Structure of the Λ(1670) resonance

We examine the internal structure of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Λ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1670</a:mn><a:mo stretchy="false">)</a:mo></a:math> through an analysis of lattice QCD simulations and experimental data within Hamiltonian effective field theory. Two scenarios are presented. The first describes the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Λ</f:mi><f:mo stretchy="false">(</f:mo><f:mn>1670</f:mn><f:mo stretchy="false">)</f:mo></f:math> as a bare three-quark basis state, which mixes with the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>π</k:mi><k:mi mathvariant="normal">Σ</k:mi></k:math>, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mover accent="true"><n:mi>K</n:mi><n:mo stretchy="false">¯</n:mo></n:mover><n:mi>N</n:mi></n:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>η</r:mi><r:mi mathvariant="normal">Λ</r:mi></r:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>K</u:mi><u:mi mathvariant="normal">Ξ</u:mi></u:math> meson-baryon channels. In the second scenario, the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi mathvariant="normal">Λ</x:mi><x:mo stretchy="false">(</x:mo><x:mn>1670</x:mn><x:mo stretchy="false">)</x:mo></x:math> is dynamically generated from these isospin-0 coupled channels. The <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>K</cb:mi><cb:mo>−</cb:mo></cb:msup><cb:mi>p</cb:mi></cb:math> scattering data and the pole structures of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi mathvariant="normal">Λ</eb:mi><eb:mo stretchy="false">(</eb:mo><eb:mn>1405</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math> and the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi mathvariant="normal">Λ</jb:mi><jb:mo stretchy="false">(</jb:mo><jb:mn>1670</jb:mn><jb:mo stretchy="false">)</jb:mo></jb:math> can be simultaneously described well in both scenarios. However, a comparison of the finite-volume spectra to lattice QCD calculations reveals significant differences between these scenarios, with a clear preference for the first case. Thus the lattice QCD results play a crucial role in allowing us to distinguish between these two scenarios for the internal structure of the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi mathvariant="normal">Λ</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mn>1670</ob:mn><ob:mo stretchy="false">)</ob:mo></ob:math>.