CMS-PAS-BPH-15-008

CMS-PAS-BPH-15-008
Measurement of the $P_1$ and $P_5'$ angular parameters of the decay $\mathrm{B}^0 \to \mathrm{K}^{*0} \mu^{+} \mu^{-}$ in proton-proton collisions at $\sqrt{s} =$ 8 TeV
CMS Collaboration
March 2017

Abstract: The angular distributions of the decay $\mathrm{B}^0 \to \mathrm{K}^{*0} \mu^{+} \mu^{-}$ are studied using data corresponding to an integrated luminosity of 20.5 fb $^{-1}$ collected with the CMS detector at the LHC in proton-proton collisions at $\sqrt{s} =$ 8 TeV. An angular analysis gives access to many physical observables, including $P_5'$ , which is of particular interest due to measurements from the LHCb Collaboration, that exibit potential discrepancy with the standard model. Based on a sample of 1397 signal events, the $P_1$ and $P_5'$ angular parameters are determined as a function of the dimuon invariant mass squared. The measurement are in agreement with standard model predictions.
Links: CDS record (PDF) ; inSPIRE record ; CADI line (restricted) ; These preliminary results are superseded in this paper, PLB 781 (2018) 517. The superseded preliminary plots can be found here.

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Sketch showing the definition of the angular variables $\theta _l$ (left), $\theta _{\mathrm{K}}$ (middle), and $\phi$ (right) for the decay ${\mathrm{B}^0 \to {\mathrm {K}^{* 0}} (\mathrm{K}^{+} \pi^{-} ) \mu^{+} \mu^{-} }$ .
png pdf	Figure 2: $\mathrm{K}^{+} \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the second and third $q^2$ bin (top four plots) 2.00 $< q^2 <$ 4.30 GeV $^2$ , and (bottom four plots) 4.30 $< q^2 <$ 6.00 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Figure 2-a: $\mathrm{K}^{+} \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the second $q^2$ bin, 2.00 $< q^2 <$ 4.30 GeV $^2$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Figure 2-b: $\mathrm{K}^{+} \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the third $q^2$ bin, 4.30 $< q^2 <$ 6.00 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Figure 3: Measured values of $P_1$ and $P_5'$ versus $q^2$ for ${\mathrm{B}^0 \to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [30] and Belle [32] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [17,24], while SM-HEPfit result from Refs. [48,49]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Figure 3-a: Measured values of $P_1$ versus $q^2$ for ${\mathrm{B}^0 \to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [30] and Belle [32] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [17,24], while SM-HEPfit result from Refs. [48,49]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Figure 3-b: Measured values of $P_5'$ versus $q^2$ for ${\mathrm{B}^0 \to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [30] and Belle [32] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [17,24], while SM-HEPfit result from Refs. [48,49]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.

Tables
png pdf	Table 1: Systematic uncertainty contributions for the measurements of $P_1$ and $P_5'$ . The total uncertainty in each $q^2$ bin is obtained by adding each contribution in quadrature. For each item, the range indicates the variation of the uncertainty in the $q^2$ bins.
png pdf	Table 2: The measured signal yields, which include both correctly tagged and mistagged events, and the $P_1$ and $P_5'$ values, in bins of $q^2$ , for the decay ${\mathrm{B}^0 \to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ . The first uncertainty is statistical and the second is systematic. The bin ranges are selected to allow comparisons to previous measurements.

Summary

Using pp collision data recorded at

$\sqrt{s} =$ 8 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb

$^{-1}$ , an angular analysis has been performed for the decay

${\mathrm{B}^0\to\mathrm{K}^{*0} \mu^{+} \mu^{-}}$ . In total, 1397 signal events are obtained. For each bin of the dimuon invariant mass squared

$(q^2)$ , unbinned maximum-likelihood fits were performed to the distributions of the

$\mathrm{K}^{+}\pi^{-}\mu^{+}\mu^{-}$ invariant mass and the three decay angles, to obtain values of the

$P_1$ and

$P_5'$ parameters. The results are among the most precise to date and are consistent with standard model predictions and previous measurements.

