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| CMS-BPH-23-004 ; CERN-EP-2024-300 | ||
| Evidence for CP violation and measurement of CP-violating parameters in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays in pp collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 26 December 2024 | ||
| Submitted to Phys. Rev. Lett. | ||
| Abstract: A pioneering machine-learning-based flavor-tagging algorithm combining same-side and opposite-side tagging is used to obtain the equivalent of 27 500 tagged $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays from pp collisions at $ \sqrt{s} = $ 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 96.5 fb$^{-1}$. A time- and flavor-dependent angular analysis of the $ \mu^{+}\mu^{-}\,\mathrm{K^+}\mathrm{K^-} $ final state is used to measure parameters of the $ \mathrm{B}_{s}^{0}$-$\overline{\mathrm{B}}_{s}^{0} $ system. The weak phase is measured to be $ \phi_\mathrm{\mathrm{s}} = - $73 $ \pm $ 23 (stat) $ \pm $ 7 (syst) mrad, which, combined with a $ \sqrt{s} = $ 8 TeV CMS result, gives $ \phi_\mathrm{\mathrm{s}} = - $74 $ \pm $ 23 mrad. This value differs from zero by 3.2 standard deviations, providing evidence for CP violation in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays. All measured physics parameters are found to agree with standard model predictions where available. | ||
| Links: e-print arXiv:2412.19952 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Left: Definition of the three decay angles $ \theta_{T} $, $ \psi_{T} $, and $ \varphi_{T} $. Right: Invariant mass distribution and fit projection of the selected candidates for the ST trigger category (2018 data). |
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Figure 1-a:
Left: Definition of the three decay angles $ \theta_{T} $, $ \psi_{T} $, and $ \varphi_{T} $. Right: Invariant mass distribution and fit projection of the selected candidates for the ST trigger category (2018 data). |
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Figure 1-b:
Left: Definition of the three decay angles $ \theta_{T} $, $ \psi_{T} $, and $ \varphi_{T} $. Right: Invariant mass distribution and fit projection of the selected candidates for the ST trigger category (2018 data). |
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Figure 2:
Distributions of the proper decay time $ ct $, its uncertainty $ \sigma_{ct} $, and mistag probability $ \omega_{\text{tag}} $ of the selected candidates for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 2-a:
Distributions of the proper decay time $ ct $, its uncertainty $ \sigma_{ct} $, and mistag probability $ \omega_{\text{tag}} $ of the selected candidates for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 2-b:
Distributions of the proper decay time $ ct $, its uncertainty $ \sigma_{ct} $, and mistag probability $ \omega_{\text{tag}} $ of the selected candidates for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 2-c:
Distributions of the proper decay time $ ct $, its uncertainty $ \sigma_{ct} $, and mistag probability $ \omega_{\text{tag}} $ of the selected candidates for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 3:
Angular observables distributions of the selected candidates and fit projection for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 3-a:
Angular observables distributions of the selected candidates and fit projection for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 3-b:
Angular observables distributions of the selected candidates and fit projection for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 3-c:
Angular observables distributions of the selected candidates and fit projection for the ST trigger category (2018 data). The projections of the fitted model are also shown. |
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Figure 4:
The two-dimensional 68% CL contours in the $ \phi_\mathrm{\mathrm{s}}-\Delta\Gamma_\mathrm{\mathrm{s}} $ plane for the combined CMS (red), ATLAS (blue) [26], and LHCb (green) [20] results. Results refer only to $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\mathrm{K^+}\mathrm{K^-} $ measurements. The contours account for both statistical and systematic uncertainties. The SM prediction neglects possible contributions from higher-order penguin diagrams and is represented by the thin black band, with the central value indicated with the black diamond [4,5,42]. |
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Figure C1:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-a:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-b:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-c:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-d:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-e:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-f:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C1-g:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2017 data). |
