σ exchange in the one-boson exchange model involving the ground state octet baryons

Based on the one-boson-exchange framework that the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>σ</a:mi></a:math> meson serves as an effective parametrization for the correlated scalar-isoscalar <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>π</c:mi><c:mi>π</c:mi></c:math> interaction, we calculate the coupling constants of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>σ</e:mi></e:math> to the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mfrac><g:mrow><g:mn>1</g:mn></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:mfrac></g:mrow><g:mrow><g:mo>+</g:mo></g:mrow></g:msup></g:mrow></g:math> ground state light baryon octet <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="double-struck">B</i:mi></i:math> by matching the amplitude of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mi mathvariant="double-struck">B</l:mi><l:mover accent="true"><l:mrow><l:mi mathvariant="double-struck">B</l:mi></l:mrow><l:mrow><l:mo stretchy="false">¯</l:mo></l:mrow></l:mover><l:mo stretchy="false">→</l:mo><l:mi>π</l:mi><l:mi>π</l:mi><l:mo stretchy="false">→</l:mo><l:mover accent="true"><l:mrow><l:mi mathvariant="double-struck">B</l:mi></l:mrow><l:mrow><l:mo stretchy="false">¯</l:mo></l:mrow></l:mover><l:mi mathvariant="double-struck">B</l:mi></l:mrow></l:math> to that of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi mathvariant="double-struck">B</x:mi><x:mover accent="true"><x:mi mathvariant="double-struck">B</x:mi><x:mo stretchy="false">¯</x:mo></x:mover><x:mo stretchy="false">→</x:mo><x:mi>σ</x:mi><x:mo stretchy="false">→</x:mo><x:mover accent="true"><x:mi mathvariant="double-struck">B</x:mi><x:mo stretchy="false">¯</x:mo></x:mover><x:mi mathvariant="double-struck">B</x:mi></x:math>. The former is calculated using a dispersion relation, supplemented with chiral perturbation theory results for the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi mathvariant="double-struck">B</jb:mi><jb:mi mathvariant="double-struck">B</jb:mi><jb:mi>π</jb:mi><jb:mi>π</jb:mi></jb:math> couplings and the Muskhelishvili-Omnès representation for the <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>π</nb:mi><nb:mi>π</nb:mi></nb:math> rescattering. Explicitly, the coupling constants are obtained as <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msub><pb:mi>g</pb:mi><pb:mrow><pb:mi>N</pb:mi><pb:mi>N</pb:mi><pb:mi>σ</pb:mi></pb:mrow></pb:msub><pb:mo>=</pb:mo><pb:mrow><pb:msubsup><pb:mn>8.7</pb:mn><pb:mrow><pb:mo>−</pb:mo><pb:mn>1.9</pb:mn></pb:mrow><pb:mrow><pb:mo>+</pb:mo><pb:mn>1.7</pb:mn></pb:mrow></pb:msubsup></pb:mrow></pb:math>, <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msub><rb:mi>g</rb:mi><rb:mrow><rb:mi mathvariant="normal">Σ</rb:mi><rb:mi mathvariant="normal">Σ</rb:mi><rb:mi>σ</rb:mi></rb:mrow></rb:msub><rb:mo>=</rb:mo><rb:mrow><rb:msubsup><rb:mn>3.5</rb:mn><rb:mrow><rb:mo>−</rb:mo><rb:mn>1.3</rb:mn></rb:mrow><rb:mrow><rb:mo>+</rb:mo><rb:mn>1.8</rb:mn></rb:mrow></rb:msubsup></rb:mrow></rb:math>, <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msub><vb:mi>g</vb:mi><vb:mrow><vb:mi mathvariant="normal">Ξ</vb:mi><vb:mi mathvariant="normal">Ξ</vb:mi><vb:mi>σ</vb:mi></vb:mrow></vb:msub><vb:mo>=</vb:mo><vb:mrow><vb:msubsup><vb:mn>2.5</vb:mn><vb:mrow><vb:mo>−</vb:mo><vb:mn>1.4</vb:mn></vb:mrow><vb:mrow><vb:mo>+</vb:mo><vb:mn>1.5</vb:mn></vb:mrow></vb:msubsup></vb:mrow></vb:math>, and <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msub><zb:mi>g</zb:mi><zb:mrow><zb:mi mathvariant="normal">Λ</zb:mi><zb:mi mathvariant="normal">Λ</zb:mi><zb:mi>σ</zb:mi></zb:mrow></zb:msub><zb:mo>=</zb:mo><zb:mrow><zb:msubsup><zb:mn>6.8</zb:mn><zb:mrow><zb:mo>−</zb:mo><zb:mn>1.7</zb:mn></zb:mrow><zb:mrow><zb:mo>+</zb:mo><zb:mn>1.5</zb:mn></zb:mrow></zb:msubsup></zb:mrow></zb:math>. These coupling constants can be used in the one-boson-exchange model calculations of the interaction of light baryons with other hadrons. Published by the American Physical Society 2024