Compact Muon Solenoid
LHC, CERN

Visit us: CMS Public Website, CMS Physics ; Contact us: CMS Publications Committee

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
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$^2$.

References
1	ATLAS Collaboration	Study of the rare decays of $ \mathrm{B}_{s}^{0} $ and $ {\mathrm{B}^0} $ mesons into muon pairs using data collected during 2015 and 2016 with the ATLAS detector	JHEP 04 (2019) 098	1812.03017
2	LHCb Collaboration	Measurement of the $ \mathrm{B}_{s}^{0}\to\mu^{+}\mu^{-} $ decay properties and search for the $ {\mathrm{B}^0}\to\mu^{+}\mu^{-} $ and $ \mathrm{B}_{s}^{0}\to\mu^{+}\mu^{-}\gamma $ decays	PRD 105 (2022) 012010	2108.09283
3	LHCb Collaboration	Analysis of neutral $ {\mathrm{B}} $-meson decays into two muons	PRL 128 (2022) 041801	2108.09284
4	CMS Collaboration	Measurement of the $ \mathrm{B}_{s}^{0}\to\mu^{+}\mu^{-} $ decay properties and search for the $ {\mathrm{B}^0}\to\mu^{+}\mu^{-} $ decay in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	PLB 842 (2023) 137955	CMS-BPH-21-006 2212.10311
5	BaBar Collaboration	Angular distributions in the decays $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)} \ell^+\ell^- $	PRD 79 (2009) 031102	0804.4412
6	Belle Collaboration	Measurement of the differential branching fraction and forward-backward asymmetry for $ {\mathrm{B}} \to K^{(*)}\ell^+\ell^- $	PRL 103 (2009) 171801	0904.0770
7	Belle Collaboration	Lepton-flavor-dependent angular analysis of $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)} \ell^+\ell^- $	PRL 118 (2017) 111801	1612.05014
8	CDF Collaboration	Measurements of the angular distributions in the decays $ {\mathrm{B}} \to K^{(*)} \mu^{+} \mu^{-} $ at CDF	PRL 108 (2012) 081807	1108.0695
9	LHCb Collaboration	Differential branching fraction and angular analysis of the decay $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+} \mu^{-} $	JHEP 08 (2013) 131	1304.6325
10	LHCb Collaboration	Measurement of form-factor-independent observables in the decay $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+} \mu^{-} $	PRL 111 (2013) 191801	1308.1707
11	LHCb Collaboration	Angular analysis of the $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+} \mu^{-} $ decay using 3 fb$ ^{-1} $ of integrated luminosity	JHEP 02 (2016) 104	1512.04442
12	CMS Collaboration	Angular analysis and branching fraction measurement of the decay $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+}\mu^{-} $	PLB 727 (2013) 77	CMS-BPH-11-009 1308.3409
13	CMS Collaboration	Angular analysis of the decay $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+}\mu^{-} $ from pp collisions at $ \sqrt s = $ 8 TeV	PLB 753 (2016) 424	CMS-BPH-13-010 1507.08126
14	CMS Collaboration	Measurement of angular parameters from the decay $ {\mathrm{B}^0} \to \mathrm{K^{*0}} \mu^{+} \mu^{-} $ in proton-proton collisions at $ \sqrt{s}= $ 8 TeV	PLB 781 (2018) 517	CMS-BPH-15-008 1710.02846
15	ATLAS Collaboration	Angular analysis of $ \mathrm{B}_{d}^{0} \rightarrow \mathrm{K^{\ast}(892)}\mu^{+}\mu^{-} $ decays in $ pp $ collisions at $ \sqrt{s}= $ 8 TeV with the ATLAS detector	JHEP 10 (2018) 047	1805.04000
16	LHCb Collaboration	Measurement of $ CP $-averaged observables in the $ {\mathrm{B}^0}\rightarrow \mathrm{K^{*0}}\mu^{+}\mu^{-} $ decay	PRL 125 (2020) 011802	2003.04831
17	M. Ciuchini et al.	Charming penguins and lepton universality violation in $ \mathrm{b} \to \mathrm{s} \ell^+ \ell^- $ decays	EPJC 83 (2023) 64	2110.10126
18	M. Algueró et al.	To (b)e or not to (b)e: no electrons at LHCb	EPJC 83 (2023) 648	2304.07330
19	M. Bordone, G. Isidori, S. Mächler, and A. Tinari	Short- vs. long-distance physics in $ {\mathrm{B}}\rightarrow K^{(*)} \ell ^+\ell ^- $: a data-driven analysis	EPJC 84 (2024) 547	2401.18007
20	CMS Collaboration	HEPData record for this analysis	link
21	W. Altmannshofer et al.	Symmetries and asymmetries of $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)} \mu^{+}\mu^{-} $ decays in the Standard Model and Beyond	JHEP 01 (2009) 019	0811.1214
22	S. Descotes-Genon, J. Matias, M. Ramon, and J. Virto	Implications from clean observables for the binned analysis of $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)}\mu^{+}\mu^{-} $ at large recoil	JHEP 01 (2013) 048	1207.2753
