Evidence of the low-lying baryon <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>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> in the process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi mathvariant="normal">Λ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">→</mml:mo> <mml:mi>η</mml:mi> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:math>

Abstract

Motivated by the Belle measurements of the process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>c</a:mi> <a:mo>+</a:mo> </a:msubsup> <a:mo stretchy="false">→</a:mo> <a:mi>η</a:mi> <a:msup> <a:mi>π</a:mi> <a:mo>+</a:mo> </a:msup> <a:mi mathvariant="normal">Λ</a:mi> </a:math> , we investigate this process by considering the contributions from 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> , <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>a</k:mi> <k:mn>0</k:mn> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mn>980</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> , and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi mathvariant="normal">Σ</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>1385</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> . In addition, we also consider the predicted low-lying baryon <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> . Our results involving the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msup> <y:mi mathvariant="normal">Σ</y:mi> <y:mo>*</y:mo> </y:msup> <y:mo stretchy="false">(</y:mo> <y:mn>1</y:mn> <y:mo>/</y:mo> <y:msup> <y:mn>2</y:mn> <y:mo>−</y:mo> </y:msup> <y:mo stretchy="false">)</y:mo> </y:math> are favored by fitting to the Belle data of the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi>η</db:mi> <db:mi mathvariant="normal">Λ</db:mi> </db:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msup> <gb:mi>π</gb:mi> <gb:mo>+</gb:mo> </gb:msup> <gb:mi mathvariant="normal">Λ</gb:mi> </gb:math> invariant mass distributions. Furthermore, we predict the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>η</jb:mi> <jb:msup> <jb:mi>π</jb:mi> <jb:mo>+</jb:mo> </jb:msup> </jb:math> invariant mass distribution and the angular distribution <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>d</lb:mi> <lb:mi mathvariant="normal">Γ</lb:mi> <lb:mo>/</lb:mo> <lb:mi>d</lb:mi> <lb:mi>cos</lb:mi> <lb:mi>θ</lb:mi> </lb:math> , which are significantly different depending on whether or not the contribution from the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msup> <ob:mi mathvariant="normal">Σ</ob:mi> <ob:mo>*</ob:mo> </ob:msup> <ob:mo stretchy="false">(</ob:mo> <ob:mn>1</ob:mn> <ob:mo>/</ob:mo> <ob:msup> <ob:mn>2</ob:mn> <ob:mo>−</ob:mo> </ob:msup> <ob:mo stretchy="false">)</ob:mo> </ob:math> is considered. Finally, we show that, with the contribution from the <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:msup> <tb:mi mathvariant="normal">Σ</tb:mi> <tb:mo>*</tb:mo> </tb:msup> <tb:mo stretchy="false">(</tb:mo> <tb:mn>1</tb:mn> <tb:mo>/</tb:mo> <tb:msup> <tb:mn>2</tb:mn> <tb:mo>−</tb:mo> </tb:msup> <tb:mo stretchy="false">)</tb:mo> </tb:math> , the calculated Dalitz plot agrees with the Belle measurements. Future precise measurements of the process <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:msubsup> <yb:mi mathvariant="normal">Λ</yb:mi> <yb:mi>c</yb:mi> <yb:mo>+</yb:mo> </yb:msubsup> <yb:mo stretchy="false">→</yb:mo> <yb:mi>η</yb:mi> <yb:msup> <yb:mi>π</yb:mi> <yb:mo>+</yb:mo> </yb:msup> <yb:mi mathvariant="normal">Λ</yb:mi> </yb:math> could shed further light on the existence of the low-lying <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"> <dc:msup> <dc:mi mathvariant="normal">Σ</dc:mi> <dc:mo>*</dc:mo> </dc:msup> <dc:mo stretchy="false">(</dc:mo> <dc:mn>1</dc:mn> <dc:mo>/</dc:mo> <dc:msup> <dc:mn>2</dc:mn> <dc:mo>−</dc:mo> </dc:msup> <dc:mo stretchy="false">)</dc:mo> </dc:math> . Published by the American Physical Society 2024

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