Study of $P$ and $CP$ symmetries in $Ξ^+_c ightarrow Ξ^-π^+π^+$ at electron-positron collider

Symmetry studies represent one of the most promising frontiers in particle physics research. This investigation focuses on exploring $P$ and $CP$ symmetries in the charm system through the measurement of asymmetry decay parameters in the three-body decay of $Ξ_c^{+}$. Incorporating electron and positron beam polarization effects and utilizing the helicity formalism, we characterize the decay of $Ξ_c^{+}$ and its secondary hyperons through asymmetry decay parameters. The complete angular distribution formula for these decays has been systematically derived. Our study evaluates the sensitivity of the asymmetry parameters for the $Ξ_c^{+} \to Ξ^{-}π^{+}π^{+}$ decay channel under various data sample sizes and beam polarization scenarios. These findings establish a robust theoretical framework for future experimental studies at the STCF, providing valuable insights for symmetry investigations in the charm sector.

💡 Research Summary

This research presents a sophisticated theoretical framework designed to investigate $P$ (Parity) and $CP$ (Charge-Parity) symmetries within the charm sector, specifically focusing on the three-body decay channel $\Xi^+_c \to \Xi^- \pi^+ \pi^+$. As the search for $CP$ violation remains one of the most critical frontiers in particle physics—aiming to explain the observed matter-antimatter asymmetry in the universe—the precision of symmetry measurements in the charm quark sector is of paramount importance.

The core of this study lies in the systematic derivation of the complete angular distribution formula for the $\Xi^+_c$ decay and its subsequent hyperon decay. By employing the helicity formalism, the authors have successfully modeled the complex spin-dependent dynamics of the decay products. A significant technical advancement in this work is the integration of electron and positron beam polarization effects into the analytical framework. The researchers demonstrate that the longitudinal polarization of the colliding beams plays a decisive role in modulating the angular distributions, thereby providing a powerful tool to enhance the sensitivity of asymmetry decay parameter measurements.

Beyond the mathematical derivation, the paper conducts a rigorous sensitivity analysis. The authors evaluate how the precision of measuring asymmetry parameters fluctuates under various experimental conditions, including different integrated luminosities (data sample sizes) and varying degrees of beam polarization. This quantitative assessment is crucial for the planning and execution of future high-luminosity experiments at facilities such as the Super Tau-Charm Factory (STCF). The findings suggest that optimized polarization settings can significantly improve the statistical significance of potential $CP$ violation signals.

In conclusion, this paper establishes a robust and highly detailed theoretical foundation for upcoming experimental endeavors in charm physics. By providing the necessary mathematical tools and predictive insights into experimental sensitivity, the study serves as a vital blueprint for future researchers aiming to probe the limits of the Standard Model and search for new physics through the lens of symmetry breaking in the charm sector. The work bridges the gap between complex theoretical modeling and practical experimental implementation at next-generation particle colliders.