Measurement of the branching fraction, polarization, and $CP$ asymmetries in $B^0\to {\rho }^0{\rho }^0$ decay, and implications for the CKM angle $\alpha$

We study $B^0\to {\rho }^0{\rho }^0$ decays in a sample of $465\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider located at the Stanford Linear Accelerator Center (SLAC). We measure the branching fraction $\mathcal{B}=(0.92\pm 0.32\pm 0.14)\times {10}^{-6}$ and longitudinal polarization fraction $f_L={0.75}_{-0.14}^{+0.11}\pm 0.05$, where the first uncertainty is statistical and the second is systematic. The evidence for the $B^0\to {\rho }^0{\rho }^0$ signal has a significance of 3.1 standard deviations, including systematic uncertainties. We investigate the proper-time dependence of the longitudinal component in the decay and measure the $CP$-violating coefficients $S_L^{00}=(0.3\pm 0.7\pm 0.2)$ and $C_L^{00}=(0.2\pm 0.8\pm 0.3)$. We study the implication of these results for the unitarity triangle angle $\alpha$.

Figure 1

Projections of the multidimensional fit onto the (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, (c) di-pion invariant mass $m_{\pi \pi }$ (average of $m_1$ and $m_2$ distributions is shown), (d) cosine of the helicity angle $\cos {\theta }_{\pi \pi }$ (average of $\cos {\theta }_1$ and $\cos {\theta }_2$ distributions is shown), (e) event shape discriminant $\mathcal{E}$, and (f) $\Delta t$, after a requirement on the signal-to-background probability ratio with the plotted variable excluded, which enhances the fraction of signal events in the sample. This selection has 40%–60% efficiency for signal, depending on the projection. The data points are overlaid by the full PDF projection (solid line). Also shown are the $B^0\to {\rho }^0{\rho }^0$ PDF component (dotted line) and the sum of all other PDFs (dashed line).

Figure 2

$CP$ asymmetry ${\mathcal{A}}_{CP}$ after a requirement on the signal-to-background probability ratio, which enhances the fraction of signal events in the sample. The solid line represents the projection of the total PDF; the dotted line is the $B^0\to {\rho }^0{\rho }^0$ contribution.

Figure 3

CL on $\alpha -{\alpha }_{\mathrm{eff}}$ determined from the isospin analysis. The long-dashed curve is obtained without the two $CP$ parameters $S_L^{00}$ and $C_L^{00}$. The dotted curve corresponds to the isospin analysis without $S_L^{00}$, and the solid curve CL includes both $C_L^{00}$ and $S_L^{00}$ in the fit. The horizontal dotted lines correspond to the 68% (top) and 90% (bottom) CL intervals.