Test of $CP$ Symmetry in Hyperon to Neutron Decays

The quantum entangled $J/\psi \to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$ pairs from $(1.0087\pm 0.0044)\times {10}^{10}J/\psi$ events taken by the BESIII detector are used to study the nonleptonic two-body weak decays ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$ and ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{n}{\pi }^{-}$. The $CP$-odd weak decay parameters of the decays ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$ (${\alpha }_{+}$) and ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{n}{\pi }^{-}$ (${\overline{\alpha }}_{-}$) are determined to be $0.0481\pm 0.0031_{\mathrm{stat}}\pm 0.0019_{\mathrm{syst}}$ and $-0.0565\pm 0.0047_{\mathrm{stat}}\pm 0.0022_{\mathrm{syst}}$, respectively. The decay parameter ${\overline{\alpha }}_{-}$ is measured for the first time, and the accuracy of ${\alpha }_{+}$ is improved by a factor of 4 compared to the previous results. The simultaneously determined decay parameters allow the first precision $CP$ symmetry test for any hyperon decay with a neutron in the final state with the measurement of $A_{CP}=({\alpha }_{+}+{\overline{\alpha }}_{-})/({\alpha }_{+}-{\overline{\alpha }}_{-})=-0.080\pm 0.052_{\mathrm{stat}}\pm 0.028_{\mathrm{syst}}$. Assuming $CP$ conservation, the average decay parameter is determined as $⟨{\alpha }_{+}⟩=({\alpha }_{+}-{\overline{\alpha }}_{-})/2=-0.0506\pm 0.0026_{\mathrm{stat}}\pm 0.0019_{\mathrm{syst}}$, while the ratios ${\alpha }_{+}/{\alpha }_0$ and ${\overline{\alpha }}_{-}/{\overline{\alpha }}_0$ are $-0.0490\pm 0.0032_{\mathrm{stat}}\pm 0.0021_{\mathrm{syst}}$ and $-0.0571\pm 0.0053_{\mathrm{stat}}\pm 0.0032_{\mathrm{syst}}$, where ${\alpha }_0$ and ${\overline{\alpha }}_0$ are the decay parameters of the decays ${\mathrm{\Sigma }}^{+}\to p{\pi }^0$ and ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{p}{\pi }^0$, respectively.

Figure 1

The helicity frame definitions for $J/\psi \to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$, ${\mathrm{\Sigma }}^{+}\to p{\pi }^0(n{\pi }^{+})$, ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{n}{\pi }^{-}(\overline{p}{\pi }^0)$. In the $e^{+}{e}^{-}$ center-of-mass system, ${\theta }_{\mathrm{\Sigma }}$ is the angle between the ${\mathrm{\Sigma }}^{+}$ and the electron beam direction. The $z_{{\mathrm{\Sigma }}^{+}}$ axis is the moving direction of ${\mathrm{\Sigma }}^{+}$ in the $J/\psi$ rest frame, the $y_{{\mathrm{\Sigma }}^{+}}$ axis is perpendicular to the plane of ${\mathrm{\Sigma }}^{+}$ and electron, and the $x_{{\mathrm{\Sigma }}^{+}}$ axis is defined by the right-handed coordinate system.

Figure 2

Distributions of (left) $M_{\overline{n}{\pi }^{-}}$ versus $M_{p{\pi }^0}$ for $J/\psi \to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$ with ${\mathrm{\Sigma }}^{+}\to p{\pi }^0$, ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{n}{\pi }^{-}$, and (right) $M_{n{\pi }^{+}}$ versus $M_{\overline{p}{\pi }^0}$ for $J/\psi \to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$ with ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$, ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{p}{\pi }^0$. The red boxes denote the signal regions and the green ones indicate the sideband regions.

Figure 3

The moment $M(\cos {\theta }_{{\mathrm{\Sigma }}^{+}})$ for data, that is not corrected for acceptance and reconstruction efficiency, as a function of $\cos {\theta }_{{\mathrm{\Sigma }}^{+}}$ for $J/\psi \to {\mathrm{\Sigma }}^{+}{\overline{\mathrm{\Sigma }}}^{-}$ with the two decay channels: ${\mathrm{\Sigma }}^{+}\to p{\pi }^0$, ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{n}{\pi }^{-}$ and ${\mathrm{\Sigma }}^{+}\to n{\pi }^{+}$, ${\overline{\mathrm{\Sigma }}}^{-}\to \overline{p}{\pi }^0$. The black points with error bars are data with background subtracted, the red solid line is the fit result and the blue dashed line represents the distribution without polarization uniformly distributed in phase space. The height of the green band shows the absolute difference between the two decay channels with background subtracted.