Amplitude analysis and branching fraction measurement of B+→D∗−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {

The decays of the B+ meson to the final state D∗−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$\end{document} are studied in proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb−1. The ratio of branching fractions of the B+→D∗−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$\end{document} and B0→D∗−Ds+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^0\to {D}^{\ast -}{D}_s^{+} $$\end{document} decays is measured to be 0.173 ± 0.006 ± 0.010, where the first uncertainty is statistical and the second is systematic. Using partially reconstructed Ds∗+→Ds+γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}_s^{\ast +}\to {D}_s^{+}\gamma $$\end{document} and Ds+π0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}_s^{+}{\pi}^0 $$\end{document} decays, the ratio of branching fractions between the B+→D∗−Ds∗+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^{+}\to {D}^{\ast -}{D}_s^{\ast +}{\pi}^{+} $$\end{document} and B+→D∗−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$\end{document} decays is determined as 1.31 ± 0.07 ± 0.14. An amplitude analysis of the B+→D∗−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$\end{document} decay is performed for the first time, revealing dominant contributions from known excited charm resonances decaying to the D*−π+ final state. No significant evidence of exotic contributions in the Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}_s^{+}{\pi}^{+} $$\end{document} or D∗−Ds+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}^{\ast -}{D}_s^{+} $$\end{document} channels is found. The fit fraction of the scalar state Tcs¯0∗2900++\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {T}_{c\overline{s}0}^{\ast }{(2900)}^{++} $$\end{document} observed in the B+→D−Ds+π+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {B}^{+}\to {D}^{-}{D}_s^{+}{\pi}^{+} $$\end{document} decay is determined to be less than 2.3% at a 90% confidence level.