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Figure C2:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-a:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-b:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-c:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-d:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-e:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-f:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C2-g:
The distributions for the input observables of the selected candidates and the projections from the fit for the MT trigger category (2018 data). |
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Figure C3:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-a:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-b:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-c:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-d:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-e:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-f:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C3-g:
The distributions for the input observables of the selected candidates and the projections from the fit for the ST trigger category (2017 data). |
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Figure C4:
The $ ct $ uncertainty calibration fits for the 2017 (left) and 2018 (right) data samples. The measured effective $ ct $ resolution is plotted versus the average (calculated) value of $ \sigma_{ct} $ in bins of $ \sigma_{ct} $. The results of a fit to a line are shown with a solid red line. The horizontal error bars indicate the bins'edges and are not used in the fit. |
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Figure C4-a:
The $ ct $ uncertainty calibration fits for the 2017 (left) and 2018 (right) data samples. The measured effective $ ct $ resolution is plotted versus the average (calculated) value of $ \sigma_{ct} $ in bins of $ \sigma_{ct} $. The results of a fit to a line are shown with a solid red line. The horizontal error bars indicate the bins'edges and are not used in the fit. |
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Figure C4-b:
The $ ct $ uncertainty calibration fits for the 2017 (left) and 2018 (right) data samples. The measured effective $ ct $ resolution is plotted versus the average (calculated) value of $ \sigma_{ct} $ in bins of $ \sigma_{ct} $. The results of a fit to a line are shown with a solid red line. The horizontal error bars indicate the bins'edges and are not used in the fit. |
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Figure C5:
Proper decay time distribution of prompt events in the MT trigger category for 2017 (left) and 2018 (right) data. The two components of the resolution function are modeled with Gaussian distributions and shown in green. The resolution function is the model for the prompt component, and the long lived components, shown in red, are modeled as two exponential distributions convoluted with the resolution function. |
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Figure C5-a:
Proper decay time distribution of prompt events in the MT trigger category for 2017 (left) and 2018 (right) data. The two components of the resolution function are modeled with Gaussian distributions and shown in green. The resolution function is the model for the prompt component, and the long lived components, shown in red, are modeled as two exponential distributions convoluted with the resolution function. |
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Figure C5-b:
Proper decay time distribution of prompt events in the MT trigger category for 2017 (left) and 2018 (right) data. The two components of the resolution function are modeled with Gaussian distributions and shown in green. The resolution function is the model for the prompt component, and the long lived components, shown in red, are modeled as two exponential distributions convoluted with the resolution function. |
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Figure C6:
Results of the mistag probability calibration fit for the OS-muon tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (top row) and 2018 (bottom row) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. The plots in the left column refer to the MT trigger category, while the ones in the right column to the ST trigger category. |
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Figure C6-a:
Results of the mistag probability calibration fit for the OS-muon tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (top row) and 2018 (bottom row) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. The plots in the left column refer to the MT trigger category, while the ones in the right column to the ST trigger category. |
