Amplitude Analysis of the $B^{\pm }\to \phi K^{*}(892{)}^{\pm }$ Decay

We perform an amplitude analysis of $B^{\pm }\to \phi (1020)K^{*}(892{)}^{\pm }$ decay with a sample of about $384\times {10}^6$ $B\overline{B}$ pairs recorded with the BABAR detector. Overall, twelve parameters are measured, including the fractions of longitudinal $f_L$ and parity-odd transverse $f_{\perp }$ amplitudes, branching fraction, strong phases, and six parameters sensitive to $CP$ violation. We use the dependence on the $K\pi$ invariant mass of the interference between the $J^P=1^{-}$ and $0^{+}$ $K\pi$ components to resolve the discrete ambiguity in the determination of the strong and weak phases. Our measurements of $f_L=0.49\pm 0.05\pm 0.03$, $f_{\perp }=0.21\pm 0.05\pm 0.02$, and the strong phases point to the presence of a substantial helicity-plus amplitude from a presently unknown source.

Figure 1

Projections onto the variables (a) $m_{K\pi }$, (b) $m_{K\overline{K}}$, (c) $\Delta E$, and (d) $m_{\mathrm{ES}}$ for the signal $B^{\pm }\to \phi (K\pi {)}^{\pm }$ candidates with a requirement discussed in the text. The solid (dashed) lines show the signal-plus-background (background) PDF projections.

Figure 2

Projections onto the variables (a) ${\mathcal{H}}_1$, (b) ${\mathcal{H}}_2$, (c) $Q\Phi$, and (d) the differences between the $Q\Phi$ projections for events with ${\mathcal{H}}_1{\mathcal{H}}_2>0$ and with ${\mathcal{H}}_1{\mathcal{H}}_2<0$ for the signal $B^{\pm }\to \phi (K\pi {)}^{\pm }$ candidates following the solid (dashed) line definitions in Fig. 1. The step in the ${\mathcal{H}}_1$ PDF distributions is due to the selection requirement ${\mathcal{H}}_1<0.6$ in the $B^{\pm }\to \phi (K^{\pm }{\pi }^0)$ channel.