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 | ||

| ||

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.
| ||

Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, PRD 98 (2018) 112011.The superseded preliminary plots can be found here.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 |
---|

Figures | |

png pdf |
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 ^- $. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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 | |

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

png pdf |
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 | |

png pdf |
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. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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/$c^{2}$. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

png pdf |
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. |

References | ||||

1 |
A. Khodjamirian, T. Mannel, and Y. M. Wang | $ {\rm B} \rightarrow {\rm K} \ell^+ \ell^- $ decay at large hadronic recoil | JHEP 02 (2013) 010 | 1211.0234 |

2 |
C. Bobeth, G. Hiller, and G. Piranishvili | Angular distributions of $ {\rm B} \rightarrow {\rm K} \ell^+ \ell^- $ decays | JHEP 12 (2007) 040 | 0709.4174 |

3 |
A. Khodjamirian, T. Mannel, A. A. Pivovarov, and Y. M. Wang | Charm-loop effect in $ {\rm B} \to {\rm K}^{(*)} \ell^{+} \ell^{-} $ and $ {\rm B} \to {\rm K}^* \gamma $ | JHEP 09 (2010) 089 | 1006.4945 |

4 |
C. Bobeth, G. Hiller, D. van Dyk, and C. Wacker | The decay $ {\rm B} \to {\rm K} \ell^+ \ell^- $ at low hadronic recoil and model-independent $ \Delta B = $ 1 constraints | JHEP 01 (2012) 107 | 1111.2558 |

5 |
A. Ali, T. Mannel, and T. Morozumi | Forward-backward asymmetry of dilepton angular distribution in the decay $ {\rm b} \to {\rm s} \ell^+ \ell^- $ | PLB 273 (1991) 505 | |

6 |
F. Beaujean, C. Bobeth, and S. Jahn | Constraints on tensor and scalar couplings from $ {\rm B} \rightarrow {\rm K} \bar{\mu} \mu $ and $ {\rm B}_s \rightarrow \bar{\mu} \mu $ | EPJC 75 (2015) 456 | 1508.01526 |

7 |
W. Altmannshofer, C. Niehoff, P. Stangl, and D. M. Straub | Status of the $ {\rm B} \rightarrow {\rm K}^{*} \mu^{+} \mu^{-} $ anomaly after Moriond 2017 | EPJC 77 (2017) 377 | 1703.09189 |

8 |
W. Altmannshofer, P. Paradisi, and D. M. Straub | Model-independent constraints on new physics in $ b \rightarrow s $ transitions | JHEP 04 (2012) 008 | 1111.1257 |

9 |
F. Sala and D. M. Straub | A new light particle in B decays? | PLB 774 (2017) 205 | 1704.06188 |

10 |
W. Altmannshofer and D. M. Straub | New physics in $ b \rightarrow s $ transitions after LHC run 1 | EPJC 75 (2015) 382 | 1411.3161 |

11 |
A. K. Alok, A. Dighe, and S. U. Sankar | Large forward-backward asymmetry in $ {\rm B} {\rightarrow} {\rm K} {{\mu}}^{+} {{\mu}}^{{-}} $ from new physics tensor operators | PRD 78 (2008) 114025 | 0810.3779 |

12 |
D. Ghosh, M. Nardecchia, and S. A. Renner | Hint of lepton flavour non-universality in B meson decays | JHEP 12 (2014) 131 | 1408.4097 |

13 |
CMS Collaboration |
CMS luminosity based on pixel cluster counting --- Summer 2013 update | CMS-PAS-LUM-13-001 | CMS-PAS-LUM-13-001 |

14 |
BABAR Collaboration | Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays $ {\rm B} \rightarrow {\rm K} \ell^+ \ell^- $ and $ {\rm B} \rightarrow {\rm K}^{\ast} \ell^+ \ell^- $ | PRD 73 (2006) 092001 | hep-ex/0604007 |

15 |
Belle Collaboration | Measurement of the differential branching fraction and forward-backword asymmetry for $ {\rm B} \rightarrow {\rm K}^{(\ast)} \ell^+ \ell^- $ | PRL 103 (2009) 171801 | 0904.0770 |