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Figure C6-b:
Results of the mistag probability calibration fit for the OS-muon tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (top row) and 2018 (bottom row) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. The plots in the left column refer to the MT trigger category, while the ones in the right column to the ST trigger category. |
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Figure C6-c:
Results of the mistag probability calibration fit for the OS-muon tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (top row) and 2018 (bottom row) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. The plots in the left column refer to the MT trigger category, while the ones in the right column to the ST trigger category. |
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Figure C6-d:
Results of the mistag probability calibration fit for the OS-muon tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (top row) and 2018 (bottom row) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. The plots in the left column refer to the MT trigger category, while the ones in the right column to the ST trigger category. |
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Figure C7:
Results of the mistag probability calibration fit for the OS-electron tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C7-a:
Results of the mistag probability calibration fit for the OS-electron tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C7-b:
Results of the mistag probability calibration fit for the OS-electron tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C8:
Results of the mistag probability calibration fit for the OS-jet tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C8-a:
Results of the mistag probability calibration fit for the OS-jet tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C8-b:
Results of the mistag probability calibration fit for the OS-jet tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C9:
Results of the mistag probability calibration fit for the SS tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C9-a:
Results of the mistag probability calibration fit for the SS tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C9-b:
Results of the mistag probability calibration fit for the SS tagger on $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays for 2017 (left) and 2018 (right) data. The measured mistag probability is plotted versus the value predicted by the tagging algorithm. The solid red line shows the results of the Platt scaling calibration fit to data. The calibration model is a linear function with the intercept fixed to 0 applied to the tagger DNN's output before the final sigmoid layer. |
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Figure C10:
Comparison of the calibration curves before (black, $ {\mathrm{B}^{+}} $) and after (red, $ \mathrm{B}_{s}^{0} $) the application of the corrections from simulation to the calibration obtained in $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays. The left plot refers to 2017 data, while the right one to 2018 data. The red function is the one used as calibration for the CPV measurement. |
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Figure C10-a:
Comparison of the calibration curves before (black, $ {\mathrm{B}^{+}} $) and after (red, $ \mathrm{B}_{s}^{0} $) the application of the corrections from simulation to the calibration obtained in $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays. The left plot refers to 2017 data, while the right one to 2018 data. The red function is the one used as calibration for the CPV measurement. |
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Figure C10-b:
Comparison of the calibration curves before (black, $ {\mathrm{B}^{+}} $) and after (red, $ \mathrm{B}_{s}^{0} $) the application of the corrections from simulation to the calibration obtained in $ {\mathrm{B}^{+}} \to \mathrm{J}/\psi\,\mathrm{K^+} $ decays. The left plot refers to 2017 data, while the right one to 2018 data. The red function is the one used as calibration for the CPV measurement. |
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Figure C11:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample as a validation to the tagging framework. The measured oscillation frequency is consistent with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-a:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-b:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-c:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-d:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-e:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-f:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-g:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C12-h:
