Measurement of the polarization amplitudes in $B^0\to J/\psi K^{*}(892{)}^0$ decays

An analysis of the decay $B^0\to J/\psi K^{*}(892{)}^0$ is presented using data, corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$, collected in $pp$ collisions at a center-of-mass energy of 7 TeV with the LHCb detector. The polarization amplitudes and the corresponding phases are measured to be $|A_{\parallel }{|}^2=0.227\pm 0.004(\mathrm{stat})\pm 0.011(\mathrm{syst})$, $|A_{\perp }{|}^2=0.201\pm 0.004(\mathrm{stat})\pm 0.008(\mathrm{syst})$, ${\delta }_{\parallel }[\mathrm{rad}]=-2.94\pm 0.02(\mathrm{stat})\pm 0.03(\mathrm{syst})$, and ${\delta }_{\perp }[\mathrm{rad}]=2.94\pm 0.02(\mathrm{stat})\pm 0.02(\mathrm{syst})$. Comparing $B^0\to J/\psi K^{*}(892{)}^0$ and ${\overline{B}}^0\to J/\psi {\overline{K}}^{*}(892{)}^0$ decays, no evidence for direct $CP$ violation is found.

Figure 1

Feynman diagrams contributing to $B^0\to J/\psi K^{*0}$ decays.

Figure 2

Definitions of the transversity angles $\theta$, $\psi$, $\phi$, as described in the text.

Figure 3

Invariant mass distribution of the selected $B^0\to J/\psi K^{*0}$ candidates. The curves for the signal (solid blue line), background (dashed red line), and total (solid black line) as determined from a fit are shown.

Figure 4

Angular acceptance $A(\Omega )$ as a function of each decay angle, integrated over the other two angles for (a) $\cos \theta$, (b) $\cos \psi$, and (c) $\phi$. The projections are normalized such that their average value over the histogram range is unity.

Figure 5

Background subtracted distribution of the $m(K^{+}{\pi }^{-})$ invariant mass. The four bins used to resolve the ambiguity in the strong phases are shown.

Figure 6

Projections of (a) the decay time and the transversity angles (b) $\cos \theta$, (c) $\cos \psi$, and (d) $\phi$ from the fit to the data (points with statistical error bars). The different curves show the P-wave parity-even (dotted blue lines) and parity-odd (dashed blue lines) components, the pure S-wave (green lines) contributions without interference, as well as the total signal component (solid blue lines).

Figure 7

Variation of (a) $F_{\mathrm{S}}$ and (b) ${\delta }_{\mathrm{S}}-{\delta }_0$ in the simultaneous fit in four bins of the $K^{+}{\pi }^{-}$ mass. There are two solutions of the relative phase, the falling trend (solid points) being the physical one.