Analyzing in the molecule picture in the Bethe–Salpeter equation approach

Zhen-Yang Wang; Jing-Juan Qi; Xin-Heng Guo; Jing Xu

doi:10.1140/epjc/s10052-019-7135-3

EPJ

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 640
https://doi.org/10.1140/epjc/s10052-019-7135-3

Regular Article - Theoretical Physics

Analyzing $\Xi (1620)$ in the molecule picture in the Bethe–Salpeter equation approach

Zhen-Yang Wang¹, Jing-Juan Qi², Xin-Heng Guo²^* and Jing Xu³

¹ Physics Department, Ningbo University, Zhejiang, 315211, China
² College of Nuclear Science and Technology, Beijing Normal University, Beijing, 100875, China
³ Physics Department, Yantai University, Yantai, 264005, China

^* e-mail: xhguo@bnu.edu.cn

Received: 23 April 2019
Accepted: 13 July 2019
Published online: 5 August 2019

Abstract

In this work, we assume that the observed state $\Xi (1620)$ is a s-wave $\Lambda {\bar{K}}$ or $\Sigma {\bar{K}}$ bound state. Based on this molecule picture, we establish the Bethe–Salpeter equations for $\Xi (1620)$ in the ladder and instantaneous approximations. We solve the Bethe–Salpeter equations for the $\Lambda {\bar{K}}$ and $\Sigma {\bar{K}}$ systems numerically and find that the $\Xi (1620)$ can be explained as $\Lambda {\bar{K}}$ and $\Sigma {\bar{K}}$ bound states with $$J^P=1/2^-$$ , respectively. Then we calculate the decay widths of $\Xi (1620)\rightarrow \Xi \pi$ in these two different molecule pictures systems, respectively.