$SU(3)_F$极限及超出情形下$\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$衰变的拓扑图分析
Topological diagram analysis of $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays in the $SU(3)_F$ limit and beyond
AI总结：
本文研究了$SU(3)_F$极限及破缺下粲重子到十重态重子衰变的拓扑振幅，发现多数图被定理抑制，仅少数振幅主导，并利用破缺效应解释非零分支比与CP破坏。
摘要：
粲重子衰变在研究非微扰重子跃迁中起重要作用。与其他强子多重态相比，重子十重态的味对称性更简单且具吸引力。本文研究了味对称及线性$SU(3)_F$破缺下粲重子衰变为十重态重子的拓扑振幅。发现在$SU(3)_F$极限下，多数拓扑图被Körner-Pati-Woo定理抑制。仅有两个独立振幅对$\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$衰变有贡献，其中一个主导分支比。在$SU(3)_F$极限下，所有$\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$模式的Lee-Yang参数相同，且CP不对称性仅有四个可能值。引入一阶$SU(3)_F$破缺效应后，$Ξ^+_c\to Σ^{* +}\overline K^0$和$Ξ^+_c\to Ξ^{* 0}π^+$衰变具有非零分支比。线性$SU(3)_F$破缺中对$\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$衰变有贡献的自由参数数目少于可用数据。通过分支比全局拟合可提取夸克圈图的$SU(3)_F$破缺部分，有助于理解粲领域的CP破坏。此外，提出了一些新同位旋方程以检验Körner-Pati-Woo定理。
英文摘要：
Charm baryon decay plays an important role in studying non-perturbative baryonic transitions. Compared to other hadron multiplets, the flavor symmetry of baryon decuplet is more simple and attractive. In this work, we study the topological amplitudes of charmed baryon decays into decuplet baryon in the flavor symmetry and the linear $SU(3)_F$ breaking. It is found most of topological diagrams are suppressed by the Körner-Pati-Woo theorem in the $SU(3)_F$ limit. Only two independent amplitudes contributing to the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays, with one dominating the branching fractions. The Lee-Yang parameters of all $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ modes are the same in the $SU(3)_F$ limit, and there are only four possible values for the CP asymmetries. After including the first-order $SU(3)_F$ breaking effects, the $Ξ^+_c\to Σ^{* +}\overline K^0$ and $Ξ^+_c\to Ξ^{* 0}π^+$ decays have non-zero branching fractions. The number of free parameter contributing to the $\mathcal{B}_{c\overline 3}\to \mathcal{B}_{10}M$ decays in the linear $SU(3)_F$ breaking is smaller than the available data. The $SU(3)_F$ breaking part of the quark loop diagram can be extracted by global fitting of branching fractions, which could help us understand the CP violation in charm sector. Additionally, some new isospin equations are proposed to test the Körner-Pati-Woo theorem.
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