CMS-BPH-21-002

CMS-BPH-21-002 ; CERN-EP-2024-268
Angular analysis of the ${\mathrm{B}^0}\to \mathrm{ K^*(892)^0 } \mu^{+}\mu^{-}$ decay in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
18 November 2024
Submitted to Phys. Lett. B
Abstract: A full set of optimized observables is measured in an angular analysis of the decay ${\mathrm{B}^0}\to \mathrm{ K^*(892)^0 } \mu^{+}\mu^{-}$ using a sample of proton-proton collisions at $\sqrt{s}=$ 13 TeV, collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 140 fb $^{-1}$ . The analysis is performed in six bins of the squared invariant mass of the dimuon system, $q^{2}$ , over the range 1.1 $< q^{2} <$ 16 GeV $^2$ . The results are among the most precise experimental measurements of the angular observables for this decay and are compared to a variety of predictions based on the standard model.
Links: e-print arXiv:2411.11820 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	Additional Figures & Tables	References	CMS Publications

Figures
png pdf	Figure 1: Sketch representing the definition of the angles $\theta_l$ (left), $\theta_{\mathrm{K}}$ (center), and $\phi$ (right).
png pdf	Figure 2: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-a: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-b: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-c: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-d: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-e: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-f: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-g: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 2-h: Mass and angular distributions for (upper two rows) 2 $< q^{2} <$ 4.3 GeV $^2$ and (lower two rows) 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (blue solid line) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Figure 3: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-a: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-b: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-c: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-d: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-e: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-f: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-g: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 3-h: Measurements of the angular observables versus $q^{2}$ . The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi(2\text{S})$ resonances. Predictions are shown, averaged in each bin, from Ref. [18] (labeled ABCDMN), and the $\texttt{EOS}$ [46], $\texttt{flavio}$ [47], and $\texttt{HEPfit}$ [51] libraries.
png pdf	Figure 4: Comparison of current measurements of $P_2$ and $P^{\prime}_5$ to a previous $P_2$ measurement by LHCb [16] and previous $P^{\prime}_5$ results from ATLAS [15], Belle [7], CMS [14], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.
png pdf	Figure 4-a: Comparison of current measurements of $P_2$ and $P^{\prime}_5$ to a previous $P_2$ measurement by LHCb [16] and previous $P^{\prime}_5$ results from ATLAS [15], Belle [7], CMS [14], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.
png pdf	Figure 4-b: Comparison of current measurements of $P_2$ and $P^{\prime}_5$ to a previous $P_2$ measurement by LHCb [16] and previous $P^{\prime}_5$ results from ATLAS [15], Belle [7], CMS [14], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.

Tables
png pdf	Table 1: The uncertainties considered in the analysis on the various angular observables. For each source of uncertainty, the range covers the absolute variation observed across the $q^{2}$ bins.
png pdf	Table 2: The measured CP-averaged angular observables, in the corresponding $q^{2}$ bins. The first uncertainty is statistical and the second is systematic.

Summary

In summary, the study of the full angular distribution of the flavor-changing neutral-current

${\mathrm{B}^0}\to \mathrm{ K^{*0} } \mu^{+}\mu^{-}$ decay has been performed using 140 fb

$^{-1}$ of proton-proton collision data recorded by the CMS detector at the LHC at

$\sqrt{s}=$ 13 TeV. A complete set of observables has been measured via unbinned maximum likelihood fits to the

${\mathrm{B}^0}$ candidate mass and angular variables, in bins of the squared invariant mass of the dimuon system ranging from 1.1 to 16 GeV

$^2$ . The measurements are compared to a variety of predictions based on the standard model, with tension in a few of the angular observables seen for some of the predictions, as is also reported by other experiments. These results are among the most precise experimental measurements of the angular observables of this decay, and provide a valuable contribution to the understanding of the

$\mathrm{b}\to\mathrm{s}\ell^{+}\ell^{-}$ processes.

