CMS-PAS-BPH-21-002

CMS-PAS-BPH-21-002
Angular analysis of the ${\mathrm{B}^0} \to \mathrm{K^{* 0}(892)} \mu^+\mu^-$ decay at $\sqrt{s}=$ 13 TeV
CMS Collaboration
4 June 2024

Abstract: The full set of optimised CP-averaged observables is measured in the angular analysis of the decay ${\mathrm{B}^0} \to \mathrm{K^{* 0}(892)} \mu^+\mu^-$ 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 bins of the invariant mass squared of the dimuon system. These results are among the most precise experimental measurements of the angular observables of the $\mathrm{B}^0 \to \mathrm{K^{* 0}(892)} \mu^+\mu^-$ decay.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to PLB. The superseded preliminary plots can be found here.

Figures & Tables	Summary	Additional Figures & Tables	References	CMS Publications

Figures
png pdf	Figure 1: Sketch representing the definition of the angular variables $\cos\theta_l$ (left), $\cos\theta_\mathrm{K}$ (centre), and $\phi$ (right).
png pdf	Figure 2: Mass and angular distributions for 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Figure 2-a: Mass and angular distributions for 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Figure 2-b: Mass and angular distributions for 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Figure 2-c: Mass and angular distributions for 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Figure 2-d: Mass and angular distributions for 4.3 $< q^{2} <$ 6 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Figure 3: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-a: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-b: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-c: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-d: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-e: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-f: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-g: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.
png pdf	Figure 3-h: Measurements of the angular parameters 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 $\psi$ (2S) resonances. The data are compared to two sets of predictions based on flavio [33] and EOS [34] libraries, averaged in each bin.

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

Summary

In summary, the study of the full angular distribution of the

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

$^{-1}$ of proton-proton collision data recorded by the CMS detector at the LHC at center-of-mass energy of 13 TeV. The complete set of CP-averaged observables has been measured via unbinned maximum-likelihood fits to the signal mass and angular distributions, in bins of

$q^{2}$ ranging from 1.1 to 16 GeV

$^{2}$ . These results are among the most precise experimental measurements of the angular observables of the

${\mathrm{B}^0}\to \mathrm{K^{* 0}}\mu^{+}\mu^{-}$ decay.

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 dashed line, and the background by the orange 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 dashed line, and the background by the orange 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 dashed line, and the background by the orange 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 dashed line, and the background by the orange 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 dashed line, and the background by the orange line.
png pdf	Additional Figure 2: Mass and angular distributions for 2 $< q^{2} <$ 4.3 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Additional Figure 2-a: Mass and angular distributions for 2 $< q^{2} <$ 4.3 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Additional Figure 2-b: Mass and angular distributions for 2 $< q^{2} <$ 4.3 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Additional Figure 2-c: Mass and angular distributions for 2 $< q^{2} <$ 4.3 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Additional Figure 2-d: Mass and angular distributions for 2 $< q^{2} <$ 4.3 GeV $^2$ . The projections of the total fitted distribution (in blue) and its different components are overlaid. The signal is shown by the red dashed line, and the background by the orange line.
png pdf	Additional Figure 3: 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 dashed line, and the background by the orange line.
png pdf	Additional Figure 3-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 3-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 3-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 3-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 4: 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 dashed line, and the background by the orange line.
png pdf	Additional Figure 4-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 4-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 4-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 4-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 5: 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 dashed line, and the background by the orange line.
png pdf	Additional Figure 5-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 5-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 5-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 5-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 dashed line, and the background by the orange line.
png pdf	Additional Figure 6: Measurements of the angular observable $F_L$ versus $q^{2}$ , in comparison to results from LHCb [12] and previous CMS publication [9]. 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 $\psi$ (2S) resonances. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 7: Measurements of the angular observable $P_1$ versus $q^{2}$ , in comparison to results from LHCb [12] and previous CMS publication [10]. 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 $\psi$ (2S) resonances. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 8: Measurements of the angular observable $P_2$ versus $q^{2}$ , in comparison to results from LHCb [12]. 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 $\psi$ (2S) resonances. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 9: Measurements of the angular observable $P_3$ versus $q^{2}$ , in comparison to results from LHCb [12]. 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 $\psi$ (2S) resonances. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 10: Measurements of the angular observable $P_4^{\prime}$ versus $q^{2}$ , in comparison to results from LHCb [12]. 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 $\psi$ (2S) resonances. The definition of the $P_4^{\prime}$ observable is the one presented in [16]: the results from the LHCb Collaboration are therefore appropriately scaled by a factor of two to superimpose them on the same plot. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 11: Measurements of the angular observable $P_5^{\prime}$ versus $q^{2}$ , in comparison to results from LHCb [12] and previous CMS publications [10]. 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 $\psi$ (2S) resonances. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 12: Measurements of the angular observable $P_6^{\prime}$ versus $q^{2}$ , in comparison to results from LHCb [12]. 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 $\psi$ (2S) resonances. The definition of the $P_6^{\prime}$ observable is the one presented in [16]: the results from the LHCb Collaboration are therefore appropriately scaled by a factor of minus one to superimpose them on the same plot. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 13: Measurements of the angular observable $P_8^{\prime}$ versus $q^{2}$ , in comparison to results from LHCb [12]. 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 $\psi$ (2S) resonances. The definition of the $P_8^{\prime}$ observable is the one presented in [16]: the results from the LHCb Collaboration are therefore appropriately scaled by a factor of two to superimpose them on the same plot. The definition of the $q^{2}$ bins may differ between the various measurements.
png pdf	Additional Figure 14: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $F_L$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 15: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_1$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 16: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_2$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 17: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_3$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 18: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_4^{\prime}$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 19: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_5^{\prime}$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 20: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_6^{\prime}$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.
png pdf	Additional Figure 21: The various sources of systematic uncertainty per each $q^{2}$ bin, for the $P_8^{\prime}$ observable. The total systematic uncertainty and the statistical uncertainty are shown by the dotted area and white bar, respectively. The vertical axis represents the index of the $q^{2}$ bins used in the analysis, ordered with increasing $q^{2}$ value and excluding the bins dominated by the resonant channels.

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

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