The $ {\mathrm{B}^0} $ mixing asymmetry as a function of the proper decay time as measured in the $ {\mathrm{B}^0} \to \mathrm{J}/\psi\,{\mathrm{K^{*}(892)^{0}}} $ control data sample in the different tagging categories. The reported uncertainties for the $ \Delta m_{\mathrm{d}} $ fitted value are statistical only. This study was conducted to validate the tagging framework and assess the consistency of information provided by various tagging techniques. Top row, from left to right: only OS muon (MT trigger category), only OS muon (ST trigger category), only OS electron, and only OS jet. Bottom row, from left to right: only SS, SS + OS muon, SS + OS electron, and SS + OS jet. All tagging categories are mutually exclusive. The oscillation frequencies measured in each category are consistent with one another and with the world-average value $ \Delta m_{\mathrm{d}}^\text{PDG} = $ 0.5069 $ \pm $ 0.0019 ps$^{-1}$ [33]. |
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Figure C13:
Comparison of CPV fit results obtained using each of the four individual flavor tagging algorithms versus the reference fit, which combines all four taggers. Only flavor-sensitive parameters are shown, and only statistical uncertainties are considered. The grey band represents the statistical uncertainty of the reference fit. |
| Tables | |
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Table 1:
Summary of the systematic and statistical uncertainties. Dashes ($ \text{---} $) indicate an uncertainty that is negligible or not evaluated. The combined systematic uncertainty is the sum in quadrature of the individual uncertainties. |
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Table 2:
Measured values and uncertainties of the main parameters of interest. |
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Table 3:
Calibrated flavor tagging performance as measured in the $ \mathrm{B}_{s}^{0} $ data sample in the various mutually exclusive categories. The effective dilution $ \mathcal{D}_\text{tag,eff}^2 $ is obtained from the measured tagging efficiency $ \varepsilon_{\text{tag}} $ and tagging power $ P_{\text{tag}} $. The uncertainties are statistical only. |
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Table C1:
Matrix of the correlations of the statistical uncertainties between pairs of physics parameters. |
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Table C2:
Matrix of the correlations of the systematic uncertainties between pairs of physics parameters. |
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Table C3:
Values and uncertainties of the physics parameters obtained from the combination of the CMS 8 TeV and 13 TeV results using the BLUE method. The uncertainty includes both statistical and systematic sources. |
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Table C4:
Matrix of the correlations between the physics parameters as obtained from the combination between the CMS 8 TeV and 13 TeV results. Correlations include both statistical and systematic uncertainties. |
| Summary |
| The weak CPV phase is measured to be $ \phi_\mathrm{\mathrm{s}} = - $73 $ \pm $ 23 (stat) $ \pm $ 7 (syst) mrad, which is within 1.5 standard deviations of the SM-based prediction. The measured value of $ |\lambda| $ is consistent with no direct CPV ($ |\lambda| = $ 1). These results are comparable in precision to the world's most precise single measurement [20] and supersede the previous results in Ref. [15]. The results are combined with those obtained by CMS at $ \sqrt{s} = $ 8 TeV [14] using the BLUE method [43,44] to obtain $ \phi_\mathrm{\mathrm{s}} = - $74 $ \pm $ 23 mrad and $ \Delta\Gamma_\mathrm{\mathrm{s}} = $ 0.0780 $ \pm $ 0.0045 ps$^{-1}$, which are both compatible with SM-based predictions. The uncertainties include both statistical and systematic components. Figure 4 shows the two-dimensional $ \phi_\mathrm{\mathrm{s}} $ vs. $ \Delta\Gamma_\mathrm{\mathrm{s}} $ contour at 68% CL for the combined results, alongside the SM-based prediction and the latest results from other LHC experiments. Tabulated results are provided in the HEPData record for this analysis [45]. The combined $ \phi_\mathrm{\mathrm{s}} $ value exhibits a deviation from zero of 3.2 standard deviations, providing the first evidence for CPV in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays. |
| References | ||||
| 1 | N. Cabibbo | Unitary symmetry and leptonic decays | PRL 10 (1963) 531 | |
| 2 | M. Kobayashi and T. Maskawa | CP violation in the renormalizable theory of weak interaction | Prog. Theor. Phys. 49 (1973) 652 | |
| 3 | M. Z. Barel, K. De Bruyn, R. Fleischer, and E. Malami | In pursuit of new physics with $ {\mathrm{B}^0} \to \mathrm{J}/\psi \, \mathrm{K^0} $ and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays at the high-precision frontier | JPG 48 (2021) 065002 | 2010.14423 |
