Study of $CP$ violation in $B^{\mp }\to D{h}^{\mp }$ ($h=K,\pi$) with the modes $D\to K^{\mp }{\pi }^{\pm }{\pi }^0$, $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $D\to K^{+}{K}^{-}{\pi }^0$

An analysis of the decays of $B^{\mp }\to D{K}^{\mp }$ and $B^{\mp }\to D{\pi }^{\mp }$ is presented in which the $D$ meson is reconstructed in the three-body final states $K^{\mp }{\pi }^{\pm }{\pi }^0$, ${\pi }^{+}{\pi }^{-}{\pi }^0$ and $K^{+}{K}^{-}{\pi }^0$. Using data from LHCb corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ of $pp$ collisions, measurements of several $CP$ observables are performed. First observations are obtained of the suppressed Atwood-Dunietz-Soni decay $B^{\mp }\to [{\pi }^{\mp }{K}^{\pm }{\pi }^0{]}_D{\pi }^{\mp }$ and the quasi-Gronau-London-Wyler decay $B^{\mp }\to [K^{+}{K}^{-}{\pi }^0{]}_D{\pi }^{\mp }$. The results are interpreted in the context of the unitarity triangle angle $\gamma$ and related parameters.

Figure 1

Invariant mass distributions of selected $B^{\mp }\to [K^{\mp }{\pi }^{\pm }{\pi }^0{]}_D{h}^{\mp }$ candidates, separated by $B$ hadron charge. $B^{\mp }\to D{K}^{\mp }$ signal events are in the upper plots and $B^{\mp }\to D{\pi }^{\mp }$ events are in the lower plots. The solid dark (red) curve represents $B^{\mp }\to D{K}^{\mp }$ events and the solid light (green) curve represents $B^{\mp }\to D{\pi }^{\mp }$ events. The solid (grey) shape indicates partially reconstructed $B^{\mp }$ decays and the heavy dotted (red) curve indicates wrongly reconstructed $D$ decays. The solid (blue) line represents the total PDF and includes the combinatorial component.

Figure 2

Invariant mass distributions of selected $B^{\mp }\to [{\pi }^{\mp }{K}^{\pm }{\pi }^0{]}_D{h}^{\mp }$ candidates. See the caption of Fig. 1 for a full description. The lightly dotted (blue) line represents the combinatorial component and the long-dashed (magenta) line indicates contributions from partially reconstructed $B_s^0\to D{K}^{\mp }{\pi }^{\pm }$ decays where the pion is not reconstructed.

Figure 3

Invariant mass distributions of selected $B^{\mp }\to [{\pi }^{+}{\pi }^{-}{\pi }^0{]}_D{h}^{\mp }$ candidates. See the caption of Fig. 1 for a full description. The lightly dotted (blue) line represents the combinatorial component.

Figure 4

Invariant mass distributions of selected $B^{\mp }\to [K^{+}{K}^{-}{\pi }^0{]}_D{h}^{\mp }$ candidates. See the caption of Fig. 1 for a full description. The lightly dotted (blue) line represents the combinatorial component.

Figure 5

Scan of the ${\chi }^2$ probabilities over the $\gamma -r_B$ parameter space. Shown are the $n\sigma$ profile likelihood contours, where $\mathrm{\Delta }{\chi }^2=n^2$, with $n=1$ being the light (blue) shaded region, $n=2$ the dark (blue) shaded region and $n=3$ corresponding to the white area. The result is seen to be compatible with the current LHCb measurement of $\gamma$ and $r_B$, indicated by the point with error bars.

Figure 6

Scan of the ${\chi }^2$ probabilities over the $\gamma -{\delta }_B$ parameter space. Shown are the $n\sigma$ profile likelihood contours, where $\mathrm{\Delta }{\chi }^2=n^2$, with $n=1$ being the light (blue) shaded region, $n=2$ the dark (blue) shaded region and $n=3$ corresponding to the white area. The result is compatible with the current LHCb measurement of $\gamma$ and ${\delta }_B$, indicated by the point with error bars.