First 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:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and Measurement of Its Decay Dynamics
M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, A. Amoroso, Q. An, Anita, Xuan Bai, 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. 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, W. S. 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, Z. Y. 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, X. L. Gao, Y. Gao, Yang Gao, Yanyan Gao, I. Garzia, E. M. Gersabeck, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, Shanqiang 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
Abstract
By analyzing a data sample corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the ${D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ decay to be ${\mathcal{B}}_{{D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}=(10.4\ifmmode\pm\else\textpm\fi{}1.{0}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.{5}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Using the world averaged value of ${\mathcal{B}}_{{D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e}}$, the ratio of the two branching fractions is determined to be ${\mathcal{B}}_{{D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}/{\mathcal{B}}_{{D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e}}=0.91\ifmmode\pm\else\textpm\fi{}{0.13}_{(\mathrm{stat}+\mathrm{syst})}$, which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain the product of the hadronic form factor ${f}_{+}^{\ensuremath{\eta}}(0)$ and the $c\ensuremath{\rightarrow}d$ Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cd}|$ to be ${f}_{+}^{\ensuremath{\eta}}(0)|{V}_{cd}|=0.087\ifmmode\pm\else\textpm\fi{}0.00{8}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.00{2}_{\mathrm{syst}}$. Taking the input of $|{V}_{cd}|$ from the global fit in the standard model, we determine ${f}_{+}^{\ensuremath{\eta}}(0)=0.39\ifmmode\pm\else\textpm\fi{}0.0{4}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.0{1}_{\mathrm{syst}}$. On the other hand, using the value of ${f}_{+}^{\ensuremath{\eta}}(0)$ calculated in theory, we find $|{V}_{cd}|=\phantom{\rule{0ex}{0ex}}0.242\ifmmode\pm\else\textpm\fi{}0.02{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.00{6}_{\mathrm{syst}}\ifmmode\pm\else\textpm\fi{}0.03{3}_{\text{theory}}$.