CMS-BPH-15-001 ; CERN-EP-2018-125 | ||
Angular analysis of the decay ${\mathrm{B^{+}} \to \mathrm{K^{+}} \mu^{+} \mu^{-}}$ in proton-proton collisions at $\sqrt{s} = $ 8 TeV | ||
CMS Collaboration | ||
2 June 2018 | ||
Phys. Rev. D 98 (2018) 112011 | ||
Abstract: The angular distribution of the flavor-changing neutral current decay ${\mathrm{B^{+}} \to \mathrm{K^{+}} \mu^{+} \mu^{-}}$ is studied in proton-proton collisions at a center-of-mass energy of 8 TeV. The analysis is based on data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 20.5 fb$^{-1}$. The forward-backward asymmetry $A_{\mathrm{FB}}$ of the dimuon system and the contribution $F_{\mathrm{H}}$ from the pseudoscalar, scalar, and tensor amplitudes to the decay width are measured as a function of the dimuon mass squared. The measurements are consistent with the standard model expectations. | ||
Links: e-print arXiv:1806.00636 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
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^+}} {\mathrm {W^-}}$ box (right) diagrams for the decay process ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$. |
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Figure 1-a:
The SM electroweak $ {\mathrm {Z}} / {\gamma}$ penguin diagram for the decay process ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$. |
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Figure 1-b:
The SM electroweak $ {\mathrm {W^+}} {\mathrm {W^-}}$ box diagram for the decay process ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$. |
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Figure 2:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for the different $q^2$ ranges (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-a:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 1 $ < q^2 < $ 2 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-b:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 2 $ < q^2 < $ 4.3 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-c:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 4.3 $ < q^2 < $ 8.68 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-d:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 10.3 $ < q^2 < $ 12.86 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-e:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 14.18 $ < q^2 < $ 16 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-f:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 16 $ < q^2 < $ 18 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-g:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 18 $ < q^2 < $ 22 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-h:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 1 $ < q^2 < $ 6 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 2-i:
The signal efficiency determined from simulated events as a function of $\cos\theta _{\ell}$ for 1 $ < q^2 < $ 22 GeV$^2$ (points). The vertical bars indicate the statistical uncertainty. The curves show the sixth-order polynomial fits to the points. |
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Figure 3:
Projections of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distributions for each $q^2$ range from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-a:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 1 $ < q^2 < $ 2 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-b:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 2 $ < q^2 < $ 4.3 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-c:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 4.3 $ < q^2 < $ 8.68 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-d:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 10.3 $ < q^2 < $ 12.86 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-e:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 14.18 $ < q^2 < $ 16 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-f:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 16 $ < q^2 < $ 18 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-g:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 18 $ < q^2 < $ 22 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-h:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 1 $ < q^2 < $ 6 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 3-i:
Projection of the $ {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}$ invariant mass distribution for 1 $ < q^2 < $ 22 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 4:
Projections of the $\cos\theta _{\ell}$ distributions for each $q^2$ range from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 4-a:
Projection of the $\cos\theta _{\ell}$ distribution for 1 $ < q^2 < $ 2 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 4-b:
Projection of the $\cos\theta _{\ell}$ distribution for 2 $ < q^2 < $ 4.3 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-c:
Projection of the $\cos\theta _{\ell}$ distribution for 4.3 $ < q^2 < $ 8.68 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-d:
Projection of the $\cos\theta _{\ell}$ distribution for 10.3 $ < q^2 < $ 12.86 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-e:
Projection of the $\cos\theta _{\ell}$ distribution for 14.18 $ < q^2 < $ 16 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-f:
Projection of the $\cos\theta _{\ell}$ distribution for 16 $ < q^2 < $ 18 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-g:
Projection of the $\cos\theta _{\ell}$ distribution for 18 $ < q^2 < $ 22 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-h:
Projection of the $\cos\theta _{\ell}$ distribution for 1 $ < q^2 < $ 6 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
png pdf |
Figure 4-i:
Projection of the $\cos\theta _{\ell}$ distribution for 1 $ < q^2 < $ 22 GeV$^2$ from the two-dimensional fit of data. The solid lines show the total fit, the shaded area the signal contribution, and the dash-dotted lines the background. The vertical bars on the points represent the statistical uncertainty in data. |