Additional Figures
png pdf	Additional Figure 1: Spectrum of the di-muon invariant mass. The two peaks correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances used as control samples.
png pdf	Additional Figure 2: Projection of the efficiency computed on simulated events along the three angular variables $\cos\theta _K$ , $\|\cos\theta _L\|$ , $\phi$ for the second bin 2.00 $< q^2 <$ 4.30 GeV $^{2}$ for correctly tagged events.
png pdf	Additional Figure 3: Projection of the efficiency computed on simulated events along the three angular variables $\cos\theta _K$ , $\|\cos\theta _L\|$ , $\phi$ for the seventh bin 16.00 $< q^2 <$ 19.00 GeV $^{2}$ for correctly tagged events.
png pdf	Additional Figure 4: Projection of the efficiency computed on simulated events along the three angular variables $\cos\theta _K$ , $\|\cos\theta _L\|$ , $\phi$ for the second bin 2.00 $< q^2 <$ 4.30 GeV $^{2}$ for wrongly tagged events.
png pdf	Additional Figure 5: Projection of the efficiency computed on simulated events along the three angular variables $\cos\theta _K$ , $\|\cos\theta _L\|$ , $\phi$ for the seventh bin 16.00 $< q^2 <$ 19.00 GeV $^{2}$ for wrongly tagged events.
png pdf	Additional Figure 6: Closure test of efficiency using simulated events for correctly tagged events. Half of the simulated events are used to compute the efficiency, and the other half is used for the test. The black dots are are the simulated events reconstructed, the red histograms are the distribution of the events at generator level, multiplied by the efficiency.
png pdf	Additional Figure 7: Closure test of efficiency using simulated events for wrongly tagged events. Half of the simulated events are used to compute the efficiency, and the other half is used for the test. The black dots are are the simulated events reconstructed, the red histograms are the distribution of the events at generator level, multiplied by the efficiency.
png pdf	Additional Figure 8: Closure test of the fitting results of $P_5'$ for each $q^2$ bin on simulated data. The results of the fit on reconstructed events (black dots) are compared with the fit on the generated events (red dots). The vertical shaded regions correspond to the $J/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 9: Closure test of the fitting results of $P_1$ for each $q^2$ bin on simulated data. The results of the fit on reconstructed events (black dots) are compared with the fit on the generated events (red dots). The vertical shaded regions correspond to the $J/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 10: Distribution of $\mathcal {L}$ computed on data for third bin 2.00 $< q^2 <$ 4.30 GeV $^{2}$ , in the $P_1,P'_5$ plane. The colored regions correspond to $\Delta \log\mathcal {L} <$ 0.5 (yellow), 0.5 $< \Delta \log\mathcal {L} <$ 2.0 (green), $\Delta \log\mathcal {L} >$ 2.0 (purple), respectively. The magenta line represents the physical boundary, the physically allowed region being above that line. Superimposed is a bivariate Gaussian fit (dot-dashed line), and the position of the maxima of the profiled $\mathcal {L}$ along $P_1$ , with $P'_5$ fixed, (blue crosses) and along $P'_5$ , with $P_1$ fixed, (red crosses).
png pdf	Additional Figure 11: Distribution of $\mathcal {L}$ computed on data for third bin $4.30< q^2 <6.00$ GeV $^{2}$ , in the $P_1,P'_5$ plane. The colored regions correspond to $\Delta \log\mathcal {L} <$ 0.5 (yellow), 0.5 $< \Delta \log\mathcal {L} <$ 2.0 (green), $\Delta \log\mathcal {L} >$ 2.0 (purple), respectively. The magenta line represents the physical boundary, the physically allowed region being above that line. Superimposed is a bivariate Gaussian fit (dot-dashed line), and the position of the maxima of the profiled $\mathcal {L}$ along $P_1$ , with $P'_5$ fixed, (blue crosses) and along $P'_5$ , with $P_1$ fixed, (red crosses).
png pdf	Additional Figure 12: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions of the control channel $\mathrm{J}/\psi$ on data. Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 13: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions of the control channel $\psi '$ on data. Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 14: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the first $q^2$ bin 1.00 $< q^2 <$ 2.00 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 15: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the second $q^2$ bin 2.00 $< q^2 <$ 4.30 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 16: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the third $q^2$ bin $4.30< q^2 <6.00$ GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 17: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the fourth $q^2$ bin $6.00< q^2 <8.68$ GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 18: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the fifth $q^2$ bin 10.09 $< q^2 <$ 12.86 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 19: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the sixth $q^2$ bin 14.18 $< q^2 <$ 16.00 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 20: $\mathrm{ K^{+} } \pi^{-} \mu^{+} \mu^{-}$ invariant mass and angular distributions for the seventh $q^2$ bin 16.00 $< q^2 <$ 19.00 GeV $^{2}$ . Overlaid on each plot is the projection of the results for the total fit, as well as for the three components: correctly tagged signal, mistagged signal, and background. The vertical bars indicate the statistical uncertainties.
png pdf	Additional Figure 21: Measured values of $P_1$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [1] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 22: Measured values of $P'_5$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [1] and Belle [2] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 23: Measured values of $P_1$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [1] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [3,4], while SM-HEPfit result from Refs. [5,6]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 24: Measured values of $P'_5$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [1] and Belle [2] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [3,4], while SM-HEPfit result from Refs. [5,6]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 25: Measured values of $P'_5$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with LHCb [1] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The red and blue hatched regions show two SM predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV result is derived from Refs. [3,4], while SM-HEPfit result from Refs. [5,6]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.
png pdf	Additional Figure 26: Measured values of $P'_5$ versus $q^2$ for ${\mathrm{ B }^0\to {\mathrm {K}^{* 0}} \mu^{+} \mu^{-} }$ from CMS, compared with Belle [2] results. The statistical uncertainty is shown by the inner vertical bars, while the outer vertical bars give the total uncertainty. The horizontal bars show the bin widths. The vertical shaded regions correspond to the $\mathrm{J}/\psi$ and $\psi '$ resonances. The blue hatched region show the SM (SM-DHMV) predictions averaging over each $q^2$ bin to provide a direct comparison to the data. The SM-DHMV prediction is derived from Refs. [3,4]. Reliable theoretical predictions are not available near the $\mathrm{J}/\psi$ and $\psi '$ resonances.

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