| 4 | CKMfitter Collaboration | Predictions of selected flavour observables within the standard model | Updated with Summer 23 results: PRD 84 (2011) 033005 |
1106.4041 |
| 5 | UTfit Collaboration | New UTfit analysis of the unitarity triangle in the Cabibbo--Kobayashi--Maskawa scheme | Rend. Lincei Sci. Fis. Nat. 34 (2023) 37 | 2212.03894 |
| 6 | CDF Collaboration | Observation of $ \mathrm{B}_{s}^{0}-\overline{\mathrm{B}}_{s}^{0} $ oscillations | PRL 97 (2006) 242003 | hep-ex/0609040 |
| 7 | C.-W. Chiang et al. | New physics in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $: a general analysis | JHEP 04 (2010) 031 | 0910.2929 |
| 8 | M. Artuso, G. Borissov, and A. Lenz | CP violation in the $ \mathrm{B}_{s}^{0} $ system | Rev. Mod. Phys. 88 (2016) 045002 | 1511.09466 |
| 9 | D0 Collaboration | Measurement of $ \mathrm{B}_{s}^{0} $ mixing parameters from the flavor-tagged decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ | PRL 101 (2008) 241801 | 0802.2255 |
| 10 | D0 Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}}^{\mathrm{J}/\psi\phi} $ using the flavor-tagged decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ in 8 fb$ ^{-1} $ of $ \mathrm{p}\overline{\mathrm{p}} $ collisions | PRD 85 (2012) 032006 | 1109.3166 |
| 11 | CDF Collaboration | First flavor-tagged determination of bounds on mixing-induced CP violation in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays | PRL 100 (2008) 161802 | 0712.2397 |
| 12 | CDF Collaboration | Measurement of the CP-violating phase $ \beta_\mathrm{\mathrm{s}}^{\mathrm{J}/\psi\phi} $ in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays with the CDF II detector | PRD 85 (2012) 072002 | 1112.1726 |
| 13 | CDF Collaboration | Measurement of the bottom-strange meson mixing phase in the full CDF data set | PRL 109 (2012) 171802 | 1208.2967 |
| 14 | CMS Collaboration | Measurement of the CP-violating weak phase $ \phi_\mathrm{\mathrm{s}} $ and the decay width difference $ \Delta\Gamma_\mathrm{\mathrm{s}} $ using the $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decay channel in pp collisions at $ \sqrt{s} = $ 8 TeV | PLB 757 (2016) 97 | CMS-BPH-13-012 1507.07527 |
| 15 | CMS Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ in the $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) \to \mu^{+}\mu^{-}\,\mathrm{K^+}\mathrm{K^-} $ channel in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | PLB 816 (2021) 136188 | CMS-BPH-20-001 2007.02434 |
| 16 | LHCb Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ in $ \overline{\mathrm{B}}_{s}^{0} \to \mathrm{J}/\psi\,\pi^{+}\pi^{-} $ decays | PLB 713 (2012) 378 | 1204.5675 |
| 17 | LHCb Collaboration | Measurement of CP violation and the $ \mathrm{B}_{s}^{0} $ meson decay width difference with $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\mathrm{K^+}\mathrm{K^-} $ and $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\pi^{+}\pi^{-} $ decays | PRD 87 (2013) 112010 | 1304.2600 |
| 18 | LHCb Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ in $ \overline{\mathrm{B}}_{s}^{0}\to \mathrm{J}/\psi\,\pi^{+}\pi^{-} $ decays | PLB 736 (2014) 186 | 1405.4140 |
| 19 | LHCb Collaboration | Precision measurement of CP violation in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\mathrm{K^+}\mathrm{K^-} $ decays | PRL 114 (2015) 041801 | 1411.3104 |
| 20 | LHCb Collaboration | Improved measurement of CP violation parameters in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\mathrm{K^+}\mathrm{K^-} $ decays in the vicinity of the $ \phi(1020) $ | PRL 132 (2024) 051802 | 2308.01468 |
| 21 | LHCb Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ in $ \overline{\mathrm{B}}_{s}^{0} \to \mathrm{D}_{s}^{+}\mathrm{D}_{s}^{-} $ decays | PRL 113 (2014) 211801 | 1409.4619 |
| 22 | LHCb Collaboration | First study of the CP-violating phase and decay-width difference in $ \mathrm{B}_{s}^{0} \to \psi(\text{2S})\,\phi $ | PLB 762 (2016) 253 | 1608.04855 |
| 23 | ATLAS Collaboration | Time-dependent angular analysis of the decay $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ and extraction of $ \Delta\Gamma_\mathrm{\mathrm{s}} $ and the CP-violating weak phase $ \phi_\mathrm{\mathrm{s}} $ by ATLAS | JHEP 12 (2012) 072 | 1208.0572 |
| 24 | ATLAS Collaboration | Flavor tagged time-dependent angular analysis of the $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decay and extraction of $ \Delta\Gamma_\mathrm{\mathrm{s}} $ and the weak phase $ \phi_\mathrm{\mathrm{s}} $ in ATLAS | PRD 90 (2014) 052007 | 1407.1796 |
| 25 | ATLAS Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ and the $ \mathrm{B}_{s}^{0} $ meson decay width difference with $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays in ATLAS | JHEP 12 (2016) 072 | 1601.03297 |
| 26 | ATLAS Collaboration | Measurement of the CP-violating phase $ \phi_\mathrm{\mathrm{s}} $ in $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi\,\phi(1020) $ decays in ATLAS at 13 TeV | EPJC 81 (2021) 342 | 2001.07115 |
