Odd-parity strange baryons <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac

We examine the spectrum of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Σ</a:mi> <a:mo stretchy="false">(</a:mo> <a:msup> <a:mfrac> <a:mn>1</a:mn> <a:mn>2</a:mn> </a:mfrac> <a:mo>−</a:mo> </a:msup> <a:mo stretchy="false">)</a:mo> </a:math> family based on the experimental <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi>K</f:mi> <f:mo>−</f:mo> </f:msup> <f:mi>p</f:mi> </f:math> scattering data and lattice QCD simulations within the Hamiltonian effective field theory. Especially, two different scenarios are constructed in order to clarify whether there is one or two <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi mathvariant="normal">Σ</h:mi> <h:mo stretchy="false">(</h:mo> <h:msup> <h:mfrac> <h:mn>1</h:mn> <h:mn>2</h:mn> </h:mfrac> <h:mo>−</h:mo> </h:msup> <h:mo stretchy="false">)</h:mo> </h:math> resonances with masses around 1.5–1.7 GeV. The relevant lattice QCD data support our scenario with two resonance poles at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mn>1687</m:mn> <m:mo>−</m:mo> <m:mn>110</m:mn> <m:mi>i</m:mi> </m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mn>1714</o:mn> <o:mo>−</o:mo> <o:mn>14</o:mn> <o:mi>i</o:mi> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>MeV</o:mi> </o:math> in which the bare strange triquark core plays an important role. We also show an extra clear cusp structure around 1.4 GeV in our scattering T matrices associated with the odd-parity strange baryons.