Improved Measurement of the Cabibbo-Kobayashi-Maskawa Angle $\alpha$ Using $B^0(\overline{B})\to {\rho }^{+}{\rho }^{-}$ Decays

We present results from an analysis of $B^0({\overline{B}}^0)\to {\rho }^{+}{\rho }^{-}$ using $232\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. We measure the longitudinal polarization fraction $f_L=0.978\pm 0.014(\mathrm{stat})\genfrac{}{}{0ex}{}{+0.021}{-0.029}(\mathrm{syst})$ and the $CP$-violating parameters $S_L=-0.33\pm 0.24(\mathrm{stat})\genfrac{}{}{0ex}{}{+0.08}{-0.14}(\mathrm{syst})$ and $C_L=-0.03\pm 0.18(\mathrm{stat})\pm 0.09(\mathrm{syst})$. Using an isospin analysis of $B\to \rho \rho$ decays, we determine the unitarity triangle parameter $\alpha$. The solution compatible with the standard model is $\alpha =(100\pm 13)°$.

Figure 1

The distributions for the highest purity tagged events for the variables (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, (c) cosine of the $\rho$ helicity angle, and (d) $m_{{\pi }^{\pm }{\pi }^0}$. The dotted lines are the sum of backgrounds, and the solid lines are the full PDF.

Figure 2

The $\Delta t$ distribution for a sample of events enriched in signal for (a) $B^0$ and (b) ${\overline{B}}^0$ tagged events. The dotted lines are the sum of backgrounds, and the solid lines are the sum of signal and backgrounds. The time-dependent $CP$ asymmetry (see text) is shown in (c), where the curve is the measured asymmetry.

Figure 3

C.L. on $\alpha$ obtained from the isospin analysis with the statistical method described in [15]. The dashed lines correspond to the 68% (top) and 90% (bottom) C.L. intervals.