Study of Time-DependentCPAsymmetry in NeutralBDecays toJ/ψπ0

We present the first study of the time-dependent $CP$-violating asymmetry in $B^0\to J/\psi {\pi }^0$ decays using $e^{+}{e}^{-}$ annihilation data collected with the BABAR detector at the ${\rm Y}\mathrm{(}\mathrm{4}\mathrm{S}\mathrm{)}$ resonance during the years 1999–2002 at the PEP-II asymmetric-energy $B$ Factory at SLAC. Using approximately $88\times {10}^6$ $B\overline{B}$ pairs, our results for the coefficients of the cosine and sine terms of the $CP$ asymmetry are $C_{J/\psi {\pi }^0}=0.38\pm 0.41\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 0.09\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$ and $S_{J/\psi {\pi }^0}=0.05\pm 0.49\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 0.16\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}$.