}π^+$ is reported as $1.41\pm 0.17\pm 0.10$. This result conflicts with the theoretical predictions made by several groups. In our previous work, following the prescription given in early literature where the $us$ diquark in $Ξ^{+}_{c}$ is assumed to be a scalar whereas in $Ξ^{'+}_{c}$ is a vector i.e. the spin-flavor structure of $Ξ^{+}_{c}$ is $[us]_0 c$ and that of $Ξ^{'+}_{c}$ is $[us]_1 c$, we studied the case of $Ξ^{++}_{cc}\toΞ^{(')+}$ with the light front quark model. Numerically we obtained $Γ(Ξ^{++}_{cc}\toΞ^{'+}π^+)/Γ(Ξ^{++}_{cc}\toΞ^{+}π^+)=0.56\pm0.18$ which is about half of the data. While abandoning the presupposition, we suppose the spin-flavor structure of $us$ in $Ξ^{+}_{c}$ may be a mixture of scalar and vector, namely the spin-flavor function of $Ξ^{+}_{c}$ could be ${\rm cos}θ\, [us]_{0}[c]+{\rm sin}θ\, [us]_{1}[c]$. An alternative combination $-{\rm sin}θ\,[us]_{0}[c]+{\rm cos}θ\, [us]_{1}[c]$ would correspond to $Ξ^{'+}_{c}$. Introducing the mixing mechanism the ratio $Γ(Ξ^{++}_{cc}\toΞ^{'+}π^+)/Γ(Ξ^{++}_{cc}\toΞ^{+}π^+)$ depends on the mixing angle $θ$. With the mixing scenario, the theoretical prediction on the ratio between the transition rate of $Ξ^{+}_{cc}\toΞ^{'+}_c$ and that of $Ξ^{+}_{cc}\toΞ^{+}_c$ can coincide with the data as long as $θ=16.27^\circ\pm2.30^\circ$ or $85.54^\circ\pm2.30^\circ$ is set. Definitely, more precise measurements on other decay portals of $Ξ^{+}_{cc}$ are badly needed for testing the mixing mechanism and further determining the mixing angle.