Study of CP-violating asymmetries in B^0 --> pi^+pi^-, K^+pi^- decays

We present a measurement of the time-dependent CP-violating asymmetries in neutral B decays to the $\pi^+\pi^-$ CP eigenstate, and an updated measurement of the charge asymmetry in $B^0\to K^+\pi^-$ decays. In a sample of 33 million $\Upsilon(4S)\to B\bar B$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric $B$ Factory, we find $65^{+12}_{-11}$ $\pi^+\pi^-$ and $217\pm 18$ $K^+\pi^-$ candidates and measure the asymmetry parameters $S_{\pi\pi} = 0.03^{+0.53}_{-0.56}\pm 0.11$, $C_{\pi\pi} = -0.25^{+0.45}_{-0.47}\pm 0.14$, and ${\cal A}_{K\pi} = -0.07 \pm 0.08 \pm 0.02$, where the first error is statistical and the second is systematic.