Measurement of the $CP$ violation parameters in $B^0\to {\pi }^{+}{\pi }^{-}$ decays

We present a measurement of the charge-parity ($CP$) violating parameters in $B^0\to {\pi }^{+}{\pi }^{-}$ decays. The results are obtained from the final data sample containing $772\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain the $CP$ violation parameters $${\mathcal{A}}_{CP}(B^0\to {\pi }^{+}{\pi }^{-})=+0.33\pm 0.06(\mathrm{stat})\pm 0.03(\mathrm{syst}),{\mathcal{S}}_{CP}(B^0\to {\pi }^{+}{\pi }^{-})=-0.64\pm 0.08(\mathrm{stat})\pm 0.03(\mathrm{syst}),$$where ${\mathcal{A}}_{CP}$ and ${\mathcal{S}}_{CP}$ represent the direct and mixing-induced $CP$ asymmetries in $B^0\to {\pi }^{+}{\pi }^{-}$ decays, respectively. Using an isospin analysis including results from other Belle measurements, we find $23.8°<{\varphi }_2<66.8°$ is disfavored at the $1\sigma$ level, where ${\varphi }_2$ is one of the three interior angles of the Cabibbo-Kobayashi-Maskawa unitarity triangle related to $B_{u,d}$ decays.

Figure 1

Leading-order Feynman diagrams for $B^0\to {\pi }^{+}{\pi }^{-}$ decays. (a) depicts the dominant first-order amplitude (tree) while (b) shows the second-order loop (penguin) diagram. In the penguin diagram, the subscript $x$ in $V_{xb}$ refers to the flavor of the intermediate-state quark $(x=u,c,t)$.

Figure 2

Complex isospin triangles from which $\Delta {\varphi }_2$ can be determined.

Figure 3

(color online) Projections of the fit to the data enhanced in the $B^0\to {\pi }^{+}{\pi }^{-}$ signal region. Points with error bars represent the data and the solid black curves or histograms represent the fit results. The signal enhancements, $M_{\mathrm{bc}}>5.27\mathrm{GeV}/c^2$, $|\Delta E|<0.04\mathrm{GeV}$, ${\mathcal{F}}_{b\overline{b}/q\overline{q}}>0$, ${\mathcal{L}}_{K/\pi }^{\pm }<0.4$ and $r>0.5$, except for the enhancement of the dimension being plotted are applied to each projection. (a), (b), (c), (d) and (e) show the $M_{\mathrm{bc}}$, $\Delta E$, ${\mathcal{L}}_{K/\pi }^{+}$, ${\mathcal{L}}_{K/\pi }^{-}$ and ${\mathcal{F}}_{b\overline{b}/q\overline{q}}$ projections, respectively. Blue hatched curves show the $B^0\to {\pi }^{+}{\pi }^{-}$ signal component, green dotted curves show the $B^0\to K^{\pm }{\pi }^{\mp }$ peaking background component, dashed red curves indicate the total background, and purple dash-dotted curves show the $B\overline{B}$ background component.

Figure 4

(color online) Background subtracted time-dependent fit results for $B^0\to {\pi }^{+}{\pi }^{-}$. (a) shows the $\Delta t$ distribution for each $B_{\mathrm{Tag}}^0$ flavor $q$. The solid blue and dashed red curves represent the $\Delta t$ distributions for $B^0$ and ${\overline{B}}^0$ tags, respectively. (b) shows the asymmetry of the plot above them, $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, where $N_{B^0}$ ($N_{{\overline{B}}^0}$) is the measured signal yield of $B^0$ (${\overline{B}}^0$) events in each bin of $\Delta t$.

Figure 5

Difference 1-CL, plotted for a range of (a) ${\varphi }_2$ and (b) $|\Delta {\varphi }_2|$ values as shown by the solid curve. The dashed lines indicate the $1\sigma$ exclusion level.