How to unravel the nature of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1430</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> state from correlation functions

Abstract

We calculate the correlation functions for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mover accent="true"> <a:mi>K</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mn>0</a:mn> </a:msup> <a:mi>p</a:mi> <a:mo>,</a:mo> <a:msup> <a:mi>π</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi mathvariant="normal">Σ</a:mi> <a:mn>0</a:mn> </a:msup> <a:mo>,</a:mo> <a:msup> <a:mi>π</a:mi> <a:mn>0</a:mn> </a:msup> <a:msup> <a:mi mathvariant="normal">Σ</a:mi> <a:mo>+</a:mo> </a:msup> <a:mo>,</a:mo> <a:msup> <a:mi>π</a:mi> <a:mo>+</a:mo> </a:msup> <a:mi mathvariant="normal">Λ</a:mi> </a:math> , and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>η</h:mi> <h:msup> <h:mi mathvariant="normal">Σ</h:mi> <h:mo>+</h:mo> </h:msup> </h:math> states, which in the chiral unitary approach predict an excited <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi mathvariant="normal">Σ</k:mi> <k:mo>*</k:mo> </k:msup> <k:mo stretchy="false">(</k:mo> <k:mn>1</k:mn> <k:mo>/</k:mo> <k:msup> <k:mn>2</k:mn> <k:mo>−</k:mo> </k:msup> <k:mo stretchy="false">)</k:mo> </k:math> state at the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mover accent="true"> <p:mi>K</p:mi> <p:mo stretchy="false">¯</p:mo> </p:mover> <p:mi>N</p:mi> </p:math> threshold, recently observed by the Belle Collaboration. Once this is done, we tackle the inverse problem of seeing how much information one can obtain from these correlation functions. With the resampling method, one can determine the scattering parameters of all the channels with relative precision, by means of the analysis in a general framework, and find a clear cusplike structure corresponding to the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msup> <t:mi mathvariant="normal">Σ</t:mi> <t:mo>*</t:mo> </t:msup> <t:mo stretchy="false">(</t:mo> <t:mn>1</t:mn> <t:mo>/</t:mo> <t:msup> <t:mn>2</t:mn> <t:mo>−</t:mo> </t:msup> <t:mo stretchy="false">)</t:mo> </t:math> in the different amplitudes at the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mover accent="true"> <y:mi>K</y:mi> <y:mo stretchy="false">¯</y:mo> </y:mover> <y:mi>N</y:mi> </y:math> threshold. Published by the American Physical Society 2024

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