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| CMS-TOP-17-006 ; ATLAS-TOPQ-2017-16 ; CERN-EP-2019-005 | ||
| Combinations of single-top-quark production cross-section measurements and ${|f_{\mathrm LV}{V_{\mathrm{tb}}} |} $ determinations at $\sqrt{s} =$ 7 and 8 TeV with the ATLAS and CMS experiments | ||
| ATLAS and CMS Collaborations | ||
| 15 February 2019 | ||
| JHEP 05 (2019) 088 | ||
| Abstract: This paper presents the combinations of single-top-quark production cross-section measurements by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at at $\sqrt{s} =$ 7 and 8 TeV corresponding to integrated luminosities of 1.17 to 5.1 fb$^{-1}$ at $\sqrt{s} =$ 7 TeV, and 12.2 to 20.3 fb$^{-1}$ at $\sqrt{s} =$ 8 TeV. These combinations are performed per centre-of-mass energy and for each production mode: $t$-channel , tW, and $s$-channel . The combined $t$-channel cross-sections are 67.5 $\pm$ 5.7 pb and 87.7 $\pm$ 5.8 pb at $\sqrt{s} =$ 7 and 8 TeV respectively. The combined qW cross-sections are 16.3 $\pm$ 4.1 pb and 23.1 $\pm$ 3.6 pb at $\sqrt{s} =$ 7 and 8 TeV respectively. For the $s$-channel \ cross-section, the combination yields 4.9 $\pm$ 1.4 pb at $\sqrt{s} =$ 8 TeV. The square of the magnitude of the CKM matrix element ${V_{\mathrm{tb}}} $ multiplied by a model-independent form factor $ {f_{\rm LV}} $ is determined for each production mode and centre-of-mass energy, using the ratio of the measured cross-section to its theoretical prediction. It is assumed that the top-quark-related CKM matrix elements obey the relation $|{V_{{\mathrm{td}}}} |,|{V_{{\mathrm{ts}}}} | \ll |{V_{\mathrm{tb}}} |$. All the $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ determinations, extracted from individual ratios at $\sqrt{s} =$ 7 and 8 TeV, are combined, resulting in ${|{f_{\rm LV}} {V_{\mathrm{tb}}} |} = $ 1.02 $\pm$ 0.04 (meas) $\pm$ 0.02 (theo). All combinations are consistent with their corresponding Standard Model predictions. | ||
| Links: e-print arXiv:1902.07158 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
|---|
| Figures | |
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Figure 1:
Representative Feynman diagrams at LO in QCD and in the five-flavour-number scheme for single-top-quark production in (left) the $t$-channel, (middle) tW production, and (right) the $s$-channel. |
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Figure 1-a:
Representative Feynman diagram at LO in QCD and in the five-flavour-number scheme for single-top-quark production in the $t$-channel. |
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Figure 1-b:
Representative Feynman diagram at LO in QCD and in the five-flavour-number scheme for single-top-quark production in tW production. |
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Figure 1-c:
Representative Feynman diagram at LO in QCD and in the five-flavour-number scheme for single-top-quark production in the $s$-channel. |
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Figure 2:
Single-top-quark cross-section measurements performed by ATLAS and CMS, together with the combined results. These measurements are compared with the theoretical predictions at NLO and NLO+NNLL for all three production modes and the prediction at NNLO for $t$-channel only. The corresponding theoretical uncertainties are also presented. The scale uncertainty for the NNLO prediction is small and is presented as a narrow band under the dashed line. |
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Figure 3:
Correlation matrix of the overall $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ combination. Each bin corresponds to a measurement in a given production mode, experiment, and at a given centre-of-mass energy. |
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Figure 4:
The combined $| {f_{\rm LV}} {V_{\mathrm{tb}} }| $ value extracted from the $t$-channel and tW cross-section measurements at $ \sqrt{s} = $ 7 and 8 TeV from ATLAS and CMS, as well as the ATLAS $s$-channel measurement at $ \sqrt{s} = $ 8 TeV, is shown together with the combined $| {f_{\rm LV}} {V_{\mathrm{tb}} }| $ values for each production mode. The theoretical predictions for $t$-channel and $s$-channel production are computed at NLO accuracy, while the theoretical predictions for tW are calculated at NLO+NNLL accuracy. The $ \sigma_{\text{teo}} $ uncertainties used to compute $| {f_{\rm LV}} {V_{\mathrm{tb}} }| $ include scale, PDF+$ \alpha_{\text{s}} $, $ m_{\mathrm{t}} $, and $ E_{\text{beam}} $ variations. |
