Eur. Phys. J. C (2024) 84: 1014
https://doi.org/10.1140/epjc/s10052-024-13389-y

Regular Article - Theoretical Physics

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

¹ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, 210023, Nanjing, Jiangsu, China
² School of Physics, East China University of Science and Technology, 200237, Shanghai, China
³ Shanghai Key Laboratory of Particle Physics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China
⁴ Particle Theory and Cosmology Group, Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), 34126, Daejeon, Korea
⁵ School of Materials Science and Physics, China University of Mining and Technology, 221116, Xuzhou, China

^a sunjin0810@ibs.re.kr

Received: 18 July 2024
Accepted: 16 September 2024
Published online: 7 October 2024

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 ${\chi }^2/d.o.f=0.788$ and find that the contribution of the amplitude proportional to $V_{\mathit{cb}}^{\ast }{V}_{\mathit{ub}}$ is of the order $\sim 0.01$, 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 $Br({\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+})$, and by excluding this data, ${\chi }^2/d.o.f$ 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 $V_{\mathit{cb}}^{\ast }{V}_{\mathit{ub}}$ 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.