Improved measurement of $CP$-violating parameters in $B\to {\rho }^{+}{\rho }^{-}$ decays

We present a measurement of the $CP$-violating asymmetry in $B^0\to {\rho }^{+}{\rho }^{-}$ decays using $535\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. We measure $CP$-violating coefficients $\mathcal{A}=0.16\pm 0.21(\mathrm{stat})\pm 0.08(\mathrm{syst})$ and $\mathcal{S}=0.19\pm 0.30(\mathrm{stat})\pm 0.08(\mathrm{syst})$. These values are used to determine the unitarity triangle angle ${\varphi }_2$ using an isospin analysis; the solution consistent with the standard model lies in the range $54°<{\varphi }_2<113°$ at the 90% confidence level.

Figure 1

Left: projections in $M_{\mathrm{bc}}$ for events satisfying $-0.10\mathrm{GeV}<\Delta E<0.06\mathrm{GeV}$. Right: projections in $\Delta E$ for events with $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$. The top plots correspond to good quality tags ($0.75<r<1.0$), and the bottom plots correspond to lower quality tags ($r<0.75$). The curves show fit projections: dashed is ${\rho }^{+}{\rho }^{-}+\rho \pi \pi$, dotted is $q\overline{q}$, dot-dashed is $b\to c$, small solid is $b\to u$, and large solid is the total. For these plots the $\mathcal{R}$ requirement has been tightened to increase the ratio of signal to background.

Figure 2

$\mathcal{R}$ distribution for high-purity tagged events satisfying $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$ and $-0.10\mathrm{GeV}<\Delta E<0.06\mathrm{GeV}$. The curves show fit projections: dashed is ${\rho }^{+}{\rho }^{-}+\rho \pi \pi$, dotted is $q\overline{q}$, dot-dashed is $b\to c$, small solid is $b\to u$, and large solid is the total.

Figure 3

The $\Delta t$ distribution and projections of the fit for events satisfying $0.5<r<1.0$: (a) $Q=+1$ tags, (b) $Q=-1$ tags. The hatched region shows signal events. The raw $CP$ asymmetry is shown in (c). For these plots the $\mathcal{R}$ requirement has been tightened to increase the ratio of signal to background.

Figure 4

$1-\mathrm{C}.\mathrm{L}.$ vs ${\varphi }_2$. The horizontal lines denote $\mathrm{C}.\mathrm{L}.=68.3\%$ (solid) and $\mathrm{C}.\mathrm{L}.=90\%$ (dashed).