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| CMS-BPH-22-005 ; CERN-EP-2023-297 | ||
| Test of lepton flavor universality in $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-} $ and $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mathrm{e}^+\mathrm{e}^- $ decays in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 12 January 2024 | ||
| Submitted to Reports on Progress in Physics | ||
| Abstract: A test of lepton flavor universality in $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-} $ and $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mathrm{e}^+\mathrm{e}^- $ decays, as well as a measurement of differential and integrated branching fractions of a nonresonant $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-} $ decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $ \sqrt{s} = $ 13 TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-}) $ to $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mathrm{e}^+\mathrm{e}^-) $ is determined from the measured double ratio $ R(\mathrm{K}) $ of these decays to the respective branching fractions of the $ {\mathrm{B}^{\pm}} \!\to\! {\mathrm{J}/\psi} \mathrm{K^{\pm}} $ with $ {\mathrm{J}/\psi} \!\to\!\mu^{+}\mu^{-} $ and $ \mathrm{e}^+\mathrm{e}^- $ decays, which allow for significant cancellation of systematic uncertainties. The ratio $ R(\mathrm{K}) $ is measured in the range 1.1 $ < q^2 < $ 6.0 GeV$^2 $, where $ q $ is the invariant mass of the lepton pair, and is found to be $ R(\mathrm{K})= $ 0.78 $ ^{+0.47}_{-0.23} $, in agreement with the standard model expectation $ R(\mathrm{K}) \approx $ 1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $ q^2 $ range, $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-}) = $ (12.42 $ \pm $ 0.68) $\times$ 10$^{-8} $, is consistent with the present world-average value and has a comparable precision. | ||
| Links: e-print arXiv:2401.07090 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative Feynman diagrams for the decay of a $ {\mathrm{B}^{+}} $ meson into a $ \mathrm{K^+} $ meson and a lepton pair in the SM (left) and in a BSM scenario that introduces a leptoquark (LQ) with flavor-dependent couplings (right). |
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Figure 2:
Analysis BDT output for signal (MC simulation, in black) and background (same-sign dilepton data, in red) for the muon channel (left) and for the PF-PF (center) and PF-LP (right) electron channels. The histograms are normalized to unit area. |
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Figure 2-a:
Analysis BDT output for signal (MC simulation, in black) and background (same-sign dilepton data, in red) for the muon channel. The histograms are normalized to unit area. |
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Figure 2-b:
Analysis BDT output for signal (MC simulation, in black) and background (same-sign dilepton data, in red) for the PF-PF electron channel. The histograms are normalized to unit area. |
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Figure 2-c:
Analysis BDT output for signal (MC simulation, in black) and background (same-sign dilepton data, in red) for the PF-LP electron channel. The histograms are normalized to unit area. |
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Figure 3:
Results of an unbinned likelihood fit to the $ \mathrm{K^+}\mu^{+}\mu^{-} $ invariant mass distributions in the low-$ q^2 $ bin (upper), and in the $ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mu^{+}\mu^{-})\mathrm{K^+} $ (lower left) and $ {\mathrm{B}^{+}} \!\to\! \psi(2\text{S})(\mu^{+}\mu^{-})\mathrm{K^+} $ (lower right) CRs. The error bars show the statistical uncertainty in data. The lower panels show the distribution of the pull, which is defined as the Poisson probability to observe the number of event counts in data, given the fit function, expressed in terms of the Gaussian significance. |
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Figure 3-a:
Results of an unbinned likelihood fit to the $ \mathrm{K^+}\mu^{+}\mu^{-} $ invariant mass distributions in the low-$ q^2 $ bin. The error bars show the statistical uncertainty in data. The lower panel shows the distribution of the pull, which is defined as the Poisson probability to observe the number of event counts in data, given the fit function, expressed in terms of the Gaussian significance. |
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Figure 3-b:
Results of an unbinned likelihood fit to the $ \mathrm{K^+}\mu^{+}\mu^{-} $ invariant mass distributions in the $ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mu^{+}\mu^{-})\mathrm{K^+} $ CR. The error bars show the statistical uncertainty in data. The lower panel shows the distribution of the pull, which is defined as the Poisson probability to observe the number of event counts in data, given the fit function, expressed in terms of the Gaussian significance. |
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Figure 3-c:
Results of an unbinned likelihood fit to the $ \mathrm{K^+}\mu^{+}\mu^{-} $ invariant mass distributions in the $ {\mathrm{B}^{+}} \!\to\! \psi(2\text{S})(\mu^{+}\mu^{-})\mathrm{K^+} $ CR. The error bars show the statistical uncertainty in data. The lower panel shows the distribution of the pull, which is defined as the Poisson probability to observe the number of event counts in data, given the fit function, expressed in terms of the Gaussian significance. |
