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arXiv 2201.01489nucl-thhep-ph
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作为真正的三夸克或分子态的$Λ(1405)$共振

The $Λ(1405)$ resonance as a genuine three-quark or molecular state

B. Golli, H. Osmanović, S. Širca

摘要:

在一个包含夸克-介子相互作用和接触(四点)相互作用的手征夸克模型中,研究了$Λ(1405)$共振的形成机制。在一个统一的耦合通道框架内计算了奇异性$-1$和$1$的负宇称$S$波散射振幅,该框架包括$KN$、$\bar{K}N$、$πΣ$、$ηΛ$、$KΞ$、$πΛ$和$ηΣ$通道以及对应于$\frac12^-$共振的可能的真正的三夸克裸单线态和八重态。我们表明,为了重现散射振幅的$S_{01}$分波,重要的是包括相关的三夸克八重态以及单重态,而列入的接触项是不是强制性的。Laurent-Pietarinen展开用于确定$S$矩阵极点。随着相互作用强度的增加,单重态的质量随着$πΣ$和$\bar{K}N$通道中的吸引自能而大幅降低;当其下降到$KN$阈值以下时,该状态获得可以用分子状态识别的主导$\bar{K}N$组分。K介子和核子之间的吸引力是通过$\bar{K}NΛ^*$相互作用产生的,而不是介子-核子力。

英文摘要:

The mechanism for the formation of the $Λ(1405)$ resonance is studied in a chiral quark model that includes quark-meson as well as contact (four point) interactions. The negative-parity $S$-wave scattering amplitudes for strangeness $-1$ and $1$ are calculated within a unified coupled-channel framework that includes the $KN$, $\bar{K}N$, $πΣ$, $ηΛ$, $KΞ$, $πΛ$, and $ηΣ$ channels and possible genuine three-quark bare singlet and octet states corresponding to $\frac12^-$ resonances. We show that in order to reproduce the scattering amplitudes in the $S_{01}$ partial wave it is important to include the pertinent three-quark octet states as well as the singlet state, while the inclusion of the contact term is not mandatory. The Laurent-Pietarinen expansion is used to determine the $S$-matrix poles. Following their evolution as a function of increasing interaction strength, the mass of the singlet state is strongly reduced due to the attractive self-energy in the $πΣ$ and $\bar{K}N$ channels; when it drops below the $KN$ threshold, the state acquires a dominant $\bar{K}N$ component which can be identified with a molecular state. The attraction between the kaon and the nucleon is generated through the $\bar{K}NΛ^*$ interaction rather than by meson-nucleon forces.

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