Observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi>η</mml:mi><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> and improved measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo stretchy="false">(</mml:mo><mml:mo>+</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>
M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, M. Alekseev, 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, I. Boyko, R. A. Briere, H. Cai, X. Z. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Çetin, J. Chai, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, J. 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. Dai, A. Dbeyssi, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, Z. L. Dou, 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, X. L. Gao, Yang Gao, Yu 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, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, Y. P. Guo, A. Guskov, S. Han, T. T. Han, X. Q. Hao, F. A. Harris
Abstract
Using an ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data sample corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the absolute branching fractions of ${D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\eta}{\ensuremath{\pi}}^{+}$, ${D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, and ${D}^{0}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ to be $(2.96\ifmmode\pm\else\textpm\fi{}0.24\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $(2.23\ifmmode\pm\else\textpm\fi{}0.15\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and $(1.20\ifmmode\pm\else\textpm\fi{}0.07\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, respectively, where the first uncertainties are statistical and the second ones are systematic. The ${D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\eta}{\ensuremath{\pi}}^{+}$ decay is observed for the first time, and the branching fractions of ${D}^{+(0)}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0(\ensuremath{-})}$ are measured with much improved precision. In addition we test for $CP$ asymmetries in the separated charge-conjugate branching fractions; no evidence of $CP$ violation is found.