Su(3) symmetry analysis in charmed baryon two body decays with penguin diagram contribution

Abstract An increasing number of experimental measurements from the BESIII, Belle, and Belle-II collaborations encourage investigations into charmed baryon two-body decay processes. By including contributions from the penguin diagrams that are ignored in previous studies, we perform a global analysis with SU(3) flavor symmetry. Assuming all form factors are real, we achieve a remarkable minimal $$\chi ^{2}/d.o.f = 0.788$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> <mml:mo>.</mml:mo> <mml:mi>o</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.788</mml:mn> </mml:mrow> </mml:math> and find that the contribution of the amplitude proportional to $$V_{cb}^*V_{ub}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>cb</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>ub</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> is of the order $$\sim 0.01$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>0.01</mml:mn> </mml:mrow> </mml:math> , comparable with the contribution of the tree-level diagram. Additionally, by using the KPW theorem to reduce the number of amplitudes from 13 to 7 in the leading contribution, it becomes possible to consider the complex form factor case for the leading IRA amplitude in the global analysis. However, the analysis of complex form factors significantly conflicts with the experimental data $$Br(\Xi _c^0\rightarrow \Xi ^-\pi ^+)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mi>r</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>Ξ</mml:mi> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>Ξ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by excluding this data, $$\chi ^2/d.o.f$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> <mml:mo>.</mml:mo> <mml:mi>o</mml:mi> <mml:mo>.</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> is reduced from 5.95 to 1.19. Although the analysis of complex form factors shows a significant central value of the penguin diagram contribution, the large errors from the corresponding form factors make it a challenge to precisely determine its true contribution. Consequently, the direct CP violation in decay processes is predicted to be approximately zero. With more data in future experiments, the penguin diagram contribution with the amplitude proportional to $$V_{cb}^*V_{ub}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>cb</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:msub> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>ub</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> will be precisely determined, allowing for a more accurate prediction of CP violation. Our analysis necessitates further theoretical investigations and experimental measurements in the future.