Amplitude analysis and branching fraction measurement of B⁺ → 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⁺ → D^*- D_s⁺ π⁺ and B⁰ → D^*- D_s⁺ 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 D_s^*+ → D_s⁺ γ and D_s⁺ π⁰ decays, the ratio of branching fractions between the B⁺ → D^*- D_s^*+ π⁺ and B⁺ → D^*- D_s⁺ π⁺  decays is determined as 1.31 ± 0.07 ± 0.14. An amplitude analysis of the B⁺ → 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^*_cs̅0 (2900)⁺⁺ observed in the  B⁺ → D^- D_s⁺ π⁺ decay is determined to be less than 2.3% at a 90% confidence level.