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| CMS-TOP-24-011 ; CERN-EP-2025-289 | ||
| Measurement of the $ t $-channel single top quark cross section in proton-proton collisions at $ \sqrt{s}= $ 5.02 TeV | ||
| CMS Collaboration | ||
| 13 March 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: The single top quark $ t $-channel production cross section is measured in proton-proton collisions at the CERN LHC at $ \sqrt{s}= $ 5.02 TeV, using data recorded with the CMS detector in 2017, corresponding to an integrated luminosity of 302$ \text{pb}^{-1}$, and resulting in the first CMS measurement of the process at that energy. Events with one electron or muon and two or more jets, among which at least one is identified as originating from a b quark fragmentation, are analyzed. The combined cross section of single top quark ($ \mathrm{t}\mathrm{q} $) and single top antiquark ($ \overline{\mathrm{t}}\mathrm{q} $) production is $ \sigma(\mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q})=25.4 ^{+3.6}_{-3.5} $ (stat) $ ^{+4.2}_{-3.9} $ (syst) $ \pm $ 0.5 (lumi) pb. The individual cross sections are measured to be $ \sigma(\mathrm{t}\mathrm{q})=17.6 ^{+2.8}_{-2.7} $ (stat) $ ^{+2.6}_{-2.4} $ (syst) $ \pm $ 0.3 (lumi) pb and $ \sigma(\overline{\mathrm{t}}\mathrm{q})=6.6 ^{+2.4}_{-1.6} $ (stat) $ ^{+2.1}_{-2.5} $ (syst) $ \pm $ 0.1 (lumi) pb. Their ratio is measured to be $ \mathcal{R}_{\mathrm{t-ch}} =2.7 ^{+1.5}_{-0.8} $ (stat) $ ^{+1.3}_{-0.3} $ (syst). The absolute value of the Cabibbo--Kobayashi--Maskawa matrix element is found to be $ |f_{\text{LV}}V_{\mathrm{t}\mathrm{b}}|= $ 0.92 $ \pm $ 0.09 (exp) $ \pm $ 0.01 (theo). The measurements are in good agreement with the standard model predictions at next-to-next-to-leading order accuracy in quantum chromodynamics. | ||
| Links: e-print arXiv:2603.13592 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative leading-order Feynman diagrams for single top quark (left) and antiquark (right) production via the $ t $ channel. |
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Figure 1-a:
Representative leading-order Feynman diagrams for single top quark (left) and antiquark (right) production via the $ t $ channel. |
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Figure 1-b:
Representative leading-order Feynman diagrams for single top quark (left) and antiquark (right) production via the $ t $ channel. |
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Figure 2:
Observed and predicted number of events in each of the twelve categories considered in the analysis, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. All uncertainties considered in the analysis are included in the uncertainty band. The lower panels show the data-to-prediction ratio. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 3:
Observed and predicted distributions of the leading jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in each distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 3-a:
Observed and predicted distributions of the leading jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in each distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 3-b:
Observed and predicted distributions of the leading jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in each distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 4:
Observed and predicted distributions of $ |\eta_{\mathrm{u}_0}| $ in the 3j1b (left) and 3j2b (right) categories, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 4-a:
Observed and predicted distributions of $ |\eta_{\mathrm{u}_0}| $ in the 3j1b (left) and 3j2b (right) categories, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 4-b:
Observed and predicted distributions of $ |\eta_{\mathrm{u}_0}| $ in the 3j1b (left) and 3j2b (right) categories, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 5:
Observed and predicted distributions of the most discriminating input variable used in the random forest training, $ |\eta_{\mathrm{u}_0}| $ (left), and the output MVA discriminator (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in the MVA output distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 5-a:
Observed and predicted distributions of the most discriminating input variable used in the random forest training, $ |\eta_{\mathrm{u}_0}| $ (left), and the output MVA discriminator (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in the MVA output distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 5-b:
Observed and predicted distributions of the most discriminating input variable used in the random forest training, $ |\eta_{\mathrm{u}_0}| $ (left), and the output MVA discriminator (right), in the 2j1b category, before the ML fit. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty in the prediction. The lower panels show the data-to-prediction ratio. The first and last bins in the MVA output distribution include underflow and overflow events, respectively. The normalizations of the processes are those of the SM predictions except for QCD, which is estimated from data. The W+jets background is split as explained in Section 5. |
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Figure 6:
Distributions for the $ \ell^+ $+jets (upper) and $ \ell^- $+jets (lower) categories where the prediction parameters are set to the values obtained in the fit. They show the MVA score and $ |\eta_{\mathrm{u}_0}| $ distributions, which are the fitted variables in the ML fit in the 2j1b category and the categories with three jets, respectively. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty of the prediction, after the fit. All uncertainties considered in the analysis are included in the uncertainty band. The lower panels show the ratio of data to prediction. The first and last bins in the MVA output distributions include underflow and overflow events, respectively. |
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Figure 6-a:
