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

TL;DR

This work develops a comprehensive, helicity-based framework to study P and CP violation in the three-body decay $\Xi_c^{+} \to \Xi^{-} \pi^{+}\pi^{+}$ produced in polarized $e^+e^-$ collisions. By integrating production via polarized virtual photons, intermediate resonances, cascade decays, and joint angular distributions through spin-density matrices, the authors define parity-violating decay parameters $\alpha_{\Xi_c^{+}}$, $\beta_{\Xi_c^{+}}$, and $\gamma_{\Xi_c^{+}}$ and CP observables $\mathcal{A}_{CP}$, $\mathcal{B}_{CP}$, and $\mathcal{C}_{CP}$, with explicit analytic expressions and a likelihood-based extraction framework. Numerical studies show that beam polarization, particularly a transverse component $p_T$, significantly improves precision, especially for $\gamma_{\Xi_c^{+}}$ and $\mathcal{A}_{CP}$, while SM expectations for CP violation in charm are tiny ($\mathcal{O}(10^{-4}-10^{-5})$); nonetheless, observing CP violation would require very large data samples, of order $10^9$ $\Xi_c^{+}\bar{\Xi}_c^{-}$ events, underscoring the need for next-generation facilities like the STCF. Overall, the paper provides a robust theoretical framework to guide future experimental investigations of $P$ and $CP$ in charm baryon decays.

Abstract

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.

Figures (15)

• Figure 1: Tree and penguin diagrams as examples for $\Xi_c^+ \to \Xi^- \pi^+\pi^+$ decay.
• Figure 2: Definition of helicity frame at $e^+e^-$ collider.
• Figure 3: Angular distributions of $\phi_1$ for $p_T=0$, $0.5$, $0.9$ (dotted, dashed and solid lines, respectively).
• Figure 4: Angular distributions of $\cos\theta_3$ for $g^{\Xi^-}_+/f^{\Xi^-}_+=0$, $0.5$, $0.9$ (dotted, dashed and solid lines, respectively).
• Figure 5: Weighted $\mathcal{P}_0$ as a function of $\cos\theta_1$ for $p_T=0$, $0.5$, $0.9$ (dotted, dashed and solid lines, respectively).