The angular distributions and the partial branching fraction of the decay $B^{0} \rightarrow K^{*0} \mu^+ \mu^$ are studied using an integrated luminosity of $0.37 fb^{1}$ of data collected with the LHCb detector. The forwardbackward asymmetry of the muons, $A_{\mathrm{FB}}$, the fraction of longitudinal polarisation, $F_{\mathrm{L}}$, and the partial branching fraction, $\mathrm{d}{\mathcal B}/\mathrm{d}q^{2}$, are determined as a function of the dimuon invariant mass. The measurements are in good agreement with the Standard Model predictions and are the most precise to date. In the dimuon invariant mass squared range $1.006.00{\mathrm{ Ge V}}^2/c^4$, the results are $A_{\mathrm{FB}}=0.06 ^{+0.13}_{0.14} \pm 0.04$, $F_{\mathrm{L}}=0.55\pm 0.10\pm 0.03$ and $\mathrm{d}{\mathcal B}/\mathrm{d}q^{2}=(0.42 \pm 0.06\pm 0.03) \times 10^{7}c^4/{\mathrm{ Ge V}}^2$. In each case, the first error is statistical and the second systematic.
$K^+\pi^\mu ^+ \mu ^ $ invariant mass distribution after the application of the full selection as data points with the fit overlaid. The signal component is the green (light) line, the background the red (dashed) line and the full distribution the blue (dark) line. 
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$ A_{\mathrm{FB}}$ , $ F_{\mathrm{L}}$ and $\mathrm{d}\cal B /\mathrm{d}q^{2}$ as a function of $q^{2}$. The SM prediction is given by the cyan (light) band, and this prediction rateaveraged across the $ q^2$ bins is indicated by the purple (dark) regions. No SM prediction is shown for the region between the two regimes in which the theoretical calculations are made (see text). 
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Fit projections for $m_{K\pi\mu\mu}$, $\cos{\theta_l}$ and $\cos{\theta_K}$ for the $ q^2$ bins: $0.10 < q^{2} < 2.00$, $2.00 < q^{2} < 4.30$ and $4.30 < q^{2} < 8.68\mathrm{ Ge V} ^{2}/c^4$. 
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Fit projections for $m_{K\pi\mu\mu}$, $\cos{\theta_l}$ and $\cos{\theta_K}$ for the $ q^2$ bins: $10.09 < q^{2} < 12.86$, $14.18 < q^{2} < 16.00$ and $16.00 < q^{2} < 19.00\mathrm{ Ge V} ^{2}/c^4$. 
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Animated gif made out of all figures. 
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Central values with statistical and systematic uncertainties for $ A_{\mathrm{FB}}$ , $ F_{\mathrm{L}}$ and $\mathrm{d}\cal B /\mathrm{d}q^{2}$ as a function of $ q^2$ . The $ B ^0 \rightarrow K ^{*0} \mu ^+ \mu ^ $ signal and background yields in the $\pm50 {\mathrm{ Me V /}c^2} $ signal mass window with their statistical uncertainties are also indicated, together with the statistical significance of the signal peak that is observed. \\ 
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Created on 08 August 2020.