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

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Abstract

An analysis of the decay B0 -> J/psi K*(892)0 is presented using data, corresponding to an integrated luminosity of 1.0fb^-1, collected in pp collisions at a centre-of-mass energy of 7TeV with the LHCb detector. The polarisation amplitudes and the corresponding phases are measured to be |A_{\parallel}|^2 = 0.227 +- 0.004 (stat.) +- 0.011 (syst.), |A_{\perp}|^2 = 0.201 +- 0.004 (stat.) +- 0.008 (syst.), \delta_{\parallel} [rad] = -2.94 +- 0.02 (stat.) +- 0.03 (syst.), \delta_{\perp} [rad] = 2.94 +- 0.02 (stat.) +- 0.02 (syst.). Comparing B0 -> J/psi K*(892)0 and \bar{B}0 -> J/psi \bar{K}*(892)0 decays, no evidence for direct CP violation is found.

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

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

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

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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) $\varphi$. The projections are normalised such that their average value over the histogram range is unity.

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

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

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CosPsi[..].pdf [15 KiB]
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Variation of (a) $F_{\rm S}$ and (b) $\delta_{\rm S} - \delta_{\rm 0}$ 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.

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Animated gif made out of all figures.

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Tables and captions

Definition of $h_k$ and $f_k$ appearing in Eq. 1. The $h_k$ factors are invariant under the phase transformation $(\delta_\parallel, \delta_\perp, \delta_{\rm S}) \longleftrightarrow (- \delta_\parallel, \pi - \delta_\perp, - \delta_{\rm S})$ [15,16]. The $f_k$ are functions defined such that their integrals over $\Omega$ are unity.

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Bins of $m(K^+\pi^-)$ and the corresponding $C_{\rm SP}$ correction factor for the S-wave interference terms, assuming a uniform distribution for the non-resonant $K^+\pi^-$ contribution and a relativistic Breit-Wigner shape for decays via the $K^{*0}$ resonance.

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Systematic uncertainties as described in the text. The contribution from omitting the $C_{\rm SP}$ factors is negligible for the P-wave parameters. The total systematic uncertainty is the sum in quadrature of the individual contributions.

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Results for $B^0\rightarrow J/\psi K^{*0}$ candidates. The uncertainties are statistical and systematic, respectively.

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Signal yield ($N_{ {sig}}$) and results for the S-wave parameters in each bin of $m(K^+\pi^-)$ mass, showing statistical and systematic uncertainties. Only the physical solution is shown for $\delta_{\mathrm{S}} -\delta_0$.

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Correlation matrix for the four-bin fit.

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Results from fits to the $B^0\rightarrow J/\psi K^{*0}$ and $\overline{B}^0\rightarrow J/\psi\overline K^{*0}$ background subtracted candidates and the direct $ C\!P$ asymmetries $\frac{\overline{X}-X}{\overline{X}+X}$, where $X$ represents the parameter in question. The uncertainties are statistical for the amplitudes and phases and both statistical and systematic for the direct $ C\!P$ measurements.

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Comparison of the LHCb results assuming no S-wave component with results from previous experiments. The uncertainties are statistical and systematic, respectively.

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.