Measurement of CP violation observables and parameters for the decays $B^{\pm }\to D{K}^{\ast \pm }$

We study the decay $B^{-}\to D{K}^{\ast -}$ using a sample of 379$\times {10}^6$ $\mathrm{{\rm Y}}(4S)\to B\bar{B}$ events collected with the BABAR detector at the PEP-II $B$-factory. We perform a “GLW” analysis where the $D$ meson decays into either a CP-even ($CP+$) eigenstate ($K^{+}{K}^{-}$, ${\pi }^{+}{\pi }^{-}$), CP-odd ($CP-$) eigenstate ($K_S^0{\pi }^0$, $K_S^0\varphi$, $K_S^0\omega$) or a non-CP state ($K^{-}{\pi }^{+}$). We also analyze $D$ meson decays into $K^{+}{\pi }^{-}$ from a Cabibbo-favored ${\bar{D}}^0$ decay or doubly suppressed $D^0$ decay (“ADS” analysis). We measure observables that are sensitive to the CKM angle $\gamma$: the partial-rate charge asymmetries ${\mathcal{A}}_{CP\pm }$, the ratios ${\cal R}{CP\pm}$oftheB-decaybranchingfractionsin$CP\pm$ and non-CP decay, the ratio ${\mathcal{R}}_{ADS}$ of the charge-averaged branching fractions, and the charge asymmetry ${\mathcal{A}}_{ADS}$ of the ADS decays: ${\cal A}{CP+}= 0.09\pm0.13 \pm 0.06$,${\cal A}{CP-}=-0.23\pm 0.21\pm 0.07$,${\cal R}{CP+} =2.17 \pm 0.35 \pm 0.09$,${\cal R}{CP-} =1.03\pm 0.27\pm 0.13$,${\cal R}{ADS}=0.066\pm0.031\pm0.010$,and${\cal A}_{ADS}=-0.34\pm0.43\pm 0.16$, where the first uncertainty is statistical and the second is systematic. Combining all the measurements and using a frequentist approach yields the magnitude of the ratio between the Cabibbo-suppressed and favored amplitudes, $r_B$ = 0.31 with a one (two) sigma confidence level interval of [0.24, 0.38] ([0.17, 0.43]). The value $r_B=0$ is excluded at the 3.3 sigma level. A similar analysis excludes values of $\gamma$ in the intervals $[0, 7]^{\circ}, [55, 111]^{\circ}$,and$[175, 180]^{\circ}$([85,99]$^{\circ}$) at the one (two) sigma confidence level.