Stringent test of $CP$ symmetry in $Σ^+$ hyperon decays

Abstract

The non-leptonic two-body weak decays $Σ^{+} \to p π^{0}$ and $\barΣ^{-} \to \bar{p} π^{0}$ are investigated, utilizing $(1.0087\pm0.0044)\times10^{10}$ $J/ψ$ events and $(2.7124\pm0.0143)\times10^{9}$ $ψ(3686)$ events collected by BESIII experiment. The precision of the weak-decay parameters for the decays $Σ^{+} \to p π^{0}$ ($α_{0}$) and $\barΣ^{-} \to \bar{p} π^{0}$ ($\barα_{0}$) is improved by a factor of three compared to the previous world average. Furthermore, the quantum-entangled $Σ^{+}\barΣ^{-}$ system enables the most precise test of $CP$ symmetry for the decay $Σ^+\to pπ^0$, through the asymmetry observable $A_{CP}=(α_{0}+\barα_{0})/(α_{0}-\barα_{0})$ that is measured to be $-0.0118\pm0.0083_{\rm stat}\pm0.0028_{\rm syst}$. Assuming $CP$ conservation, the average decay parameter is determined to be ${\left< α_{\rm 0}\right>} = (α_0-\barα_0)/2=-0.9869\pm0.0011_{\rm stat}\pm0.0016_{\rm syst}$, which is the most precise measurement of the asymmetry decay parameters in baryon sectors. The angular dependence of the ratio of the polarization of the $Σ^+$ in both $J/ψ$ and $ψ(3686)$ decays is studied for the first time.

Figures (4)

• Figure 1: The helicity frame definition for the decay processes $\Psi \to\Sigma^+\bar{\Sigma}^-$, $\Sigma^+\to p \pi^0$, $\bar{\Sigma}^-\to \bar{p} \pi^0$ in the center-of-mass (CM) system of the $e^{+} e^{-}$ collision. The helicity angles are defined with respect to the direction of the outgoing hyperon in the CM frame, where $\hat{z}_{\Sigma^+}$ is defined along the $\Sigma^+$ momentum direction in the CM of the $e^{+} e^{-}$ collision.
• Figure 2: Distribution of $M_{\bar{p} \pi^{0}}$ versus $M_{p \pi^{0}}$ for the $\psi(3686)$ data sample. The variation in event density distribution is caused by the kinematic fit. The green box denotes the signal region, and the red ones indicate the sideband regions.
• Figure 3: The moment $M(\cos\theta_{\Sigma^{+}})$ is a function of $\cos\theta_{\Sigma^{+}}$ for $\Psi\to\Sigma^{+}\bar{\Sigma}^{-}\to p\pi^0\bar{p}\pi^0$. The black and red data points with error bars are obtained independently via Eq. \ref{['fig:moment']} for $\psi(3686)$ and $J/\psi$ decays. The blue and green solid lines are drawn with the measured parameters, and the cyan dashed line represents the distribution without polarization uniformly distributed in phase space.
• Figure 4: The angular distribution of the ratio of polarization between $J/\psi$ and $\psi(3686)$ decays. The black dots with error bars are the data, the blue solid line is the fitting results, The red line represents a ratio of $-1$. Comparing the $\Sigma^+$ from the $J/\psi$ decay, the range of $\cos\theta_{\Sigma^+}$ in the shaded area (perpendicular to the electron beam direction) indicates the enhanced polarization of the $\Sigma^+$ in $\psi(3686)$ decays.