Study of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><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:mo>−</mml:mo></mml:msup><mml:mi>η</mml:mi></mml:math> and observation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-annihilation decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ρ</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>
M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Çetin, 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, Z. J. Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. Dai, A. Dbeyssi, R. E. de Boer, 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, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. Gao, I. Garzia, P. Ge, C. Geng, 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, A. Guskov, T. T. Han, W. Y. Han
Abstract
The decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ is observed for the first time, using ${e}^{+}{e}^{\ensuremath{-}}$ collision data corresponding to an integrated luminosity of $6.32\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta})=(3.12\ifmmode\pm\else\textpm\fi{}0.1{3}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{9}_{\mathrm{syst}})%$. The first amplitude analysis of this decay reveals the substructures in ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ and determines the relative fractions and the phases among these substructures. The dominant intermediate process is ${D}_{s}^{+}\ensuremath{\rightarrow}{a}_{1}(1260{)}^{+}\ensuremath{\eta},{a}_{1}(1260{)}^{+}\ensuremath{\rightarrow}\ensuremath{\rho}(770{)}^{0}{\ensuremath{\pi}}^{+}$ with a branching fraction of $(1.73\ifmmode\pm\else\textpm\fi{}0.1{4}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{8}_{\mathrm{syst}})%$. We also observe the $W$-annihilation process ${D}_{s}^{+}\ensuremath{\rightarrow}{a}_{0}(980{)}^{+}\ensuremath{\rho}(770{)}^{0}$, ${a}_{0}(980{)}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\eta}$ with a branching fraction of $(0.21\ifmmode\pm\else\textpm\fi{}0.0{8}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{5}_{\mathrm{syst}})%$, which is larger than the branching fractions of other measured pure $W$-annihilation decays by 1 order of magnitude.