Measurement of Time-Dependent $CP$ Asymmetries in $B^0\to D^{(*)\pm }{\pi }^{\mp }$ Decays and Constraints on $\sin (2\beta +\gamma )$

We present a measurement of $CP$-violating asymmetries in fully reconstructed $B^0\to D^{(*)\pm }{\pi }^{\mp }$ decays in approximately $88\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. From a time-dependent maximum-likelihood fit we obtain the following for the $CP$-violating parameters: $a=-0.022\pm 0.038(\mathrm{stat})\pm 0.020(\mathrm{syst})$, $a^{*}=-0.068\pm 0.038(\mathrm{stat})\pm 0.020(\mathrm{syst})$, $c_{\mathrm{lep}}=+0.025\pm 0.068(\mathrm{stat})\pm 0.033(\mathrm{syst})$, and $c_{\mathrm{lep}}^{*}=+0.031\pm 0.070(\mathrm{stat})\pm 0.033(\mathrm{syst})$. Using other measurements and theoretical assumptions we interpret the results in terms of the angles of the Cabibbo-Kobayashi-Maskawa unitarity triangle, and find $|\sin (2\beta +\gamma )|>0.69$ at $68\%$ confidence level. We exclude the hypothesis of no $CP$ violation $[\sin (2\beta +\gamma )=0]$ at $83\%$ confidence level.