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Figure 5:
Results of the stability tests performed by varying of the correlation assumptions in different uncertainty categories: theory modelling (scales and radiation modelling, NLO matching, and PS and hadronisation), JES, dominant theoretical cross-section predictions (i.e. PDF+$ \alpha_{\text{s}} $ and scale) and integrated luminosity. Two or three variations are considered depending on the uncertainty category. The corresponding relative shifts (with shift = varied - nominal) in the central value, $ \Delta| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 / | {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $, and in its uncertainty, $ \Delta(\delta | {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 )/(\delta | {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $), are shown. |
| Tables | |
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Table 1:
Predicted cross-sections for single-top-quark production at $ \sqrt{s} = $ 7 and 8 TeV at the LHC. Uncertainties include scale and PDF+$ \alpha_{\text{s}} $ variations, except for the NNLO predictions, which only contain the scale variation. The PDF+$ \alpha_{\text{s}} $ uncertainties are evaluated according to the PDF4LHC prescription only for the NLO predictions. The uncertainties associated with the top-quark mass $ m_{\mathrm{t}} $ and beam energy $ E_{\text{beam}} $ are also given for the NLO predictions for the $t$- and $s$-channels, and for the NLO+NNLL prediction for tW production. The value of $ m_{\mathrm{t}} $ is set to 172.5 GeV in all predictions. The cross-sections marked with $\dagger$ are those used in the ${f_{\rm LV}} {V_{\mathrm{tb}} }$ combination. |
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Table 2:
Summary of the single-top-quark cross-section measurements published by the ATLAS and CMS Collaborations at $ \sqrt{s} = $ 7 and 8 TeV. Total uncertainties are shown. Small differences between the integrated luminosity values in different analyses within the same experiment and centre-of-mass energy are due to different luminosity calibrations at the time of publication. |
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Table 3-a:
Contribution from each uncertainty category to the combined $t$-channel cross-section ($ \sigma_{\text{t-chan.}} $) uncertainty at (a) $ \sqrt{s} = $ 7 TeV. The total uncertainty is computed by adding in quadrature all the individual systematic uncertainties (including the uncertainty in the integrated luminosity) and the statistical uncertainty in data. |
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Table 3-b:
Contribution from each uncertainty category to the combined $t$-channel cross-section ($ \sigma_{\text{t-chan.}} $) uncertainty at (a) $ \sqrt{s} = $ 8 TeV. The total uncertainty is computed by adding in quadrature all the individual systematic uncertainties (including the uncertainty in the integrated luminosity) and the statistical uncertainty in data. |
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Table 4-a:
Contribution from each uncertainty category to the combined tW cross-section ($ \sigma_{\mathrm{tW}} $) uncertainty at (a) $ \sqrt{s} = $ 7 TeV. The total uncertainty is computed by adding in quadrature all the individual systematic uncertainties (including the uncertainty in the integrated luminosity) and the statistical uncertainty in data. |
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Table 4-b:
Contribution from each uncertainty category to the combined tW cross-section ($ \sigma_{\mathrm{tW}} $) uncertainty at (a) $ \sqrt{s} = $ 8 TeV. The total uncertainty is computed by adding in quadrature all the individual systematic uncertainties (including the uncertainty in the integrated luminosity) and the statistical uncertainty in data. |
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Table 5:
Contribution from each uncertainty category to the combined $s$-channel cross-section ($ \sigma_{\text{s-chan.}} $) uncertainty at $ \sqrt{s} = $ 8 TeV. The total uncertainty is computed by adding in quadrature all the individual systematic uncertainties (including the uncertainty in the integrated luminosity) and the statistical uncertainty in data. |
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Table 6:
