Phenomenological study of $Ω_c\rightarrow Ω^-π^+$ at polarized electron-positron collider

TL;DR

The paper develops a helicity-based, spin-density-matrix framework to study P and CP violation in the charm-baryon decay $\Omega_c \to \Omega^- \pi^+$ at polarized $e^+e^-$ colliders. It defines angular and CP-sensitive asymmetry parameters ($\alpha_c$, $\alpha_{\Omega_c}$, $\alpha_{\Omega^-}$, $\alpha_{\Lambda}$, and $\mathcal{A}_{CP}$) and derives the full joint angular distributions for the decay chain, incorporating beam polarizations. Sensitivity studies using a maximum-likelihood approach show how transverse and longitudinal beam polarizations improve parameter precision, with quantitative expectations for STCF under realistic efficiencies and data samples; the analysis also provides CP-violation reach estimates and emphasizes the need for large data samples ($\sim 10^9$ events) to observe tiny SM-level CP effects. Overall, the work offers a concrete theoretical and statistical foundation to guide future charm CP tests at STCF and related facilities, and it extends the methodology to analogous decay channels such as $\Xi_c^+ \to \Xi^0 \pi^+$ and $\Xi_c^0 \to \Xi^- \pi^+$.

Abstract

The exploration of symmetry laws stands as a cutting-edge direction in modern physics research. This work delves into the examination of P and CP symmetry properties within the charm quark system by analyzing asymmetry parameters in the two-body decay process of $Ω_c$. By accounting for the polarization effects of electron and positron beams and employing the helicity formalism, we systematically analyze the decay characteristics of $Ω_c$ and its subsequent hyperon decays through specific asymmetry parameters. A comprehensive formulation of the angular distribution for these decay processes has been developed. The research assesses the detection sensitivity of asymmetry parameters in the $Ω_c\rightarrow Ω^-π^+$ decay mode across different experimental conditions, including varying data sample sizes and beam polarization configurations. These results contribute to enriching a theoretical foundation for forthcoming experimental endeavors at the STCF, offering significant implications for symmetry studies in the charm sector.

Figures (12)

• Figure 1: Definition of helicity angles at $e^+e^-$ collider.
• Figure 2: Tree and penguin diagrams as examples for $\Omega_c\rightarrow\Omega^-\pi^+$ decay.
• Figure 3: The $\cos\theta_1$ distributions of polarization $\mathcal{P}_y$ for different transverse polarizations of beams. Here $p_L=0$ is used.
• Figure 4: The $\cos\theta_1$ distributions of polarization $\mathcal{P}_z$ for different transverse polarizations of beams. Here $p_L=0.5$ is used.
• Figure 5: Magnitudes of the $\Omega_c$ polarization as a function of $\cos\theta_1$ for different beam polarizations.