16 |
CDF Collaboration | Measurements of the angular distributions in the decays $ {\rm B} \rightarrow {\rm K}^{(\ast)} \mu^+ \mu^- $ at CDF | PRL 108 (2012) 081807 | 1108.0695 |

17 |
LHCb Collaboration |
Differential branching fraction and angular analysis of the $ {\rm B}^+ \rightarrow {\rm K}^+ \mu^+ \mu^- $ decay | JHEP 02 (2013) 105 | 1209.4284 |

18 |
LHCb Collaboration |
Angular analysis of charged and neutral $ {\rm B} \rightarrow {\rm K} \mu^+ \mu^- $ decays | JHEP 05 (2014) 082 | 1403.8045 |

19 |
CMS Collaboration |
The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | CMS-00-001 |

20 |
CMS Collaboration |
The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-0011609.02366 |

21 |
T. Sjostrand et al. | An introduction to PYTHIA 8.2 | Comp. Phys. Commu. 191 (2015) 159 | 1410.3012 |

22 |
D. J. Lange | The EvtGen particle decay simulation package | NIMA 462 (2001) 152 | |

23 |
GEANT4 Collaboration | GEANT4 --- a simulation toolkit | NIMA 506 (2003) 250 | |

24 |
CMS Collaboration |
Performance of muon identification in pp collisions at $ \sqrt{s} = $ 7 TeV | CDS | |

25 |
CMS Collaboration |
Muon ID performance: low-$ p_{\rm{T}} $ muon efficiencies | CDS | |

26 |
Particle Data Group, C. Patrignani et al. | Review of Particle Physics | CPC 40 (2016) 100001 | |

27 |
A. Ali, P. Ball, L. T. Handoko, and G. Hiller | A comparative study of the decays $ {\rm B} \rightarrow {\rm K}^{(\ast)} \ell^+ \ell^- $ in standard model and supersymmetric theories | PRD 61 (2000) 074024 | hep-ph/9910221 |

28 |
C. Bobeth, T. Ewerth, F. Kruger, and J. Urban | Analysis of neutral Higgs-boson contributions to the decays $ {\rm B}_s \rightarrow \ell^+ \ell^- $ and $ {\rm B} \rightarrow {\rm K} \ell^+ \ell^- $ | PRD 64 (2001) 074014 | hep-ph/0104284 |

29 |
G. J. Feldman and R. D. Cousins | A unified approach to the classical statistical analysis of small signals | PRD 57 (1998) 3873 | physics/9711021 |

30 |
S. Descotes-Genon, L. Hofer, J. Matias, and J. Virto | On the impact of power corrections in the prediction of $ {\rm B} \to {\rm K}^* \mu^+ \mu^- $ observables | JHEP 12 (2014) 125 | 1407.8526 |

31 |
S. Descotes-Genon, L. Hofer, J. Matias, and J. Virto | Global analysis of $ {\rm b}\to {\rm s} \ell \ell $ anomalies | JHEP 06 (2016) 092 | 1510.04239 |

32 |
D. van Dyk, C. Bobeth, F. Beaujean, and T. Blake | EOS (lambda-polarised release) | 2017 | |

33 |
HPQCD Collaboration | Rare decay $ {\rm B} \to {\rm K} \ell^+ \ell^- $ form factors from lattice QCD | PRD 88 (2013) 054509 | 1306.2384 |

34 |
P. Ball and R. Zwicky | New results on $ {\rm B} {\rightarrow} {\pi}, {\rm K}, {\eta} $ decay form factors from light-cone sum rules | PRD 71 (2005) 014015 | hep-ph/0406232 |

35 |
D. Straub et al. | flav-io/flavio v0.15.1 | 2016 | |

36 |
Fermilab Lattice and MILC Collaboration | $ {\rm B} \to {\rm K} \ell^ + \ell^- $ decay form factors from three-flavor lattice QCD | PRD 93 (2016) 025 | 1509.06235 |

Compact Muon Solenoid LHC, CERN |