Limit on the $B^0\to {\rho }^0{\rho }^0$ Branching Fraction and Implications for the Cabibbo-Kobayashi-Maskawa Angle $\alpha$

We search for the decay $B^0\to {\rho }^0{\rho }^0$ in a data sample of about $227\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. We find no significant signal and set an upper limit of $1.1\times {10}^{-6}$ at 90% C.L. on the branching fraction. As a result, the uncertainty due to penguin contributions on the Cabibbo-Kobayashi-Maskawa unitarity angle $\alpha$ measured in $B\to \rho \rho$ decays is decreased to 11° at 68% C.L.

Figure 1

Definition of helicity angles ${\theta }_1$, ${\theta }_2$, and $\varphi$ for the decay $B^0\to {\rho }^0{\rho }^0$. The ${\rho }^0$ final states are shown in the ${\rho }^0$ rest frames.

Figure 2

Projections of the multidimensional fit onto $m_{\mathrm{ES}}$ and $\Delta E$ after a requirement on the signal-to-background probability ratio ${\mathcal{P}}_{\mathrm{sig}}/{\mathcal{P}}_{\mathrm{bkg}}$ with the plotted variable excluded. This requirement maximizes the fraction of signal events in the sample, which contains 22.5% and 23.9% of signal, and less than 0.5% and 0.2% of continuum background, respectively. The histogram shows the data and the solid (dashed) line shows the full (background only) PDF projection.

Figure 3

$\Delta {\chi }^2$ on $\Delta {\alpha }_{\rho \rho }$ obtained from the isospin analysis discussed in the text. The dashed lines at $\Delta {\chi }^2=1$ and $\Delta {\chi }^2=2.7$ are taken for the $1\sigma$ (68%) and $1.64\sigma$ (90%) interval estimates.