Improved Measurements of $CP$-Violating Asymmetry Amplitudes in $B^0\to {\pi }^{+}{\pi }^{-}$ Decays

We present updated measurements of the $CP$-violating parameters $S_{\pi \pi }$ and $C_{\pi \pi }$ in $B^0\to {\pi }^{+}{\pi }^{-}$ decays. Using a sample of $227\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC, we observe $467\pm 33$ signal decays and measure $S_{\pi \pi }=-0.30\pm 0.17(\mathrm{stat})\pm 0.03(\mathrm{syst})$ and $C_{\pi \pi }=-0.09\pm 0.15(\mathrm{stat})\pm 0.04(\mathrm{syst})$.

Figure 1

Distributions of (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, and (c) $\mathcal{F}$ for signal ${\pi }^{+}{\pi }^{-}$ events (points with error bars), and (d) the distribution of $\mathcal{F}$ for $q\overline{q}$ background events, using the weighting technique described in Ref. [16]. Solid curves represent the corresponding PDFs used in the fit.

Figure 2

Distributions of the decay-time difference $\Delta t$ using the event-weighting technique described in the text. The top two plots show events where $B_{\mathrm{tag}}$ is identified as (a) $B^0$ ($n_{B^0}$) or (b) ${\overline{B}}^0$ ($n_{{\overline{B}}^0}$), where the solid curves indicate the signal PDFs used in the fit. (c) The asymmetry (points with errors), defined as $(n_{B^0}-n_{{\overline{B}}^0})/(n_{B^0}+n_{{\overline{B}}^0})$, for signal events in each $\Delta t$ bin, and the projection of the fit (solid curve).

Figure 3

Constraints on $\alpha$ derived from the isospin analysis using $S_{\pi \pi }$, $C_{\pi \pi }$, and $\Delta {\alpha }_{\pi \pi }$ (Ref. [7]). Values of $\alpha$ for which the solid line lies below the dashed line are excluded at 90% C.L.