Additional Figures
png pdf	Additional Figure 1: Mass and angular distributions for 1.1 $< q^{2} <$ 2 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 1-a: Mass and angular distributions for 1.1 $< q^{2} <$ 2 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 1-b: Mass and angular distributions for 1.1 $< q^{2} <$ 2 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 1-c: Mass and angular distributions for 1.1 $< q^{2} <$ 2 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 1-d: Mass and angular distributions for 1.1 $< q^{2} <$ 2 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 2: Mass and angular distributions for 6 $< q^{2} <$ 8.68 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 2-a: Mass and angular distributions for 6 $< q^{2} <$ 8.68 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 2-b: Mass and angular distributions for 6 $< q^{2} <$ 8.68 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 2-c: Mass and angular distributions for 6 $< q^{2} <$ 8.68 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 2-d: Mass and angular distributions for 6 $< q^{2} <$ 8.68 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 3: Mass and angular distributions for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 3-a: Mass and angular distributions for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 3-b: Mass and angular distributions for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 3-c: Mass and angular distributions for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 3-d: Mass and angular distributions for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 4: Mass and angular distributions for 14.18 $< q^{2} <$ 16 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 4-a: Mass and angular distributions for 14.18 $< q^{2} <$ 16 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 4-b: Mass and angular distributions for 14.18 $< q^{2} <$ 16 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 4-c: Mass and angular distributions for 14.18 $< q^{2} <$ 16 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 4-d: Mass and angular distributions for 14.18 $< q^{2} <$ 16 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dotted line, and the background by the orange dashed line.
png pdf	Additional Figure 5: Comparison of current measurements of $F_\mathrm{L}$ to previous results from ATLAS [15], CMS [13], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.
png pdf	Additional Figure 6: Comparison of current measurements of $P_1$ to previous results from ATLAS [15], CMS [14], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.
png pdf	Additional Figure 7: Comparison of current measurements of $P_3$ to previous results from LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths.
png pdf	Additional Figure 8: Comparison of current measurements of $P_4^{\prime}$ to previous results from ATLAS [15], Belle [7], and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The definition of the $P_4^{\prime}$ observable is the one presented in Ref. [22]: the results from ATLAS, Belle, and LHCb Collaborations are therefore scaled by a factor of two to superimpose them on the same plot.
png pdf	Additional Figure 9: Comparison of current measurements of $P_6^{\prime}$ to previous results from ATLAS [15] and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The definition of the $P_6^{\prime}$ observable is the one presented in Ref. [22]: the results from the LHCb Collaboration are therefore scaled by a factor of minus one to superimpose them on the same plot.
png pdf	Additional Figure 10: Comparison of current measurements of $P_8^{\prime}$ to previous results from ATLAS [15] and LHCb [16]. The inner vertical bars represent the statistical uncertainties, while the outer vertical bars give the total uncertainties. The horizontal bars show the bin widths. The definition of the $P_8^{\prime}$ observable is the one presented in Ref. [22]: the results from LHCb and ATLAS Collaborations are therefore scaled by a factor of two to superimpose them on the same plot.
png pdf	Additional Figure 11: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $F_\mathrm{L}$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 12: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_1$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 13: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_2$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 14: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_3$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 15: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_4^{\prime}$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 16: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_5^{\prime}$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 17: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_6^{\prime}$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 18: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_8^{\prime}$ observable. In all cases where the statistical uncertainty is asymmetric, the maximum of the two uncertainties is represented. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively.
png pdf	Additional Figure 19: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 1.1 $< q^{2} <$ 2 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 19-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 1.1 $< q^{2} <$ 2 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 19-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 1.1 $< q^{2} <$ 2 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 19-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 1.1 $< q^{2} <$ 2 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 20: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 2 $< q^{2} <$ 4.3 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 20-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 2 $< q^{2} <$ 4.3 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 20-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 2 $< q^{2} <$ 4.3 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 20-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 2 $< q^{2} <$ 4.3 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 21: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 4.3 $< q^{2} <$ 6 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 21-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 4.3 $< q^{2} <$ 6 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 21-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 4.3 $< q^{2} <$ 6 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 21-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 4.3 $< q^{2} <$ 6 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 22: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 6 $< q^{2} <$ 8.68 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 22-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 6 $< q^{2} <$ 8.68 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 22-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 6 $< q^{2} <$ 8.68 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 22-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 6 $< q^{2} <$ 8.68 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 23: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 23-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 23-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 23-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 10.09 $< q^{2} <$ 12.86 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 24: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 14.18 $< q^{2} <$ 16 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 24-a: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 14.18 $< q^{2} <$ 16 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 24-b: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 14.18 $< q^{2} <$ 16 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 24-c: Projections on the angular variables of the three-dimensional efficiency functions for signal candidates with correct (blue line) and wrong (orange line) flavor assignment, for 14.18 $< q^{2} <$ 16 GeV $^2$ . These functions represent the combination of detector acceptance and efficiency for signal candidates, calculated on a sample of simulated ${\mathrm{B}^0}$ mesons with $\|\eta\| <$ 3, with conditions corresponding to the data collected in 2018.
png pdf	Additional Figure 25: Invariant mass of the ${\mathrm{B}^0}$ meson candidates as a function of $q^{2}$ .

Additional Tables
png pdf	Additional Table 1: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 1.1 $< q^{2} <$ 2 GeV $^2$ .
png pdf	Additional Table 2: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 2 $< q^{2} <$ 4.3 GeV $^2$ .
png pdf	Additional Table 3: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 4.3 $< q^{2} <$ 6 GeV $^2$ .
png pdf	Additional Table 4: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 6 $< q^{2} <$ 8.68 GeV $^2$ .
png pdf	Additional Table 5: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 10.09 $< q^{2} <$ 12.86 GeV $^2$ .
png pdf	Additional Table 6: Correlation matrix of angular observables, considering only the statistical uncertainties, from the maximum-likelihood fit in the region 14.18 $< q^{2} <$ 16 GeV $^2$ .

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