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Figure 4:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the low-$ q^2 $ region (upper row), $ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR (middle row), and $ {\mathrm{B}^{+}} \!\to\! \psi(2\text{S})(\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR (lower row) for the PF-PF (left column) and PF-LP (right column) categories. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-a:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the low-$ q^2 $ region for the PF-PF category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-b:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the low-$ q^2 $ region for the PF-LP category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-c:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the $ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR for the PF-PF category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-d:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the $ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR for the PF-LP category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-e:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the $ {\mathrm{B}^{+}} \!\to\! \psi(2\text{S})(\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR for the PF-PF category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 4-f:
The $ \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $ invariant mass spectrum with the results of the fit shown with the red line in the $ {\mathrm{B}^{+}} \!\to\! \psi(2\text{S})(\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ CR for the PF-LP category. The shoulder below the nominal $ {\mathrm{B}^{+}} $ meson mass for the $\psi$(2S) CR is due to the narrow $ q^2 $ range in this bin compared to the size of the radiative tail. Notations are as in Fig. 3. |
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Figure 5:
Comparison of the measured differential $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-} $ branching fraction with the theoretical predictions obtained using HEPFIT, SUPERISO, FLAVIO, and EOS packages. The HEPFIT predictions are available only for $ q^2 < $ 8 GeV$^2 $. |
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Figure 6:
Log likelihood function from the fit profiled as a function of $ R(\mathrm{K})^{-1} $. The dark and light grey area indicates the $ \pm $ 1 and $ \pm $ 2 $ \sigma $ bands respectively. |
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Figure A1:
The product of acceptance and efficiency ($ \mathcal{A}\epsilon $) of the $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-} $ channel, as a function of the muon pair $ q^2 $, as measured in simulated signal events, after all the corrections applied. Regions corresponding to resonances are displayed with red markers. |
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Figure A2:
Relative uncertainties in the differential branching fraction measurement of $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-} $ per $ q^2 $ bin. Different colors correspond to data statistical, simulation statistical, and systematic uncertainties. |
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Figure A3:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in various $ q^2 $ bins, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends for (from upper left to lower right): $ [0,0.98] $, $ [1.1,2.0] $, $ [2.0,3.0]$, $ [3.0,4.0] $, $ [4.0,5.0] $, $ [5.0,6.0] $, $ [6.0,7.0] $, and $ [7.0,8.0] $, $ q^2 $ bins. Notations are as in Fig. 3. |
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Figure A3-a:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [0,0.98] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-b:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [1.1,2.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-c:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [2.0,3.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-d:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $[3.0,4.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-e:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [4.0,5.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-f:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [5.0,6.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-g:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [6.0,7.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A3-h:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [7.0,8.0] $ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. |
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Figure A4:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in various $ q^2 $ bins, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends for (from upper left to lower right): $ [11.0,11.8] $, $ [11.8,12.5] $, $ [14.82,16.0] $, $ [16.0,17.0] $, $ [17.0,18.0] $, $ [18.0,19.24] $, and $ [19.24,22.9]$ GeV$^{2}$ $q^2 $ bin. Notations are as in Fig. 3. |
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Figure A4-a:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [11.0,11.8] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-b:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [11.8,12.5] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-c:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [14.82,16.0] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-d:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [16.0,17.0] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-e:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [17.0,18.0] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-f:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [18.0,19.24] $ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A4-g:
The $ \mathrm{K^+} \mu^{+} \mu^{-} $ invariant mass distributions in the $ [19.24,22.9]$ GeV$^{2}$ $ q^2 $ bin, with the result of the simultaneous fit overlaid in blue and the individual fit components as described in the legends. Notations are as in Fig. 3. |
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Figure A5:
Correlation matrix for the differential branching fraction extraction between different $ q^2 $ bins in the simultaneous fit. |
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Figure A6:
