Amplitude analysis and branching fraction measurement of B+→D∗−Ds+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 B ⁰→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 ⁺π ⁰ 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 _cs¯0 ^∗2900 ⁺⁺ observed in the B ⁺→D ⁻D _s ⁺π ⁺ decay is determined to be less than 2.3% at a 90% confidence level.