Measurement of the $B^0\to \varphi K^{*0}$ Decay Amplitudes

With a sample of about $227\times {10}^6$ $B\overline{B}$ pairs recorded with the BABAR detector we perform a full angular analysis of the decay $B^0\to \varphi K^{*0}(892)$. We make novel measurements of five parameters sensitive to $CP$ violation. We also measure the branching fraction to be $(9.2\pm 0.9\pm 0.5)\times {10}^{-6}$ and determine the fractions of longitudinal and parity-odd transverse contributions as $f_L=0.52\pm 0.05\pm 0.02$ and $f_{\perp }=0.22\pm 0.05\pm 0.02$. The phases of the parity-even and parity-odd transverse amplitudes relative to the longitudinal amplitude are found to be ${\varphi }_{\parallel }={2.34}_{-0.20}^{+0.23}\pm 0.05\mathrm{r}\mathrm{a}\mathrm{d}$ and ${\varphi }_{\perp }=2.47\pm 0.25\pm 0.05\mathrm{r}\mathrm{a}\mathrm{d}$. We also observe the decay $B^0\to \varphi K^{*0}(1430)$.

Figure 1

Projections onto the variables $m_{\mathrm{E}\mathrm{S}}$ (a), $\Delta E$ (b), $m_{K\overline{K}}$ (c), and $m_{K\pi }$ (d) for the signal $B^0\to \varphi K^{*0}(892)$ and $\varphi K^{*0}(1430)$ candidates combined.

Figure 2

Projections onto the variables ${\mathcal{H}}_1$ (a), ${\mathcal{H}}_2$ (b), $Q\Phi$ (c), and the differences between the $Q\Phi$ projections for events with ${\mathcal{H}}_1{\mathcal{H}}_2>0$ and with ${\mathcal{H}}_1{\mathcal{H}}_2<0$ (d) for the signal $B^0\to \varphi K^{*0}(892)$ candidates.

Figure 3

Projections onto the variables ${\mathcal{H}}_1$ (a) and ${\mathcal{H}}_2$ (b) for the signal $B^0\to \varphi K^{*0}(1430)$ candidates. The difference between the solid and dotted lines in (a) shows the contribution of the tensor state to the angular distribution.

Figure 4

Likelihood function contours with $1\sigma$ intervals for polarization (a) and phase (b) measurements in the $B^0\to \varphi K^{*0}(892)$ analysis. The fit results are shown with dots. Diagonal dashed lines $f_{\perp }=(1-f_L)/2$ and ${\varphi }_{\perp }={\varphi }_{\parallel }$ correspond to $|A_{+1}|\gg |A_{-1}|$. In (b) the $(\pi ,\pi )$ point is indicated by the crossed dashed lines.