Study of $B^0\to D^{*\mathbf{-}}{\pi }^{\mathbf{+}}{\pi }^{\mathbf{-}}{\pi }^{\mathbf{+}}$ and $B^0\to D^{*\mathbf{-}}{K}^{\mathbf{+}}{\pi }^{\mathbf{-}}{\pi }^{\mathbf{+}}$ decays

Using proton-proton collision data collected by the LHCb experiment at $\sqrt{s}=7\mathrm{TeV}$, corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$, the ratio of branching fractions of the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ decay relative to the $B^0\to D^{*-}{\pi }^{+}$ decay is measured to be $\frac{\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})}{\mathcal{B}(B^0\to D^{*-}{\pi }^{+})}=2.64\pm 0.04(\mathrm{stat})\pm 0.13(\mathrm{syst})$. The Cabibbo-suppressed decay $B^0\to D^{*-}{K}^{+}{\pi }^{-}{\pi }^{+}$ is observed for the first time, and the measured ratio of branching fractions is $\frac{\mathcal{B}(B^0\to D^{*-}{K}^{+}{\pi }^{-}{\pi }^{+})}{\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})}=(6.47\pm 0.37(\mathrm{stat})\pm 0.35(\mathrm{syst}))\times {10}^{-2}$. A search for orbital excitations of charm mesons contributing to the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ final state is also performed, and the first observation of the $B^0\to {\overline{D}}_1(2420{)}^0{\pi }^{+}{\pi }^{-}$ decay is reported with the ratio of branching fractions $\frac{\mathcal{B}(B^0\to ({\overline{D}}_1(2420{)}^0\to D^{*-}{\pi }^{+}){\pi }^{-}{\pi }^{+})}{\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})}=(2.04\pm 0.42(\mathrm{stat})\pm 0.22(\mathrm{syst}))\times {10}^{-2}$, where the numerator represents a product of the branching fractions $\mathcal{B}(B^0\to {\overline{D}}_1(2420{)}^0{\pi }^{-}{\pi }^{+})$ and $\mathcal{B}({\overline{D}}_1(2420{)}^0\to D^{*-}{\pi }^{+})$.

Figure 1

Invariant mass distributions of selected (a) $B^0\to D^{*-}{K}^{+}{\pi }^{-}{\pi }^{+}$, (b) $B^0\to D^{*-}{K}^{+}$, (c) $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ and (d) $B^0\to D^{*-}{\pi }^{+}$ candidates. Green (red) solid lines represent the CF (CS) signal shapes and their respective particle misidentification backgrounds. Orange dashed lines at low invariant mass represent backgrounds from partially reconstructed decays. Cyan dotted lines represent combinatorial backgrounds. The pink dash-dotted line below the signal peak in the fit to $B^0\to D^{*-}{K}^{+}{\pi }^{-}{\pi }^{+}$ candidates represents the background from misidentified $B^0\to D^{*-}{D}_s^{+}$ and $B^0\to D^{*-}{K}^{+}{\overline{K}}^{*0}$ decays.

Figure 2

Corrected mass $M(D^{*-}{\pi }^{+})=m(D^{*-}{\pi }^{+})-m(D^{*-})+m(D^{*-}{)}_{\mathrm{PDG}}\mathrm{MeV}/c^2$ distribution from background-subtracted $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ candidates. The red solid line represents the contribution from ${\overline{D}}_1(2420{)}^0$; the red dashed lines represent contributions from the higher excited charm states $D_2^{*}(2460{)}^0$, $D(2550{)}^0$, $D(2600)$ and $D(2750)$, which are expected to be present [22] but are not significant in this dataset. The blue dashed line represents $B^0$ decays that have not passed through an excited charm resonance.