Summary of $ R(\mathrm{K}) $ measurements from BaBar [71], Belle [72], and LHCb [10,11,9] experiments, as well as the present CMS measurement. The pink data points of the first three LHCb measurements were superseded by the latest one, shown as the red point. |
| Tables | |
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Table 1:
Summary of the loosest muon trigger requirements imposed by the L1 and HLT algorithms for each instantaneous luminosity scenario: the L1 and HLT muon transverse momentum thresholds $ p^\mu_{\mathrm{T}} $, and the HLT muon impact parameter significance $ \text{IP}_{\text{sig}} $. Also shown are the trigger purity, peak HLT rate, and $ \int\!\!\!\;{\mathcal L}{\mathrm d}t $. The second trigger was the highest threshold one during early data taking, corresponding to $ \int\!\!\!\;{\mathcal L}{\mathrm d}t = 6.9\mbox{\,\text{fb}^{-1}} $, and then the second-highest for the rest of the data taking, accumulating $ \int\!\!\!\;{\mathcal L}{\mathrm d}t = 26.7\mbox{\,\text{fb}^{-1}} $ out of 34.7 fb$^{-1}$ collected by the highest threshold trigger. |
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Table 2:
Input variables used in the muon and electron channel BDTs. |
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Table 3:
The product of acceptance, and offline and trigger efficiency ($ \mathcal{A}\epsilon\epsilon_{\text{trig}} $) for the signal in the low-$ q^2 $ region and for the two resonance CRs. In the case of electrons, the trigger efficiency is not included in the quoted $ \mathcal{A}\epsilon $ numbers, as it cancels out in the $ R(\mathrm{K}) $ double ratio. Uncertainties are statistical only. |
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Table 4:
Fit functions used for signal and background sources in each $ q^2 $ bin in the muon channel. The $ \text{---} $ symbol indicates this background is not included in this region. |
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Table 5:
Signal yields in the muon channel in the low-$ q^2 $ bin and resonant CRs. |
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Table 6:
Fit functions used to describe signal and various background components for the electron channel. The $ \text{---} $ symbol indicates this background is not included in this region. |
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Table 7:
Signal yields in the electron channel in the low-$ q^2 $ bin and resonant CRs. |
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Table 8:
Major sources of uncertainty in the $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-} $/$ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mu^{+}\mu^{-})\mathrm{K^+} $ ratio measurement. |
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Table 9:
Major sources of uncertainty in the $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mathrm{e}^+\mathrm{e}^- $/$ {\mathrm{B}^{+}} \!\to\! {\mathrm{J}/\psi} (\mathrm{e}^+\mathrm{e}^-)\mathrm{K^+} $ ratio measurement in the PF-PF and PF-LP categories. The last row shows the statistical uncertainty, which is the same as the total uncertainty within the quoted precision. |
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Table 10:
The $ {\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-} $ branching fraction, $ \mathrm{d}{\mathcal{B}({\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-})}{q^2} / \mathrm{d}q^2 $ integrated over the specified $ q^2 $ range, for the individual $ q^2 $ bins.. The uncertainties in the yields are statistical uncertainties from the fit, while the branching fraction uncertainties include both the statistical and systematic components. |
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Table 11:
Comparison of the $ \mathcal{B}({\mathrm{B}^{+}} \!\to\! \mathrm{K^+}\mu^{+}\mu^{-}) $ branching fraction measurement in the low-$ q^2 $ range and the theoretical predictions based on the EOS, FLAVIO, SUPERISO, and HEPFIT packages. |
| Summary |
| We have reported the first test of lepton flavor universality with the CMS experiment at the LHC in $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-} $ and $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mathrm{e}^+\mathrm{e}^- $ decays, as well as a measurement of differential and integrated branching fractions of the nonresonant $ {\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-} $ decay. The analysis has been made possible by a dedicated data set of proton-proton collisions at $ \sqrt{s} = $ 13 TeV recorded in 2018, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-}) $ to $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mathrm{e}^+\mathrm{e}^-) $ has been is determined from the measured double ratio $ R(\mathrm{K}) $ of these decays to the respective branching fractions of the $ {\mathrm{B}^{\pm}} \!\to\! {\mathrm{J}/\psi} \mathrm{K^{\pm}} ({\mathrm{J}/\psi} \!\to\!\mu^{+}\mu^{-}) $ and $ ({\mathrm{J}/\psi} \!\to\!\mathrm{e}^+\mathrm{e}^-) $ decays, which allow for significant cancellation of systematic uncertainties. The ratio $ R(\mathrm{K}) $ has been measured in the range 1.1 $ < q^2 < $ 6.0 GeV$^2 $, where $ q $ is the invariant mass of the lepton pair, and was found to be $ R(\mathrm{K})= $ 0.78 $ ^{+0.47}_{-0.23} $, in agreement with the standard model expectation of $ \approx $1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $ q^2 $ range, $ \mathcal{B}({\mathrm{B}^{\pm}} \!\to\! \mathrm{K^{\pm}}\mu^{+}\mu^{-}) = $ (12.42 $ \pm $ 0.68) $\times$ 10$^{-8} $, is consistent with and has a comparable precision to the present world average. This work has demonstrated the flexibility of the CMS trigger and data acquisition system and has paved the way to many other studies of a large unbiased sample of b hadron decays collected by CMS in 2018. |
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