CP violation in hadronic weak decays of charmed baryons in the topological diagrammatic approach

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> violation in the charmed baryon sector is generally expected to be very small, of order <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>10</c:mn><c:mrow><c:mo>−</c:mo><c:mn>4</c:mn></c:mrow></c:msup></c:math> or even smaller. Nevertheless, large long-distance penguin topologies can be induced through final-state rescattering. At the hadron level, they are manifested as the triangle and bubble diagrams. However, these diagrams consist of not only the penguin but also other tree topologies. Therefore, we focus on the flavor structure of the these diagrams and project out their contributions to penguin and tree topologies. The analysis is performed within the framework of the topological diagram approach and the irreducible SU(3) approach in which the SU(3) flavor symmetry of QCD is realized to describe the nonleptonic decays of charmed baryons. <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>C</e:mi><e:mi>P</e:mi></e:mrow></e:math> violation at the per mille level is found in the following decay modes: <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msubsup><g:mrow><g:mi mathvariant="normal">Λ</g:mi></g:mrow><g:mrow><g:mi>c</g:mi></g:mrow><g:mrow><g:mo>+</g:mo></g:mrow></g:msubsup><g:mo stretchy="false">→</g:mo><g:mi>p</g:mi><g:msup><g:mrow><g:mi>π</g:mi></g:mrow><g:mrow><g:mn>0</g:mn></g:mrow></g:msup><g:mo>,</g:mo><g:msubsup><g:mrow><g:mi mathvariant="normal">Λ</g:mi></g:mrow><g:mrow><g:mi>c</g:mi></g:mrow><g:mrow><g:mo>+</g:mo></g:mrow></g:msubsup><g:mo stretchy="false">→</g:mo><g:mi>p</g:mi><g:msup><g:mrow><g:mi>η</g:mi></g:mrow><g:mrow><g:mo>′</g:mo></g:mrow></g:msup><g:mo>,</g:mo><g:msubsup><g:mrow><g:mi mathvariant="normal">Ξ</g:mi></g:mrow><g:mrow><g:mi>c</g:mi></g:mrow><g:mrow><g:mn>0</g:mn></g:mrow></g:msubsup><g:mo stretchy="false">→</g:mo><g:msup><g:mrow><g:mi mathvariant="normal">Σ</g:mi></g:mrow><g:mrow><g:mn>0</g:mn></g:mrow></g:msup><g:mi>η</g:mi></g:mrow></g:math>, and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msubsup><p:mrow><p:mi mathvariant="normal">Ξ</p:mi></p:mrow><p:mrow><p:mi>c</p:mi></p:mrow><p:mrow><p:mo>+</p:mo></p:mrow></p:msubsup><p:mo stretchy="false">→</p:mo><p:msup><p:mrow><p:mi mathvariant="normal">Σ</p:mi></p:mrow><p:mrow><p:mo>+</p:mo></p:mrow></p:msup><p:mi>η</p:mi></p:mrow></p:math>. <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>C</u:mi><u:mi>P</u:mi></u:math> asymmetries in the last three modes receive sizable contributions from the SU(3)-flavor-singlet hairpin diagram.