Measurement of branching fractions and search for $CP$ violation in $D^{0}\toπ^{+}π^{-}η$, $D^{0}\to K^{+}K^{-}η$, and $D^{0}\toφη$ at Belle

Belle Collaboration, L. K. Li, A. J. Schwartz, K. Kinoshita, I. Adachi, H. Aihara, S. Al Said, D. M. Asner, H. Atmacan, V. Aulchenko, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. Behera, J. Bennett, M. Bessner, T. Bilka, J. Biswal, A. Bobrov, G. Bonvicini, A. Bozek, M. Bra\v, P. Branchini, T. E. Browder, A. Budano, M. Campajola, D. \v, M. -C. Chang, P. Chang, V. Chekelian, A. Chen, Y. Q. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, S. -J. Cho, S. -K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, N. Dash, G. De Nardo, G. De Pietro, R. Dhamija, F. Di Capua, Z. Dole\v, T. V. Dong, S. Eidelman, D. Epifanov, T. Ferber, B. G. Fulsom, R. Garg, V. Gaur, A. Giri, P. Goldenzweig, B. Golob, E. Graziani, T. Gu, Y. Guan, C. Hadjivasiliou, S. Halder, K. Hayasaka, W. -S. Hou, K. Inami, A. Ishikawa, M. Iwasaki, Y. Iwasaki, W. W. Jacobs, E. -J. Jang, S. Jia, Y. Jin, K. K. Joo, K. H. Kang, G. Karyan, C. Kiesling, C. H. Kim, D. Y. Kim, K. -H. Kim, S. H. Kim, Y. -K. Kim, P. Kody\v, T. Konno, A. Korobov, S. Korpar, E. Kovalenko, P. Kri\v, R. Kroeger, P. Krokovny, T. Kuhr, M. Kumar, K. Kumara, A. Kuzmin, Y. -J. Kwon, K. Lalwani, M. Laurenza, S. C. Lee, C. H. Li, L. Li Gioi, J. Libby, K. Lieret, D. Liventsev, M. Masuda, D. Matvienko, M. Merola, F. Metzner, K. Miyabayashi, R. Mizuk, G. B. Mohanty, T. Mori, M. Nakao, Z. Natkaniec, A. Natochii, L. Nayak, M. Nayak, M. Niiyama, N. K. Nisar, S. Nishida, K. Nishimura, H. Ono, P. Oskin, P. Pakhlov, G. Pakhlova, S. Pardi, S. -H. Park, A. Passeri, S. Paul, T. K. Pedlar, R. Pestotnik, L. E. Piilonen, T. Podobnik, V. Popov, E. Prencipe, M. T. Prim, N. Rout, G. Russo, D. Sahoo, Y. Sakai, S. Sandilya, A. Sangal, L. Santelj, T. Sanuki, V. Savinov, G. Schnell, C. Schwanda, Y. Seino, K. Senyo, M. Shapkin, C. Sharma, C. P. Shen, J. -G. Shiu, B. Shwartz, A. Sokolov, E. Solovieva, M. Stari\v, Z. S. Stottler, M. Sumihama, T. Sumiyoshi, M. Takizawa, K. Tanida, F. Tenchini, M. Uchida, T. Uglov, Y. Unno, K. Uno, S. Uno, S. E. Vahsen, R. Van Tonder, G. Varner, A. Vinokurova, E. Waheed, C. H. Wang, M. -Z. Wang, P. Wang, X. L. Wang, S. Watanuki, E. Won, B. D. Yabsley, W. B. Yan, S. B. Yang, H. Ye, J. Yelton, J. H. Yin, Y. Yusa, Z. P. Zhang, V. Zhilich, V. Zhukova

Published 2021-06-08Version 1

We measure the branching fractions and $CP$ asymmetries for the singly Cabibbo-suppressed decays $D^{0}\to\pi^{+}\pi^{-}\eta$, $D^{0}\to K^{+}K^{-}\eta$, and $D^{0}\to\phi\eta$, using 980 fb$^{-1}$ of data from the Belle experiment at the KEKB $e^+e^-$ collider. We obtain \begin{eqnarray} \mathcal{B}(D^{0}\to\pi^{+}\pi^{-}\eta) & = & [1.22\pm 0.02\,({\rm stat})\pm 0.02\,({\rm syst})\pm 0.03\,(\mathcal{B}_{\rm ref})]\times 10^{-3}\,, \nonumber \\ \mathcal{B}(D^{0}\to K^{+}K^{-}\eta) & = & [1.80\,^{+0.07}_{-0.06}\,({\rm stat})\pm 0.04\,({\rm syst})\pm 0.05\,(\mathcal{B}_{\rm ref})]\times 10^{-4}\,, \nonumber \\ \mathcal{B}(D^{0}\to\phi\eta) & = & [1.84\pm 0.09\,({\rm stat})\pm 0.06\,({\rm syst})\pm 0.05\,(\mathcal{B}_{\rm ref})]\times 10^{-4}\,, \nonumber \end{eqnarray} where the third uncertainty ($\mathcal{B}_{\rm ref}$) is from the uncertainty in the branching fraction of the reference mode $D^{0}\to K^{-}\pi^{+}\eta$. The color-suppressed decay $D^{0}\to\phi\eta$ is observed for the first time, with very high significance. The results for the $CP$ asymmetries are \begin{eqnarray} A_{CP}(D^{0}\to\pi^{+}\pi^{-}\eta) & = & [0.9\pm 1.2\,({\rm stat})\pm 0.5\,({\rm syst})]\%\,, \nonumber \\ A_{CP}(D^{0}\to K^{+}K^{-}\eta) & = & [-1.4\pm 3.3\,({\rm stat})\pm 1.1\,({\rm syst})]\%\,, \nonumber \\ A_{CP}(D^{0}\to\phi\eta)&= & [-1.9\pm 4.4\,({\rm stat})\pm 0.6\,({\rm syst})]\%\,. \nonumber \end{eqnarray} The results for $D^{0}\to\pi^{+}\pi^{-}\eta$ are a significant improvement over previous results. The branching fraction and $A_{CP}$ results for $D^{0}\to K^{+}K^{-}\eta$, and the $A_{CP}$ result for $D^{0}\to\phi\eta$, are the first such measurements. No evidence for $CP$ violation is found in any of these decays.