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Figure 5:
Results of the $A_{\mathrm {FB}}$ (left) and $F_{{\mathrm {H}}}$ (right) measurements in ranges 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 $q^2$ range widths. The vertical shaded regions are 8.68-10.09 and 12.86-14.18 GeV$ ^2$, corresponding to the $ {{\mathrm {J}/\psi}}$ - and $ {\psi \mathrm {(2S)}} $-dominated control regions, respectively. The horizontal lines in the right plot show the DHMV SM theoretical predictions [31,32], whose uncertainties are smaller than the line width. |
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Figure 5-a:
Results of the $A_{\mathrm {FB}}$ measurements in ranges 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 $q^2$ range widths. The vertical shaded regions are 8.68-10.09 and 12.86-14.18 GeV$ ^2$, corresponding to the $ {{\mathrm {J}/\psi}}$ - and $ {\psi \mathrm {(2S)}} $-dominated control regions, respectively. The horizontal lines in the right plot show the DHMV SM theoretical predictions [31,32], whose uncertainties are smaller than the line width. |
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Figure 5-b:
Results of the $F_{{\mathrm {H}}}$ measurements in ranges 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 $q^2$ range widths. The vertical shaded regions are 8.68-10.09 and 12.86-14.18 GeV$ ^2$, corresponding to the $ {{\mathrm {J}/\psi}}$ - and $ {\psi \mathrm {(2S)}} $-dominated control regions, respectively. The horizontal lines in the right plot show the DHMV SM theoretical predictions [31,32], whose uncertainties are smaller than the line width. |
Tables | |
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Table 1:
Absolute values of the uncertainty contributions in the measurements of $A_{\mathrm {FB}}$ and $F_{{\mathrm {H}}}$. For each item, the range indicates the variation of the uncertainty in the signal $q^2$ ranges. |
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Table 2:
Results of the fit for each $q^2$ range, together with several SM predictions. The inclusive $q^2=$ 1.00-22.00 GeV$ ^2$ range in the bottom line does not include events from the $ {{\mathrm {J}/\psi}}$ and $ {\psi \mathrm {(2S)}}$ resonance regions. The signal yield $Y_{\mathrm {S}}$ is given, along with its statistical uncertainty. The measured values of $A_{\mathrm {FB}}$ and $F_{{\mathrm {H}}}$ are presented, where the first uncertainties are statistical and the second are systematic. The fifth column is a theoretical prediction by C. Bobeth et al. [1,3] using the EOS package [33] with the form factors from Refs. [34,35,2]. The sixth column is the calculation from S. Descotes-Genon et al. (DHMV) based on Refs. [31,32]. The last column is the prediction using the FLAVIO package [36] with the form factors from Ref. [37]. Only the central values of the theoretical predictions are shown, since their uncertainties are insignificant compared to those in the measurements. |
Summary |
An angular analysis of the decay ${\mathrm{B^{+}} \to \mathrm{K^{+}} \mu^{+} \mu^{-}} $ has been performed using a data sample of proton-proton collisions corresponding to an integrated luminosity of 20.5 fb$^{-1}$ recorded with the CMS detector at $ \sqrt{s} = $ 8 TeV. The forward-backward asymmetry $A_{\mathrm{FB}}$ of the muon system and the contribution $F_{\mathrm{H}}$ of the pseudoscalar, scalar, and tensor amplitudes to the decay width are measured as a function of the dimuon mass squared. The results are consistent with previous measurements, and are also compatible with three different 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 ${\psi \mathrm {(2S)}}$ resonances used as control samples. |
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Additional Figure 2:
Closure test of the fitting results of $A_{\text {FB}}$ 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 ${\psi \mathrm {(2S)}}$ resonances. |
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Additional Figure 3:
Closure test of the fitting results of $F_{\text {H}}$ 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 ${\psi \mathrm {(2S)}}$ resonances. |
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Additional Figure 4:
Measured values of the differential branching fraction of ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$ in each of the $q^2$ bins from CMS, compared with standard model prediction [18] and LHCb [18,19] results. The uncertainties of CMS values are statistical only. |
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Additional Figure 5:
Measured values of $A_{\text {FB}}$ versus $q^2$ for ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$ from CMS, compared with LHCb [18,19] 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 ${\psi \mathrm {(2S)}}$ resonances. |
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Additional Figure 6:
Measured values of $F_{\text {H}}$ versus $q^2$ for ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {{\mu ^+}} {{\mu ^-}}}$ from CMS, compared with LHCb [18,19] 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 ${\psi \mathrm {(2S)}}$ resonances. |
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Additional Figure 7:
The angular distributions of ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} \mathrm{J}/\psi ({{\mu ^+}} {{\mu ^-}})}$ control channel. The black points are data, the blue band is MC simulation. |
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Additional Figure 8:
The angular distributions of ${{{\mathrm {B}^{+}}}\to {\mathrm {K^+}} {\psi \mathrm {(2S)}} ({{\mu ^+}} {{\mu ^-}})}$ control channel. The black points are data, the blue band is MC simulation. |
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Compact Muon Solenoid LHC, CERN |