Measurement of $CP$ Asymmetry in a Time-Dependent Dalitz Analysis of $B^0\to (\rho \pi {)}^0$ and a Constraint on the Quark Mixing Matrix Angle ${\varphi }_2$

We present a measurement of $CP$ asymmetry using a time-dependent Dalitz plot analysis of $B^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ decays based on a $414{\mathrm{fb}}^{-1}$ data sample containing $449\times {10}^{6}B\overline{B}$ pairs. The data was collected on the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. Combining our analysis with information on charged $B$ decay modes, we perform a full Dalitz and isospin analysis and obtain a constraint on the CKM angle ${\varphi }_2$, $68°<{\varphi }_2<95°$ as the 68.3% confidence interval for the ${\varphi }_2$ solution consistent with the standard model (SM). A large SM-disfavored region also remains.

Figure 1

(a) $M_{\mathrm{bc}}$ and (b) $\Delta E$ distributions within the $\Delta E$ and $M_{\mathrm{bc}}$ signal regions. Solid, dot-dashed, dotted, and dashed-hatched histograms correspond to correctly reconstructed signal, SCF, $B\overline{B}$, and continuum PDF’s, respectively.

Figure 2

Mass (a)–(c) and helicity (d)–(f) distributions, and background-subtracted $\Delta t$ asymmetry plots in the good tagging quality region $l\ge 3$ [14] (g)–(i), corresponding to the ${\rho }^{+}{\pi }^{-}$ [(a),(d),(g)], ${\rho }^{-}{\pi }^{+}$ [(b),(e),(h)], and ${\rho }^0{\pi }^0$ [(c),(f),(i)] enhanced regions. The notations for histograms (a)–(f) are the same as Fig. 1.

Figure 3

$1-\mathrm{C}.\mathrm{L}.$ vs ${\varphi }_2$. Dotted and solid curves correspond to the result from the TDPA only and that from the TDPA and an isospin (pentagon) combined analysis, respectively.