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重新访问转换$Ξ^{+}_{cc}\toΞ^{(')+}_c$以了解LHCb的数据

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

Hong-Wei Ke, Xue-Qian Li

备注：
14 pages, 5 figures and 5 tables. arXiv admin note: text overlap with arXiv:1912.01435
发表信息：
Phys.Rev.D 105 (2022) 9, 096011
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摘要：

LHCb合作组新测量了双粲重子$Ξ^{++}_{cc}\toΞ^{'+}π^+$的衰变率及其分支分数与衰变$Ξ^{++}_{cc}\toΞ^{+}π^+$分支分数之比，并将其记为$1.41\pm 0.17\pm 0.10$。这一结果与几个研究小组的理论预测相矛盾。在我们以前的工作中，我们按照早期文献中的规定，即$Ξ^{+}_{c}$中的$us$双夸克是标量，而$Ξ^{'+}_{c}$中的$us$双夸克是矢量，即$Ξ^{+}_{c}$的自旋-味道结构是$[us]_0 c$，$Ξ^{'+}_{c}$的自旋-味道结构是$[us]_1 c$，我们用轻前夸克模型研究了$Ξ^{++}_{cc}\toΞ^{(')+}$的情况。从数值上我们得到了约为数据一半的$Γ(Ξ^{++}_{cc}\toΞ^{'+}π^+)/Γ(Ξ^{++}_{cc}\toΞ^{+}π^+)=0.56\pm0.18$。在放弃这一假设的前提下，我们假设$Ξ^{+}_{c}$中$us$的自旋-味道结构可能是标量和矢量的混合，即$Ξ^{+}_{c}$的自旋-味道函数可能是${\rm cos}θ\, [us]_{0}[c]+{\rm sin}θ\, [us]_{1}[c]$。替代组合$-{\rm sin}θ\,[us]_{0}[c]+{\rm cos}θ\, [us]_{1}[c]$将对应于$Ξ^{'+}_{c}$。引入混合机制，比率$Γ(Ξ^{++}_{cc}\toΞ^{'+}π^+)/Γ(Ξ^{++}_{cc}\toΞ^{+}π^+)$取决于混合角$θ$。在混合情况下，只要设定$θ=16.27^\circ\pm2.30^\circ$或$85.54^\circ\pm2.30^\circ$，理论预测的$Ξ^{+}_{cc}\toΞ^{'+}_c$和$Ξ^{+}_{cc}\toΞ^{+}_c$跃迁速率之比与实验数据吻合较好。当然，更精确的测量$Ξ^{+}_{cc}$的其他衰变门户是迫切需要测试的混合机制，并进一步确定混合角。

英文摘要：

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.

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