Cluster phenomena using few-body and Lattice QCD theories

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 $$N\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> potential obtained by the HAL QCD method to investigate the few-body systems $$NN\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> and $$NNN\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> . Our analysis indicates that the lightest bound $$\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ξ</mml:mi> </mml:math> hypernucleus is the $$NNN\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> system. To extract detailed information on the isospin and spin components of the $$N\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> interaction, we perform a four-body calculation for the $$\alpha \alpha N\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mi>α</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> system with the total isospin $$T = 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and $$T = 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We demonstrate that the level structure of this system is sensitive to the isospin and spin dependencies of the $$N\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> interaction. Furthermore, we propose experimental investigations to produce the $$NNN\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> and $$\alpha \alpha N\Xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mi>α</mml:mi> <mml:mi>N</mml:mi> <mml:mi>Ξ</mml:mi> </mml:mrow> </mml:math> systems via the $$(K^-, K^+)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(K^-, K^0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math>