Test of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> Symmetry in Hyperon to Neutron Decays
M. Ablikim, М. Н. Ачасов, P. Adlarson, X. Ai, R. Aliberti, A. Amoroso, M. R. An, Q. An, Yu Bai, O. Bakina, I. Balossino, Y. Ban, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. Bertani, D. Bettoni, F. Bianchi, E. Bianco, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Çetin, J. F. Chang, T. T. Chang, W. L. Chang, G. R., G. Chelkov, C. Chen, Chao Chen, G. Chen, Haifeng Chen, M. L. Chen, S. J. Chen, S. M. Chen, T. Chen, Xiaoyan Chen, X. T. Chen, Y. B. Chen, Y. Q. Chen, Z. J. Chen, W. S. Cheng, S. K. Choi, X. Chu, G. Cibinetto, S. C. Coen, F. Cossio, J. J. Cui, H. L. Dai, J. P. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Zhenhong Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, B. Ding, X. X. Ding, Y. Ding, Y. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, Z. H. Duan, P. Egorov, Y. L. Fan, J. Fang, S. S. Fang, Wenxing Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, K. Fischer, M. Fritsch, C. Fritzsch, C. D. Fu, J. Fu, Y. W. Fu, He Gao, Y. N. Gao, Yang Gao, S. Garbolino, I. Garzia, P. T. Ge
Abstract
The quantum entangled $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}{\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}$ pairs from $(1.0087\ifmmode\pm\else\textpm\fi{}0.0044)\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }\text{ }J/\ensuremath{\psi}$ events taken by the BESIII detector are used to study the nonleptonic two-body weak decays ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}n{\ensuremath{\pi}}^{+}$ and ${\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{n}{\ensuremath{\pi}}^{\ensuremath{-}}$. The $CP$-odd weak decay parameters of the decays ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}n{\ensuremath{\pi}}^{+}$ (${\ensuremath{\alpha}}_{+}$) and ${\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{n}{\ensuremath{\pi}}^{\ensuremath{-}}$ (${\overline{\ensuremath{\alpha}}}_{\ensuremath{-}}$) are determined to be $0.0481\ifmmode\pm\else\textpm\fi{}0.003{1}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.001{9}_{\mathrm{syst}}$ and $\ensuremath{-}0.0565\ifmmode\pm\else\textpm\fi{}0.004{7}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.002{2}_{\mathrm{syst}}$, respectively. The decay parameter ${\overline{\ensuremath{\alpha}}}_{\ensuremath{-}}$ is measured for the first time, and the accuracy of ${\ensuremath{\alpha}}_{+}$ 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 ${A}_{CP}=({\ensuremath{\alpha}}_{+}+{\overline{\ensuremath{\alpha}}}_{\ensuremath{-}})/({\ensuremath{\alpha}}_{+}\ensuremath{-}{\overline{\ensuremath{\alpha}}}_{\ensuremath{-}})=\ensuremath{-}0.080\ifmmode\pm\else\textpm\fi{}0.05{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.02{8}_{\mathrm{syst}}$. Assuming $CP$ conservation, the average decay parameter is determined as $⟨{\ensuremath{\alpha}}_{+}⟩=({\ensuremath{\alpha}}_{+}\ensuremath{-}{\overline{\ensuremath{\alpha}}}_{\ensuremath{-}})/2=\ensuremath{-}0.0506\ifmmode\pm\else\textpm\fi{}0.002{6}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.001{9}_{\mathrm{syst}}$, while the ratios ${\ensuremath{\alpha}}_{+}/{\ensuremath{\alpha}}_{0}$ and ${\overline{\ensuremath{\alpha}}}_{\ensuremath{-}}/{\overline{\ensuremath{\alpha}}}_{0}$ are $\ensuremath{-}0.0490\ifmmode\pm\else\textpm\fi{}0.003{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.002{1}_{\mathrm{syst}}$ and $\ensuremath{-}0.0571\ifmmode\pm\else\textpm\fi{}0.005{3}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.003{2}_{\mathrm{syst}}$, where ${\ensuremath{\alpha}}_{0}$ and ${\overline{\ensuremath{\alpha}}}_{0}$ are the decay parameters of the decays ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}$ and ${\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{p}{\ensuremath{\pi}}^{0}$, respectively.