Eur. Phys. J. A (2025) 61: 270
https://doi.org/10.1140/epja/s10050-025-01747-7

Review

Cluster phenomena using few-body and Lattice QCD theories

¹ Department of Physics, Tohoku University, Aoba 6-3, 980-8578, Sendai, Miyagi, Japan
² Nishina Center, RIKEN, Hirosawa 2-1, 351-0198, Wako, Saitama, Japan
³ RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Hirosawa 2-1, 351-0198, Wako, Saitama, Japan

^a hiyama@riken.jp

Received: 24 August 2025
Accepted: 7 November 2025
Published online: 26 November 2025

Abstract

With the advancement of first-principles calculations for baryon–baryon interactions, it becomes possible to obtain reliable hyperon–nucleon potentials by lattice QCD simulations with the HAL QCD method. High-precision few-body methods, such as the Gaussian Expansion Method (GEM), are applicable to solve quantum few-body systems up to four- and five-body systems. By combining the HAL QCD potentials with the GEM, one can predict the level structure of novel hypernuclei prior to experimental observation. In this review, we utilize the lattice QCD $N\mathrm{\Xi }$ potential obtained by the HAL QCD method to investigate the few-body systems $NN\mathrm{\Xi }$ and $NNN\mathrm{\Xi }$. Our analysis indicates that the lightest bound $\mathrm{\Xi }$ hypernucleus is the $NNN\mathrm{\Xi }$ system. To extract detailed information on the isospin and spin components of the $N\mathrm{\Xi }$ interaction, we perform a four-body calculation for the $\alpha \alpha N\mathrm{\Xi }$ system with the total isospin $T=0$ and $T=1$. We demonstrate that the level structure of this system is sensitive to the isospin and spin dependencies of the $N\mathrm{\Xi }$ interaction. Furthermore, we propose experimental investigations to produce the $NNN\mathrm{\Xi }$ and $\alpha \alpha N\mathrm{\Xi }$ systems via the $(K^{-},K^{+})$ and $(K^{-},K^0)$ reactions on ⁴He and ¹⁰B targets, respectively.