Topological amplitudes of charmed baryon decays in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:msub><mml:mo stretchy="fals

Charmed baryon decay plays an important role in studying the weak and strong interactions. Topological diagram is an intuitive tool for analyzing the dynamics of heavy hadron decays. In this work, we investigate the topological diagrams of charmed baryon antitriplet (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="script">B</a:mi><a:mrow><a:mi>c</a:mi><a:mover accent="true"><a:mn>3</a:mn><a:mo stretchy="false">¯</a:mo></a:mover></a:mrow></a:msub></a:math>) decays into a light baryon octet (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi mathvariant="script">B</f:mi><f:mn>8</f:mn></f:msub></f:math>) and a light meson (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>M</i:mi></i:math>). A one-to-one mapping between the topological diagram and the invariant tensor is established. The topological diagrams of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="script">B</k:mi><k:mrow><k:mi>c</k:mi><k:mover accent="true"><k:mn>3</k:mn><k:mo stretchy="false">¯</k:mo></k:mover></k:mrow></k:msub><k:mo stretchy="false">→</k:mo><k:msubsup><k:mi mathvariant="script">B</k:mi><k:mn>8</k:mn><k:mi>S</k:mi></k:msubsup><k:mi>M</k:mi></k:math> modes (where <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi mathvariant="script">B</r:mi><r:mn>8</r:mn><r:mi>S</r:mi></r:msubsup></r:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi mathvariant="script">B</u:mi><u:mn>8</u:mn><u:mi>A</u:mi></u:msubsup></u:math> are the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi>q</x:mi><x:mn>1</x:mn></x:msub><x:mo stretchy="false">↔</x:mo><x:msub><x:mi>q</x:mi><x:mn>2</x:mn></x:msub></x:math> symmetric and antisymmetric octets) and the diagrams with a quark loop are presented for the first time. The completeness of topologies is confirmed by permutation. The linear relations of topologies are obtained by deriving the relation between the topological amplitudes constructed by the third- and second-rank octet tensors. It is found the topologies contributing to the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi mathvariant="script">B</ab:mi><ab:mrow><ab:mi>c</ab:mi><ab:mover accent="true"><ab:mn>3</ab:mn><ab:mo stretchy="false">¯</ab:mo></ab:mover></ab:mrow></ab:msub><ab:mo stretchy="false">→</ab:mo><ab:msubsup><ab:mi mathvariant="script">B</ab:mi><ab:mn>8</ab:mn><ab:mi>S</ab:mi></ab:msubsup><ab:mi>M</ab:mi></ab:math> modes can be determined by the topologies contributing to the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi mathvariant="script">B</hb:mi><hb:mrow><hb:mi>c</hb:mi><hb:mover accent="true"><hb:mn>3</hb:mn><hb:mo stretchy="false">¯</hb:mo></hb:mover></hb:mrow></hb:msub><hb:mo stretchy="false">→</hb:mo><hb:msubsup><hb:mi mathvariant="script">B</hb:mi><hb:mn>8</hb:mn><hb:mi>A</hb:mi></hb:msubsup><hb:mi>M</hb:mi></hb:math> modes, and vice versa. The equations of <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>S</ob:mi><ob:mi>U</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mn>3</ob:mn><ob:mo stretchy="false">)</ob:mo></ob:math> irreducible amplitudes decomposed by topologies are derived through two different intermediate amplitudes. However, the inverse solution does not exist since the number of topologies exceeds number of <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>S</sb:mi><sb:mi>U</sb:mi><sb:mo stretchy="false">(</sb:mo><sb:mn>3</sb:mn><sb:mo stretchy="false">)</sb:mo></sb:math> irreducible amplitudes. Applying this framework to the Standard Model, it is found there are thirteen independent <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mi>S</wb:mi><wb:mi>U</wb:mi><wb:mo stretchy="false">(</wb:mo><wb:mn>3</wb:mn><wb:mo stretchy="false">)</wb:mo></wb:math> irreducible amplitudes contributing to the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:msub><ac:mi mathvariant="script">B</ac:mi><ac:mrow><ac:mi>c</ac:mi><ac:mover accent="true"><ac:mn>3</ac:mn><ac:mo stretchy="false">¯</ac:mo></ac:mover></ac:mrow></ac:msub><ac:mo stretchy="false">→</ac:mo><ac:msub><ac:mi mathvariant="script">B</ac:mi><ac:mn>8</ac:mn></ac:msub><ac:mi>M</ac:mi></ac:math> decays. Among these, four amplitudes associated with three-dimensional operators are significant for <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:mi>C</hc:mi><hc:mi>P</hc:mi></hc:math> asymmetries. Considering the suppressions due to small Cabibbo-Kobayashi-Maskawa matrix elements and the Körner-Pati-Woo theorem, the branching fractions of charmed baryon decays are dominated by five <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mi>S</jc:mi><jc:mi>U</jc:mi><jc:mo stretchy="false">(</jc:mo><jc:mn>3</jc:mn><jc:mo stretchy="false">)</jc:mo></jc:math> irreducible amplitudes in the <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:mi>S</nc:mi><nc:mi>U</nc:mi><nc:mo stretchy="false">(</nc:mo><nc:mn>3</nc:mn><nc:msub><nc:mo stretchy="false">)</nc:mo><nc:mi>F</nc:mi></nc:msub></nc:math> limit. Quark-loop diagrams could enhance the <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:mi>U</rc:mi></rc:math>-spin breaking effects and increase the branching fraction difference of two decay channels. Systematic measurements of branching fractions of the singly Cabibbo-suppressed modes could help identify promising channels for searching for <tc:math xmlns:tc="http://www.w3.org/1998/Math/MathML" display="inline"><tc:mi>C</tc:mi><tc:mi>P</tc:mi></tc:math> asymmetries in the charmed baryon sector. Published by the American Physical Society 2024