Analysis of hadronic weak decays of charmed baryons in the topological diagrammatic approach

We perform a global fit to the experimental data of two-body charmed baryon decays based on the topological diagrammatic approach (TDA) and take into account the phase shifts between <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi></a:math>- and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>P</c:mi></c:math>-wave amplitudes as inspired by the recent BESIII measurement of the decay asymmetry in the decay <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi mathvariant="normal">Λ</e:mi><e:mi>c</e:mi><e:mo>+</e:mo></e:msubsup><e:mo stretchy="false">→</e:mo><e:msup><e:mi mathvariant="normal">Ξ</e:mi><e:mn>0</e:mn></e:msup><e:msup><e:mi>K</e:mi><e:mo>+</e:mo></e:msup></e:math>. The TDA has the advantage that it is more intuitive, graphic, and easier to implement model calculations. The measured branching fractions and decay asymmetries are well accommodated in the TDA except for a few modes, in particular, the predicted <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi mathvariant="script">B</j:mi><j:mo stretchy="false">(</j:mo><j:msubsup><j:mi mathvariant="normal">Ξ</j:mi><j:mi>c</j:mi><j:mn>0</j:mn></j:msubsup><j:mo stretchy="false">→</j:mo><j:msup><j:mi mathvariant="normal">Ξ</j:mi><j:mo>−</j:mo></j:msup><j:msup><j:mi>π</j:mi><j:mo>+</j:mo></j:msup><j:mo stretchy="false">)</j:mo><j:mo>=</j:mo><j:mo stretchy="false">(</j:mo><j:mn>2.83</j:mn><j:mo>±</j:mo><j:mn>0.10</j:mn><j:mo stretchy="false">)</j:mo><j:mo>%</j:mo></j:math> is larger than its current value. The equivalence of the TDA and the irreducible SU(3) approach (IRA) is established. We show that the number of the minimum set of tensor invariants in the IRA and the topological amplitudes in the TDA is the same and present their relations. The predicted magnitudes of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>S</t:mi></t:math>- and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>P</v:mi></v:math>-wave amplitudes and their phase shifts are presented for measured and yet-to-be-measured modes in both the TDA and IRA which can be tested in the near future. Besides the decay <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msubsup><x:mi mathvariant="normal">Λ</x:mi><x:mi>c</x:mi><x:mo>+</x:mo></x:msubsup><x:mo stretchy="false">→</x:mo><x:msup><x:mi mathvariant="normal">Ξ</x:mi><x:mn>0</x:mn></x:msup><x:msup><x:mi>K</x:mi><x:mo>+</x:mo></x:msup></x:math>, there exist several modes which proceed only through <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>W</cb:mi></cb:math>-exchange. In particular, the observed channel <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mi mathvariant="normal">Ξ</eb:mi><eb:mi>c</eb:mi><eb:mn>0</eb:mn></eb:msubsup><eb:mo stretchy="false">→</eb:mo><eb:msup><eb:mi mathvariant="normal">Σ</eb:mi><eb:mo>+</eb:mo></eb:msup><eb:msup><eb:mi>K</eb:mi><eb:mo>−</eb:mo></eb:msup></eb:math> should have phase shifts similar to that in <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msubsup><jb:mi mathvariant="normal">Λ</jb:mi><jb:mi>c</jb:mi><jb:mo>+</jb:mo></jb:msubsup><jb:mo stretchy="false">→</jb:mo><jb:msup><jb:mi mathvariant="normal">Ξ</jb:mi><jb:mn>0</jb:mn></jb:msup><jb:msup><jb:mi>K</jb:mi><jb:mo>+</jb:mo></jb:msup></jb:math> and its decay asymmetry is predicted to be <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mo>−</ob:mo><ob:mn>0.21</ob:mn><ob:mo>±</ob:mo><ob:mn>0.17</ob:mn></ob:math> which can be used to test our theoretical framework. In contrast, the TDA leads to a large <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>α</qb:mi></qb:math> of order <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mo>−</sb:mo><sb:mn>0.93</sb:mn></sb:math> for the decay <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msubsup><ub:mi mathvariant="normal">Ξ</ub:mi><ub:mi>c</ub:mi><ub:mo>+</ub:mo></ub:msubsup><ub:mo stretchy="false">→</ub:mo><ub:msup><ub:mi mathvariant="normal">Ξ</ub:mi><ub:mn>0</ub:mn></ub:msup><ub:msup><ub:mi>π</ub:mi><ub:mo>+</ub:mo></ub:msup></ub:math> even after the phase-shift effect is incorporated in the fit.