23	S. Descotes-Genon, T. Hurth, J. Matias, and J. Virto	Optimizing the basis of $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)} \ell^+ \ell^- $ observables in the full kinematic range	JHEP 05 (2013) 137	1303.5794
24	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
25	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
26	CMS Tracker Group	The CMS Phase-1 pixel detector upgrade	JINST 16 (2021) P02027	2012.14304
27	CMS Collaboration	Track impact parameter resolution for the full pseudo rapidity coverage in the 2017 dataset with the CMS Phase-1 Pixel detector	CMS Detector Performance Summary CMS-DP-2020-049, 2020 CDS
28	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
29	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
30	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
31	T. Sjöstrand et al.	An introduction to PYTHIA 8.2	Comput. Phys. Commun. 191 (2015) 159	1410.3012
32	D. J. Lange	The EvtGen particle decay simulation package	NIM A 462 (2001) 152
33	E. Barberio, B. van Eijk, and Z. Was	PHOTOS --- a universal Monte Carlo for QED radiative corrections in decays	Comput. Phys. Commun. 66 (1991) 115
34	E. Barberio and Z. Was	PHOTOS---a universal Monte Carlo for QED radiative corrections: version 2.0	Comput. Phys. Commun. 79 (1994) 291
35	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
36	Particle Data Group	Review of particle physics	PRD 110 (2024) 030001
37	M. Pivk and F. R. Le Diberder	$ _\mathrm{{s}}\mathcal{P}\mathrm{lot} $: a statistical tool to unfold data distributions	NIM A 555 (2005) 356	physics/0402083
38	M. J. Oreglia	A study of the reactions $ \psi^\prime \to \gamma \gamma \psi $	PhD thesis, Stanford University, SLAC Report SLAC-R-236, 1980 link
39	J. E. Gaiser	Charmonium spectroscopy from radiative decays of the $ \mathrm{J}/\psi $ and $ \psi^\prime $	PhD thesis, Stanford University, SLAC Report SLAC-R-255, 1982 link
40	CMS Collaboration	Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV	EPJC 75 (2015) 212	CMS-HIG-14-009 1412.8662
41	R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate	Lattice QCD calculation of form factors describing the rare decays $ {\mathrm{B}} \to \mathrm{K^{\ast}(892)} \ell^+ \ell^- $ and $ \mathrm{B}_{s} \to \phi \ell^+ \ell^- $	PRD 89 (2014) 094501	1310.3722
42	R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate	Rare B decays using lattice QCD form factors	in Proceedings of the 32nd International Symposium on Lattice Field Theory -- PoS(LATTICE), 2014 Proceedings of The 3 (2014) 372
43	N. Gubernari, A. Kokulu, and D. van Dyk	$ {\mathrm{B}}\to P $ and $ {\mathrm{B}}\to V $ form factors from $ {\mathrm{B}} $-meson light-cone sum rules beyond leading twist	JHEP 01 (2019) 150	1811.00983
44	N. Gubernari, D. van Dyk, and J. Virto	Non-local matrix elements in $ B_{(s)}\to \{K^{(*)},\phi\}\ell^+\ell^- $	JHEP 02 (2021) 088	2011.09813
45	N. Gubernari, M. Reboud, D. van Dyk, and J. Virto	Improved theory predictions and global analysis of exclusive $ \mathrm{b} \to \mathrm{s}\mu^{+}\mu^{-} $ processes	JHEP 09 (2022) 133	2206.03797
46	D. van Dyk et al.	eos/eos: EOS Version 1.0.10	link
47	D. M. Straub	$\texttt{flavio}$: a Python package for flavour and precision phenomenology in the Standard Model and beyond		1810.08132
48	A. Bharucha, D. M. Straub, and R. Zwicky	$ {\mathrm{B}} \to V\ell^+\ell^- $ in the Standard Model from light-cone sum rules	JHEP 08 (2016) 098	1503.05534
49	M. Beneke, T. Feldmann, and D. Seidel	Exclusive radiative and electroweak $ \mathrm{b} \to \mathrm{d} $ and $ \mathrm{b} \to \mathrm{s} $ penguin decays at NLO	EPJC 41 (2005) 173	hep-ph/0412400
50	M. Beneke, T. Feldmann, and D. Seidel	Systematic approach to exclusive $ {\mathrm{B}} \to V \ell^+ \ell^- $, $ V \gamma $ decays	NPB 612 (2001) 25	hep-ph/0106067
51	J. De Blas et al.	$ \texttt{HEPfit} $: a code for the combination of indirect and direct constraints on high energy physics models	EPJC 80 (2020) 456	1910.14012
52	M. Ciuchini et al.	$ {\mathrm{B}}\to \mathrm{K^{\ast}(892)} \ell^+ \ell^- $ decays at large recoil in the Standard Model: a theoretical reappraisal	JHEP 06 (2016) 116	1512.07157

Compact Muon Solenoid LHC, CERN

© Copyright CERN 2024 for the benefit of the CMS Collaboration