Distributions for the $ \ell^+ $+jets (upper) and $ \ell^- $+jets (lower) categories where the prediction parameters are set to the values obtained in the fit. They show the MVA score and $ |\eta_{\mathrm{u}_0}| $ distributions, which are the fitted variables in the ML fit in the 2j1b category and the categories with three jets, respectively. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty of the prediction, after the fit. All uncertainties considered in the analysis are included in the uncertainty band. The lower panels show the ratio of data to prediction. The first and last bins in the MVA output distributions include underflow and overflow events, respectively. |
png pdf |
Figure 6-b:
Distributions for the $ \ell^+ $+jets (upper) and $ \ell^- $+jets (lower) categories where the prediction parameters are set to the values obtained in the fit. They show the MVA score and $ |\eta_{\mathrm{u}_0}| $ distributions, which are the fitted variables in the ML fit in the 2j1b category and the categories with three jets, respectively. The vertical error bars represent the statistical uncertainty associated to the data, and the hatched band the uncertainty of the prediction, after the fit. All uncertainties considered in the analysis are included in the uncertainty band. The lower panels show the ratio of data to prediction. The first and last bins in the MVA output distributions include underflow and overflow events, respectively. |
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Figure 7:
The largest impacts of nuisance parameters on the signal strength, $ \Delta\widehat{\text{r-inc.}} $ (right column) and ratios $ (\hat{\theta}-\theta_0)/\Delta\theta $ (middle column) for the nuisance parameters listed in the left column from the ML fit used to determine the measured $ \mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q} $ cross section. The horizontal bars in the middle column show the ratio of the uncertainties of the fit result to the pre-fit ones, indicating the constraint on the nuisance parameter. The JES uncertainties are divided into several sources related to the various methods used to extract the uncertainties as described in Ref. [29]. |
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Figure 8:
Two-dimensional 68 and 95% confidence level regions for the signal strengths modifying the top quark ($ r_{\mathrm{t}} $) and antiquark ($ r_{\overline{\mathrm{t}}} $) cross sections individually, represented by the solid and dashed lines respectively. The blue cross indicates the SM prediction and the red dot, the best fit for both signal strengths. |
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Figure 9:
Summary of the CMS measurements of the $ t $-channel single top quark production cross section as a function of $ \sqrt{s} $. |
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Figure 10:
Comparison of the measured values at $ \sqrt{s}= $ 5.02 TeV with predictions using different PDF sets, calculated with the MCFM program [51] for $ \sigma(\mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q}) $ (left) and $ \mathcal{R}_{\mathrm{t-ch}} $ (right). |
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Figure 10-a:
Comparison of the measured values at $ \sqrt{s}= $ 5.02 TeV with predictions using different PDF sets, calculated with the MCFM program [51] for $ \sigma(\mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q}) $ (left) and $ \mathcal{R}_{\mathrm{t-ch}} $ (right). |
png pdf |
Figure 10-b:
Comparison of the measured values at $ \sqrt{s}= $ 5.02 TeV with predictions using different PDF sets, calculated with the MCFM program [51] for $ \sigma(\mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q}) $ (left) and $ \mathcal{R}_{\mathrm{t-ch}} $ (right). |
| Tables | |
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Table 1:
Summary of simulated samples used to model the signal and background processes. The last column corresponds to the pQCD and EW order of approximation used to normalize the distributions provided by the generators. |
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Table 2:
Summary of the variables used for training the MVA classifier in the 2j1b categories. The variables are ordered according to their discriminating power, assessed via the mean decrease in impurity method [52]. ``Leading'' jet refers to the jet with the highest $ p_{\mathrm{T}} $ in the event. |
| Summary |
| A measurement of the single top quark $ t $-channel production cross section in proton-proton collisions at a centre-of-mass energy of 5.02 TeV is performed for events with one electron or one muon and multiple jets using data collected by the CMS experiment in 2017 in conditions of low number of additional interactions per bunch crossing, corresponding to an integrated luminosity of 302$ \text{pb}^{-1}$. This represents the first CMS measurement of the process at that energy. The main background in the analysis originates from W+jets and top quark pair production, both estimated using simulation. Smaller contributions from quantum chromodynamics multijet events are derived from data. The cross section is measured through a maximum likelihood fit to the observed event yields in twelve categories defined in terms of the number of jets and b-tagged jets, the lepton flavour and electric charge. The cross sections are found to be $ \sigma(\mathrm{t}\mathrm{q}\text{+}\overline{\mathrm{t}}\mathrm{q})=25.4 ^{+3.6}_{-3.5} $ (stat) $ ^{+4.2}_{-3.9} $ (syst) $ \pm $ 0.5 (lumi) pb, $ \sigma(\mathrm{t}\mathrm{q})=17.6 ^{+2.8}_{-2.7} $ (stat) $ ^{+2.6}_{-2.4} $ (syst) $ \pm $ 0.3 (lumi) pb, and $ \sigma(\overline{\mathrm{t}}\mathrm{q})=6.6 ^{+2.4}_{-1.6} $ (stat) $ ^{+2.1}_{-2.5} $ (syst) $ \pm $ 0.1 (lumi) pb. The ratio between the individual cross sections is found to be $ \mathcal{R}_{\mathrm{t-ch}} =2.7 ^{+1.5}_{-0.8} $ (stat) $ ^{+1.3}_{-0.3} $ (syst). These results are used to calculate the absolute value of the Cabibbo--Kobayashi--Maskawa matrix element, which is found to be $ |f_{\text{LV}}V_{\mathrm{t}\mathrm{b}}|= $ 0.92 $ \pm $ 0.09 (exp) $ \pm $ 0.01 (theo). All the results are in good agreement with the standard model predictions. |
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