Amplitude analysis and branching fraction measurement of $B^{+}\to D^{*-}D^{+}_{s}π^{+}$ decays
The decays of the $B^{+}$ meson to the final state $D^{*-}D^{+}_{s}π^{+}$ 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 $B^{+}\to D^{*-}D^{+}_{s}π^{+}$ and $B^{0}\to D^{*-}D^{+}_{s}$ decays is measured to be $0.173\pm 0.006\pm 0.010$, where the first uncertainty is statistical and the second is systematic. Using partially reconstructed $D^{*+}_{s}\to D^{+}_{s}γ$ and $D^{+}_{s}π^{0}$ decays, the ratio of branching fractions between the $B^{+}\to D^{*-}D^{*+}_{s}π^{+}$ and $B^{+}\to D^{*-}D^{+}_{s}π^{+}$ decays is determined as $1.31\pm 0.07\pm 0.14$. An amplitude analysis of the $B^{+}\to D^{*-}D^{+}_{s}π^{+}$ 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 $D^{+}_{s}π^{+}$ or $D^{*-}D^{+}_{s}$ channels is found. The fit fraction of the scalar state $T_{c\bar{s} 0}^{\ast}(2900)^{++}$ observed in the $B^{+}\to D^{-}D^{+}_{s}π^{+}$ decay is determined to be less than 2.3% at a 90% confidence level.