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Cluster phenomena using few-body and Lattice QCD theories

E. Hiyama, T. Doi

TL;DR

This work demonstrates that first-principles lattice QCD via the HAL QCD method, when paired with high-precision few-body solutions from the Gaussian Expansion Method, can predict the level structure of novel Xi hypernuclei. By extracting the $N\Xi$ interaction from (2+1)-flavor lattice QCD and solving three-, four-, and five-body systems, the authors show that the lightest bound Xi hypernucleus is the $NNN\Xi$ system, and that the binding patterns in $\alpha\alpha N\Xi$ are highly sensitive to the spin-isospin components of the $N\Xi$ interaction, particularly the $^{11}$S$_0$, $^{13}$S$_1$, $^{31}$S$_0$, and $^{33}$S$_1$ channels. The results include weakly bound or unbound $NN\Xi$ states, a weakly bound $NNN\Xi$ in the $(0,1^+)$ channel, and bound $\alpha\alpha N\Xi$ states in both $T=0$ and $T=1$ sectors with narrow decay widths, offering concrete experimental targets via $K$-induced reactions at J-PARC. These predictions provide stringent constraints on hyperon-nucleon and hyperon-hyperon interactions and guide future measurements of spin-isospin dependent effects in Xi-bearing nuclei.

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 $NΞ$ potential obtained by the HAL QCD method to investigate the few-body systems $NNΞ$ and $NNNΞ$. Our analysis indicates that the lightest bound $Ξ$ hypernucleus is the $NNNΞ$ system. To extract detailed information on the isospin and spin components of the $NΞ$ interaction, we perform a four-body calculation for the $ααNΞ$ 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 $NΞ$ interaction. Furthermore, we propose experimental investigations to produce the $NNNΞ$ and $ααNΞ$ systems via the $(K^-, K^+)$ and $(K^-, K^0)$ reactions on $^4$He and $^{10}$B targets, respectively.

Cluster phenomena using few-body and Lattice QCD theories

TL;DR

This work demonstrates that first-principles lattice QCD via the HAL QCD method, when paired with high-precision few-body solutions from the Gaussian Expansion Method, can predict the level structure of novel Xi hypernuclei. By extracting the interaction from (2+1)-flavor lattice QCD and solving three-, four-, and five-body systems, the authors show that the lightest bound Xi hypernucleus is the system, and that the binding patterns in are highly sensitive to the spin-isospin components of the interaction, particularly the S, S, S, and S channels. The results include weakly bound or unbound states, a weakly bound in the channel, and bound states in both and sectors with narrow decay widths, offering concrete experimental targets via -induced reactions at J-PARC. These predictions provide stringent constraints on hyperon-nucleon and hyperon-hyperon interactions and guide future measurements of spin-isospin dependent effects in Xi-bearing nuclei.

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 potential obtained by the HAL QCD method to investigate the few-body systems and . Our analysis indicates that the lightest bound hypernucleus is the system. To extract detailed information on the isospin and spin components of the interaction, we perform a four-body calculation for the system with the total isospin and . We demonstrate that the level structure of this system is sensitive to the isospin and spin dependencies of the interaction. Furthermore, we propose experimental investigations to produce the and systems via the and reactions on He and B targets, respectively.

Paper Structure

This paper contains 12 sections, 25 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. HAL QCD method
  4. Basic formulation
  5. Time-dependent HAL QCD method
  6. HAL QCD method for coupled channel systems
  7. Gaussian Expansion Method
  8. Results
  9. Lattice QCD results for the $N\Xi$ interactions
  10. Level structure of $NN\Xi$ and $NNN\Xi$ systems
  11. Level structure of $\alpha\alpha N\Xi$ system
  12. Summary

Figures (5)

  • Figure 1: The strategy for extracting information used so far is shown in (a), and the new strategy is shown in (b).
  • Figure 2: Jacobi coordinate of three-body system.
  • Figure 3: Jacobi coordinate of $NNN\Xi$ and $\alpha\alpha N\Xi$ systems.
  • Figure 4: $N\Xi$ phase shifts in the $^{11}{\rm S}_0$, $^{13}{\rm S}_1$, $^{33}{\rm S}_1$ and $^{31}{\rm S}_0$ channels using the HAL QCD potential ($t/a=12$) Hiyama:2019kpw.
  • Figure 5: The energy levels of $\alpha \alpha N \Xi$ system for $T=0$ and $T=1$Hiyama:2022jqh. The energies are measured with respect to $\alpha \alpha N \Xi$ breakup threshold.