arXiv 2503.045862025-03-06hep-ph

在淬灭手征夸克模型中研究$N(1535)$和$Λ(1405)$的本质

Investigating the nature of $N(1535)$ and $Λ(1405)$ in a quenched chiral quark model

Yue Tan, Zi-Xuan Ma, Xiaoyun Chen, Xiaohuang Hu, Youchang Yang, Qi Huang, Jialun Ping

AI总结：

本文在手征夸克模型中利用高斯展开法系统研究了$N(1440)$、$N(1535)$和$Λ(1405)$的性质，结果表明$N(1535)$为三夸克态，$N(1440)$既非三夸克也非五夸克态，而$Λ(1405)$需三夸克与五夸克成分混合才能稳定。

摘要：

在这项工作中，我们在手征夸克模型中使用高斯展开法（GEM）系统地在淬灭三夸克和五夸克框架下研究了$N(1440)$、$N(1535)$和$Λ(1405)$。我们的计算表明，$N(1535)$可以再现为三夸克态（$N(1P)$），而$N(1440)$和$Λ(1405)$分别无法作为三夸克候选态（$N(2S)$和$Λ(1P)$）被容纳。在五夸克框架中，我们发现$N(1535)$的$ΛK$态无法形成束缚态，而在$N\ar{K}$通道中，$Λ(1405)$将形成一个浅束缚态。基于复标度法，我们进行了完整的耦合道计算，获得了能量在1.8 GeV至2.2 GeV之间的六个共振态，此外还有一个位于$Σπ$通道附近的束缚态。然而，这些态中既不包括$N(1535)$在$ΛK$通道中的分子候选态，也不包括$Λ(1405)$在$N\ar{K}$通道中的分子候选态。这是因为$N\ar{K}$与$Σπ$之间的强耦合会使$N\ar{K}$解除束缚，而$ΛK$与$ΣK$之间的弱耦合无法帮助在$ΛK$阈值附近形成稳定结构。因此，在淬灭夸克模型下，我们的结果支持$N(1535)$为三夸克态，而$N(1440)$既不是三夸克态也不是五夸克态。此外，我们发现尽管$Λ(1405)$可能主要是五夸克态，但它需要三夸克和五夸克成分的混合才能保持稳定。未来，我们将探索裸重子与这些相关两体强子通道成分之间的混合效应，以进一步检验我们的结论。

英文摘要：

In this work, we systematically study $N(1440)$, $N(1535)$, and $Λ(1405)$ in both the quenched three-quark and five-quark frameworks using the Gaussian Expansion Method (GEM) within the chiral quark model. Our calculations show that $N(1535)$ can be reproduced as a three-quark state ($N(1P)$), while $N(1440)$ and $Λ(1405)$ cannot be accommodated as the three-quark candidates, ($N(2S)$ and $Λ(1P)$), respectively. In the five-quark framework, we find that the $ΛK$ state for $N(1535)$ can not form a bound state, while in the $N\bar{K}$ channel there will $Λ(1405)$ form a shallow bound state. Based on the complex-scaling method, we performed complete coupled-channels calculations and obtained six resonance states with energies ranging from 1.8 GeV to 2.2 GeV, in addition with one bound state located around $Σπ$ channel. However, neither molecular candidates in $ΛK$ channel for $N(1535)$ nor $N\bar{K}$ for $Λ(1405)$ are included in these states. This is because the strong coupling between $N\bar{K}$ and $Σπ$ will make the $N\bar{K}$ unbound, while the weak coupling between $ΛK$ and $ΣK$ can not help form a stable structure around $ΛK$ threshold. Thus, under the quenched quark model, our results support $N(1535)$ as a three-quark state, while $N(1440)$ is neither a three-quark nor a five-quark state. In addition, we find that although $Λ(1405)$ can be primarily a five-quark state, it requires a mixture of three-quark and five-quark components for stability. In the future, an exploration on the mixing effects between bare baryons with these relevant two-body hadronic channel components will be carried out to further test our conclusions.

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