Amplitude analysis and branching fraction measurement of $$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$ decays

The decays of the B + meson to the final state $$ {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$ 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 $$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$ B + → D ∗ − D s + π + and $$ {B}^0\to {D}^{\ast -}{D}_s^{+} $$ 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 $$ {D}_s^{\ast +}\to {D}_s^{+}\gamma $$ D s ∗ + → D s + γ and $$ {D}_s^{+}{\pi}^0 $$ D s + π 0 decays, the ratio of branching fractions between the $$ {B}^{+}\to {D}^{\ast -}{D}_s^{\ast +}{\pi}^{+} $$ B + → D ∗ − D s ∗ + π + and $$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$ B + → D ∗ − D s + π + decays is determined as 1 . 31 ± 0 . 07 ± 0 . 14. An amplitude analysis of the $$ {B}^{+}\to {D}^{\ast -}{D}_s^{+}{\pi}^{+} $$ 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 $$ {D}_s^{+}{\pi}^{+} $$ D s + π + or $$ {D}^{\ast -}{D}_s^{+} $$ D ∗ − D s + channels is found. The fit fraction of the scalar state $$ {T}_{c\overline{s}0}^{\ast }{(2900)}^{++} $$ T c s ¯ 0 ∗ 2900 + + observed in the $$ {B}^{+}\to {D}^{-}{D}_s^{+}{\pi}^{+} $$ B + → D − D s + π + decay is determined to be less than 2.3% at a 90% confidence level.