<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mover accent="true"><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo>−</mml:mo></mml:msup></mml:math> Polarization in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3686</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> Decays
M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, A. Amoroso, Q. An, Anita, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Biernat, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Z. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, W. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, R. B. de Boer, D. Dedovich, Zhenhong Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, S. X. Du, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, M. Fritsch, C. D. Fu, Y. Fu, Xinlei Gao, Y. Gao, Y. Gao, Y. Gao, I. Garzia, E. Gersabeck, A Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, C. Y. Guan, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, Y. P. Guo, A. Guskov, S. Han, T. T. Han, T. Z. Han, X. Q. Hao, F. A. Harris
Abstract
From $1310.6\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }J/\ensuremath{\psi}$ and $448.1\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\ensuremath{\psi}(3686)$ events collected with the BESIII experiment, we report the first observation of ${\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}$ spin polarization in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}[\ensuremath{\psi}(3686)]\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}{\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}$ decays. The relative phases of the form factors $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}$ have been measured to be $(\ensuremath{-}15.5\ifmmode\pm\else\textpm\fi{}0.7\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode^\circ\else\textdegree\fi{}$ and $(21.7\ifmmode\pm\else\textpm\fi{}4.0\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode^\circ\else\textdegree\fi{}$ with $J/\ensuremath{\psi}$ and $\ensuremath{\psi}(3686)$ data, respectively. The nonzero value of $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Phi}}$ allows for a direct and simultaneous measurement of the decay asymmetry parameters of ${\mathrm{\ensuremath{\Sigma}}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}({\ensuremath{\alpha}}_{0}=\ensuremath{-}0.998\ifmmode\pm\else\textpm\fi{}0.037\ifmmode\pm\else\textpm\fi{}0.009)$ and ${\overline{\mathrm{\ensuremath{\Sigma}}}}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{p}{\ensuremath{\pi}}^{0}({\overline{\ensuremath{\alpha}}}_{0}=0.990\ifmmode\pm\else\textpm\fi{}0.037\ifmmode\pm\else\textpm\fi{}0.011)$, the latter value being determined for the first time. The average decay asymmetry, $({\ensuremath{\alpha}}_{0}\ensuremath{-}{\overline{\ensuremath{\alpha}}}_{0})/2$, is calculated to be $\ensuremath{-}0.994\ifmmode\pm\else\textpm\fi{}0.004\ifmmode\pm\else\textpm\fi{}0.002$. The $CP$ asymmetry ${A}_{CP,\mathrm{\ensuremath{\Sigma}}}=({\ensuremath{\alpha}}_{0}+{\overline{\ensuremath{\alpha}}}_{0})/({\ensuremath{\alpha}}_{0}\ensuremath{-}{\overline{\ensuremath{\alpha}}}_{0})=\ensuremath{-}0.004\ifmmode\pm\else\textpm\fi{}0.037\ifmmode\pm\else\textpm\fi{}0.010$ is extracted for the first time, and is found to be consistent with $CP$ conservation.