Precision measurement of the matrix elements for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> decays
M. Ablikim, М. Н. Ачасов, P. Adlarson, R. Aliberti, A. Amoroso, M. R. An, Q. An, Yusong Bai, O. Bakina, I. Balossino, Y. Ban, V. Batozskaya, K. Begzsuren, N. Berger, M. Berłowski, M. Bertani, D. Bettoni, F. Bianchi, E. Bianco, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, X. Z. 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, Guanxi Chen, H. S. Chen, M. L. Chen, Shipeng Chen, S. M. Chen, T. Chen, X. R. 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, Z. Y. 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, Y. W. Fu, He Gao, Yang Gao, Yang Gao, S. Garbolino, I. Garzia, P. Ge, Z. W. Ge, C. Geng
Abstract
A precision measurement of the matrix elements for $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decays is performed using a sample of $(10087\ifmmode\pm\else\textpm\fi{}44)\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }J/\ensuremath{\psi}$ decays collected with the BESIII detector. The decay $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\eta}$ is used to select clean samples of $631,686\text{ }\text{ }\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ decays and $272,322\text{ }\text{ }\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The nonzero $g{X}^{2}Y$ term for the decay mode $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decay, and no obvious structure around the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ mass threshold is observed.