Towards hypernuclei from nuclear lattice effective field theory
Fabian Hildenbrand, Serdar Elhatisari, Z. X. Ren, Ulf-G. Meißner
Abstract
Abstract Understanding the strong interactions within baryonic systems beyond the up and down quark sector is pivotal for a comprehensive description of nuclear forces. This study explores the interactions involving hyperons, particularly the $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> particle, within the framework of nuclear lattice effective field theory (NLEFT). By incorporating $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> hyperons into the NLEFT framework, we extend our investigation into the $$S = -1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> sector, allowing us to probe the third dimension of the nuclear chart. We calculate the $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> separation energies ( $$B_{\varLambda }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>Λ</mml:mi> </mml:msub> </mml:math> ) of hypernuclei up to the medium-mass region, providing valuable insights into hyperon–nucleon ( YN ) and hyperon–nucleon–nucleon ( YNN ) interactions. Our calculations employ high-fidelity chiral interactions at N $$ ^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:math> LO for nucleons and extend it to $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> hyperons with leading-order S-wave YN interactions as well as YNN forces constrained only by the $$A=4,5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> systems. Our results contribute to a deeper understanding of the SU(3) symmetry breaking and establish a foundation for future improvements in hypernuclear calculations.