| 27 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | |
| 28 | CMS Collaboration | Development of the CMS detector for the CERN LHC Run 3 | JINST 19 (2024) P05064 | CMS-PRF-21-001 2309.05466 |
| 29 | CMS Collaboration | Precision luminosity measurement in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS | EPJC 81 (2021) 800 | CMS-LUM-17-003 2104.01927 |
| 30 | CMS Collaboration | CMS luminosity measurement for the 2017 data-taking period at $ \sqrt{s} = $ 13 TeV | CMS Physics Analysis Summary, 2018 link |
CMS-PAS-LUM-17-004 |
| 31 | CMS Collaboration | CMS luminosity measurement for the 2018 data-taking period at $ \sqrt{s} = $ 13 TeV | CMS Physics Analysis Summary, 2019 link |
CMS-PAS-LUM-18-002 |
| 32 | A. S. Dighe, I. Dunietz, and R. Fleischer | Extracting CKM phases and $ \mathrm{B}_{s}^{0} $--$ \overline{\mathrm{B}}_{s}^{0} $ mixing parameters from angular distributions of non-leptonic $ {\mathrm{B}} $ decays | EPJC 6 (1999) 647 | hep-ph/9804253 |
| 33 | Particle Data Group | Review of Particle Physics | PRD 2024 (2024) 030001 | |
| 34 | G. C. Branco, L. Lavoura, and J. P. Silva | CP Violation | Volume 103 of International Series of Monographs on Physics, Clarendon Press, Oxford, UK, ISBN~003997, 1999 | |
| 35 | LHCb Collaboration | Determination of the sign of the decay width difference in the $ \mathrm{B}_{s}^{0} $ system | PRL 108 (2012) 241801 | 1202.4717 |
| 36 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 37 | CMS Collaboration | Supplemental material: additional figures and tables | [URL will be inserted by publisher at publication] | |
| 38 | M. Rosenblatt | Remarks on some nonparametric estimates of a density function | Ann. Math. Statist. 27 (1956) 832 | |
| 39 | E. Parzen | On estimation of a probability density function and mode | Ann. Math. Statist. 33 (1962) 1065 | |
| 40 | N. L. Johnson | Systems of frequency curves generated by methods of translation | Biometrika 36 (1949) 149 | |
| 41 | B. Efron and R. J. Tibshirani | An introduction to the bootstrap | Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton, Florida, USA, 1993 | |
| 42 | A. Lenz and G. Tetlalmatzi-Xolocotzi | Model-independent bounds on new physics effects in non-leptonic tree-level decays of $ {\mathrm{B}} $-mesons | JHEP 07 (2020) 177 | 1912.07621 |
| 43 | L. Lyons, D. Gibaut, and P. Clifford | How to combine correlated estimates of a single physical quantity | NIM A 270 (1988) 110 | |
| 44 | A. Valassi | Combining correlated measurements of several different physical quantities | NIM A 500 (2003) 391 | |
| 45 | CMS Collaboration | HEPData record for this analysis | link | |
| 46 | CMS Collaboration | Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | JINST 15 (2020) P10017 | CMS-TRG-17-001 2006.10165 |
| 47 | CMS Collaboration | Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC | JINST 16 (2021) P05014 | CMS-EGM-17-001 2012.06888 |
| 48 | CMS Collaboration | Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV | JINST 13 (2018) P06015 | CMS-MUO-16-001 1804.04528 |
| 49 | CMS Collaboration | Description and performance of track and primary-vertex reconstruction with the CMS tracker | JINST 9 (2014) P10009 | CMS-TRK-11-001 1405.6569 |
| 50 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 51 | T. Sjöstrand et al. | An introduction to PYTHIA 8.2 | Comput. Phys. Commun. 191 (2015) 159 | 1410.3012 |
| 52 | CMS Collaboration | Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements | EPJC 80 (2020) 4 | CMS-GEN-17-001 1903.12179 |
| 53 | NNPDF Collaboration | Parton distributions from high-precision collider data | EPJC 77 (2017) 663 | 1706.00428 |
| 54 | D. J. Lange | The EvtGen particle decay simulation package | NIM A 462 (2001) 152 | |
| 55 | E. Barberio and Z. Was | PHOTOS --- a universal Monte Carlo for QED radiative corrections: version 2.0 | Comput. Phys. Commun. 79 (1994) 291 | |
| 56 | GEANT4 Collaboration | GEANT 4 --- a simulation toolkit | NIM A 506 (2003) 250 | |
| 57 | R. Frühwirth | Application of Kalman filtering to track and vertex fitting | NIM A 262 (1987) 444 | |
| 58 | M. Zaheer et al. | Deep Sets | 1703.06114 | |
| 59 | CMS Collaboration | Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV | JINST 13 (2018) P05011 | CMS-BTV-16-002 1712.07158 |
| 60 | D.-A. Clevert, T. Unterthiner, and S. Hochreiter | Fast and accurate deep network learning by Exponential Linear Units (ELUs) | 1511.07289 | |
| 61 | J. Platt | Probabilities for SV machines | ch. 5, Advances in large-margin classifiers. The MIT Press, 2000 link |
|
| 62 | D. Kingma and J. Ba | Adam: a method for stochastic optimization | in \textitProc. Int. Conf. on Learning Representations, 2014 | 1412.6980 |
|
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