Illustration of the $q^2$ spectrum in $B^0\rightarrow K^{*0}\mu ^+\mu ^- $ decays. The dashed line corresponds to the pure rare semileptonic decay, while the solid line includes the impact of different charmonium resonances. The gray bands correspond to the regions dominated by $B^0\rightarrow { J \mskip -3mu/\mskip -2mu\psi } K^{*0}$ and $B^0\rightarrow \psi {(2S)} K^{*0}$ tree-level decays, which are selected as control channels. Magnitudes and phases of $c\bar{c}$ resonant components have been arbitrarily chosen for illustrative purposes. The dominant Wilson coefficients in each region of the spectrum are also highlighted for reference.

Invariant mass distribution of $B^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi } K^{*0}$ decays for the (left) Run 1 and (right) 2016 datasets.

Distribution of the fit variables for the combined Run 1 and 2016 datasets. The distributions of the three angles, $q^2$, and $k^2$ are given for candidates within $50\text{ Me V /}c^2 $ of the known $B^0$ mass. The total fit projections together with the individual signal and background components are overlaid.

Form factor results as a function of $q^2$ obtained from the amplitude fit in the two fit configurations, compared to the predictions from Refs. [16,62,63] that are used as external constraint in the fit.

Real and imaginary part of the non-local contributions $\mathcal{H}_\lambda (q^2)$ normalised to the size of the local form factors $\mathcal{F}_\lambda (q^2) $ obtained for the two fit configurations. The black dots correspond to the predictions at $q^2<0$ from [16,24]. The result obtained without the constraints is also extrapolated to the negative $q^2$ region for comparison. The shaded gray regions correspond to the vetoed $ { J \mskip -3mu/\mskip -2mu\psi } $ and $\psi(2S)$ regions.

One-dimensional profile likelihood scan of the Wilson coefficients. Shaded regions correspond to the 68% and 95% confidence intervals.

Two-dimensional profile likelihood scan of the Wilson coefficients. Shaded areas correspond to the 68% C.I. and 95% C.I. contour regions. Dotted contours in the top left plot assume right-handed Wilson coefficients fixed to their SM values, i.e. $\mathcal{C}_9^\prime = \mathcal{C}_{10}^\prime = 0$.

Angular observables ($S$-basis) obtained a posteriori from the fit results of the two fit configurations; the subfigures isolate the contribution from non-local effects to the given angular observables. The LHCb result from Ref. [9] is overlaid for comparison, together with the SM prediction from GRvDV [16].

Angular observables ($P$-basis) obtained a posteriori from the fit results of the two fit configurations; the subfigures isolate the contribution from non-local effects to the given angular observables. The LHCb result from Ref. [9] is overlaid for comparison, together with the SM predictions from DHMV [14,15] and (for $P_5^\prime$) GRvDV [16].

Branching fraction and S-wave fraction obtained a posteriori from the fit results of the two fit configurations. The published Run 1 measurement from LHCb [1] has been overlaid for comparison. The SM branching fraction prediction from GRvDV [16] is also reported.

Results for the ratio $\mathcal{H}_\lambda (q^2) / \mathcal{F}_\lambda (q^2)$ obtained from the amplitude fit model with theory. The central values are shown with solid lines, while shaded bands indicate the 68% confidence intervals. The theoretical prediction at $q^2<0$ are overlaid for comparison.

Animated gif made out of all figures.

Central values and uncertainties used to constrain the CKM parameters in the fit. All values are taken from the CKMfitter group as of Summer 2019 [57].

Summary of external inputs from $B^0 \rightarrow \psi_{n}K^{*0}$ measurements used in the analysis. When measurements from different experiments are available, these are averaged taking into account correlations. A shift of $+\pi$ is introduced for the phase differences $\delta^{\psi_{n}}_{\perp,\parallel}$ to account for the different convention between this analysis and Refs. [68,70,71].

Log-likelihood differences between the fits to data with different truncation orders of the non-local hadronic parameterisation ${\mathcal{H}}_\lambda[z^{n}]$ for the two considered fit configurations.

Summary of the systematic uncertainties on the Wilson coefficients. The individual sources are described in the text. The subtotal and total values are obtained by adding individual sources in quadrature.

Best fit value, confidence intervals and deviation from the SM predictions [29,30] for the four Wilson coefficients and the two fit configurations. For each Wilson coefficient, the likelihood has been profiled over the other coefficients. The SM predictions at the $b$-quark energy scale [29,30] are also reported for reference.

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