CMS-PAS-BPH-15-001 | ||

Measurement of angular observables in the decay $\mathrm{B}^{+} \to \mathrm{K}^{+} \mu^+\mu^-$ from proton-proton collisions at $\sqrt{s}= $ 8 TeV | ||

CMS Collaboration | ||

March 2018 | ||

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Abstract:
The angular distribution of the flavor-changing neutral current decay $\mathrm{B}^{+} \to \mathrm{K}^{+} \mu^+\mu^- $ is studied in pp collisions at the center-of-mass energy of 8 TeV. The analysis is based on data collected by the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb$^{-1}$. The forward-backward asymmetry $A_{FB}$ of the dimuon system and the contribution $F_{H}$ from the pseudo-scalar, scalar, and tensor amplitudes to the decay width are measured with respect to the squared dimuon mass. The measurements are consistent with the standard model expectations.
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Links:
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These preliminary results are superseded in this paper, PRD 98 (2018) 112011.The superseded preliminary plots can be found here. |

Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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Figures | |

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Figure 1:
The SM electroweak $\mathrm {Z}/\gamma $ penguin (left) and $\mathrm {W^+W^-}$ box (right) diagrams for the decay process $\mathrm {B}^{+} \to \mathrm {K}^{+} \mu ^+\mu ^- $. |

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Figure 2:
Projections of the fit results from the data in the $\mathrm {B}$ meson invariant mass (left) and $\cos\theta _{\ell}$ (right) distributions in the low-$q^2$ range 1.00-6.00 GeV$^2$. The solid lines show the total fit results, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in the data. The lower plots show the distributions of pulls, the difference between the data and the fit result, divided by the statistical uncertainty in the data. |

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Figure 2-a:
Projections of the fit results from the data in the $\mathrm {B}$ meson invariant mass (left) and $\cos\theta _{\ell}$ (right) distributions in the low-$q^2$ range 1.00-6.00 GeV$^2$. The solid lines show the total fit results, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in the data. The lower plots show the distributions of pulls, the difference between the data and the fit result, divided by the statistical uncertainty in the data. |

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Figure 2-b:
Projections of the fit results from the data in the $\mathrm {B}$ meson invariant mass (left) and $\cos\theta _{\ell}$ (right) distributions in the low-$q^2$ range 1.00-6.00 GeV$^2$. The solid lines show the total fit results, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in the data. The lower plots show the distributions of pulls, the difference between the data and the fit result, divided by the statistical uncertainty in the data. |

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Figure 3:
Results of the measurement of $A_{FB}$ (left) and $F_{H}$ (right) in bins of $q^2$. The statistical uncertainties are shown by the inner vertical bars, 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 $\psi '$ resonances. The horizontal shaded band shows the DHMV SM theoretical prediction [30,31]. The predictions from two other calculations are given in Table xxxxx. |

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Figure 3-a:
Results of the measurement of $A_{FB}$ (left) and $F_{H}$ (right) in bins of $q^2$. The statistical uncertainties are shown by the inner vertical bars, 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 $\psi '$ resonances. The horizontal shaded band shows the DHMV SM theoretical prediction [30,31]. The predictions from two other calculations are given in Table xxxxx. |

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Figure 3-b:
Results of the measurement of $A_{FB}$ (left) and $F_{H}$ (right) in bins of $q^2$. The statistical uncertainties are shown by the inner vertical bars, 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 $\psi '$ resonances. The horizontal shaded band shows the DHMV SM theoretical prediction [30,31]. The predictions from two other calculations are given in Table xxxxx. |

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Figure 4:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-a:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-b:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-c:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-d:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-e:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-f:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-g:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-h:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 4-i:
Projections of the fit results from data for the ${\rm K}^+\mu ^+\mu ^-$ invariant mass distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 5:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

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Figure 5-a:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-b:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-c:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-d:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-e:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-f:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-g:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-h:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

png pdf |
Figure 5-i:
Projections of the fit results from data for $\cos(\theta _{\ell})$ distributions for the $q^2$ bins given in each figure. The vertical bars represent the statistical uncertainties in the data. The lower plots show the pulls, the differences between the data and the fit results, divided by the statistical uncertainty in the data. |

Tables | |

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Table 1:
Systematic uncertainty contributions in the measurement of $A_{FB}$ for each $q^2$ bin. |

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Table 2:
Systematic uncertainty contributions in the measurement of $F_{H}$ for each $q^2$ bin. |

Summary |

In summary, using a data sample corresponding to an integrated luminosity of 20.5 fb$^{-1}$ recorded with the CMS detector at $\sqrt{s}= $ 8 TeV, an angular analysis of the decay $\mathrm{B}^{+} \to \mathrm{K}^{+} \mu^+\mu^- $ has been performed. A measurement of the forward-backward asymmetry $A_{FB}$ of the muon system and the contribution $F_{H}$ of the pseudo-scalar, scalar, and tensor amplitudes to the decay width is reported as a function of the squared dimuon mass. The results are consistent with previous measurements and with various standard model predictions. |

Additional Figures | |

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Additional Figure 1:
Spectrum of the dimuon invariant mass. The two peaks correspond to the $\mathrm {J}/\psi $ and $\psi '$ resonances used as control samples. |

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Additional Figure 2:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 1.00-2.00 GeV/$c^{2}$. |

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Additional Figure 3:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 2.00-4.30 GeV/$c^{2}$. |

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Additional Figure 4:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 4.30-8.68 GeV/$c^{2}$. |

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Additional Figure 5:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 10.09-12.86 GeV/$c^{2}$. |

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Additional Figure 6:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 14.18-16.00 GeV/$c^{2}$. |

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Additional Figure 7:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 16.00-18.00 GeV/$c^{2}$. |

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Additional Figure 8:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 18.00-22.00 GeV/$c^{2}$. |

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Additional Figure 9:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 1.00-6.00 GeV/$c^{2}$. |

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Additional Figure 10:
The signal efficiency computed on simulated events along the angular variable $\cos\theta _{l}$ for the $q^{2}$ bin: 1.00-8.68, 10.09-12.86, and 14.18-22.00 GeV/$c^{2}$. |

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Additional Figure 11:
Closure test of the fitting results of $A_{FB}$ for each $q^{2}$ bin on simulated data. The results of the fit on reconstructed events (blue dots) are compared with the fit on the generated events (green circles). The vertical shaded regions correspond to the $\mathrm {J}/\psi $ and $\psi '$ resonances. |

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Additional Figure 12:
Closure test of the fitting results of $F_{H}$ for each $q^{2}$ bin on simulated data. The results of the fit on reconstructed events (blue dots) are compared with the fit on the generated events (green circles). The vertical shaded regions correspond to the $\mathrm {J}/\psi $ and $\psi '$ resonances. |

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Additional Figure 13:
Measured values of the differential branching fraction in each of the $q^2$ bins from CMS, compared with standard model prediction [17] and LHCb [17,18] results. |

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Additional Figure 14:
Measured values of $A_{FB}$ versus $q^2$ for $\mathrm {B}^{+}$ \to $\mathrm {K}^{+}$ \mu ^+\mu ^- from CMS, compared with LHCb [17,18] 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. |

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Additional Figure 15:
Measured values of $F_{H}$ versus $q^2$ for $\mathrm {B}^{+}$ \to $\mathrm {K}^{+}$ \mu ^+\mu ^- from CMS, compared with LHCb [17,18] 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. |

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Compact Muon Solenoid LHC, CERN |