Lattice QCD study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>−</mml:mo><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>N</mml:mi></mml:math> scattering and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Λ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1405</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> resonance

Abstract

A lattice QCD computation of the coupled channel <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>π</a:mi><a:mi mathvariant="normal">Σ</a:mi><a:mi>–</a:mi><a:mover accent="true"><a:mi>K</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>N</a:mi></a:math> scattering amplitudes in 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>1405</f:mn><f:mo stretchy="false">)</f:mo></f:math> region is detailed. Results are obtained using a single ensemble of gauge field configurations with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>N</k:mi><k:mi mathvariant="normal">f</k:mi></k:msub><k:mo>=</k:mo><k:mn>2</k:mn><k:mo>+</k:mo><k:mn>1</k:mn></k:math> dynamical quark flavors and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>m</n:mi><n:mi>π</n:mi></n:msub><n:mo>≈</n:mo><n:mn>200</n:mn><n:mtext> </n:mtext><n:mtext> </n:mtext><n:mi>MeV</n:mi></n:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>m</p:mi><p:mi>K</p:mi></p:msub><p:mo>≈</p:mo><p:mn>487</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>MeV</p:mi></p:math>. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>K</r:mi></r:math>-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>π</t:mi><t:mi mathvariant="normal">Σ</t:mi></t:math> threshold and a resonance pole just below the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mover accent="true"><w:mi>K</w:mi><w:mo stretchy="false">¯</w:mo></w:mover><w:mi>N</w:mi></w:math> threshold. Published by the American Physical Society 2024

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