Results of the ATLAS and CMS individual $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ determinations that are the inputs to the overall $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ combination together with their experimental uncertainties. The values of $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ may slightly differ from those published for the different analyses since in this paper the theoretical cross-sections used are those marked with $ \dagger $ in Table 1. Experimental uncertainties contributing less than 1% are denoted by $<$0.01. Entries with - mean that this uncertainty was not evaluated for this analysis. |
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Table 7:
Contributions from each experimental and theoretical uncertainty category to the overall $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ combination. The total uncertainty is computed by adding in quadrature all of the individual systematic uncertainties (including the integrated luminosity and theoretical cross-section) and the statistical uncertainty in data. |
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Table 8:
BLUE weights for the overall $| {f_{\rm LV}} {V_{\mathrm{tb}} }|^2 $ combination. |
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Table 9:
Measured cross-sections, uncertainty components, their magnitudes (relative to the individual measurements) and the correlation ($\rho$) between the ATLAS and CMS $ \sigma_{\text{t-chan.}} $ measurements at $ \sqrt{s} = $ 7 TeV. Uncertainties in the same row can be compared between experiments, as detailed in the text. The naming conventions follow those of the corresponding experiments. |
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Table 10:
Measured cross-sections, uncertainty components, their magnitudes (relative to the individual measurements) and the correlation ($\rho$) between the ATLAS and CMS $ \sigma_{\text{t-chan.}} $ measurements at $ \sqrt{s} = $ 8 TeV. Uncertainties in the same row can be compared between experiments, as detailed in the text. The naming conventions follow those of the corresponding experiments. |
png pdf |
Table 11:
Measured cross-sections, uncertainty components, their magnitudes (relative to the individual measurements) and the correlation ($\rho$) between the ATLAS and CMS $ \sigma_{\mathrm{tW}} $ measurements at $ \sqrt{s} = $ 7 TeV. Uncertainties in the same row can be compared between experiments, as detailed in the text. The naming conventions follow those of the corresponding experiments. |
png pdf |
Table 12:
Measured cross-sections, uncertainty components, their magnitudes (relative to the individual measurements) and the correlation ($\rho$) between the ATLAS and CMS $ \sigma_{\mathrm{tW}} $ measurements at $ \sqrt{s} = $ 8 TeV. Uncertainties in the same row can be compared between experiments, as detailed in the text. The naming conventions follow those of the corresponding experiments. |
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Table 13:
Measured cross-sections, uncertainty components, their magnitudes (relative to the individual measurements) and the correlation ($\rho$) between the ATLAS and CMS $ \sigma_{\text{s-chan.}} $ measurements at $ \sqrt{s} = $ 8 TeV. Uncertainties in the same row can be compared between experiments, as detailed in the text. The naming conventions follow those of the corresponding experiments. |
| Summary |
| The combinations of single-top-quark production cross-section measurements in the $t$-channel, tW, and $s$-channel production modes are presented, using data from LHC pp collisions collected by the ATLAS and CMS Collaborations. The combinations for each production mode are performed at $ \sqrt{s} = $ 7 and 8 TeV, using data corresponding to integrated luminosities of 1.17 to 5.1 fb${-1}$ at $ \sqrt{s} = $ 7 TeV, and of 12.2 to 20.3 fb${-1}$ at $ \sqrt{s} = $ 8 TeV. The combined $t$-channel cross-sections are found to be 67.5 $\pm$ 5.7 pb and 87.7 $\pm$ 5.8 pb at $ \sqrt{s} = $ 7 and 8 TeV respectively. The values of the combined tW cross-sections at 740 $ \sqrt{s} = $ 7 and 8 TeV are 16.3 $\pm$ 4.1 pb and 23.1 $\pm$ 3.6 pb respectively. For the $s$-channel cross-section, the combination yields 4.9 $\pm$ 1.4 pb at $ \sqrt{s} = $ 8 TeV. The square of the magnitude of the CKM matrix element $V_{\mathrm{tb}}$ multiplied by a form factor accounting for possible contributions from physics beyond the SM, $ f_{\rm LV} $, is determined from each production mode at each centre-of-mass energy, using the ratio of the measured cross-section to its theoretical prediction, and assuming that the top-quark-related CKM matrix elements obey the relation $|V_{\mathrm{td}} |$, $|V_{\mathrm{ts}} | \ll |V_{\mathrm{tb}} |$. The values of $| f_{\rm LV} V_{\mathrm{tb}} |^2$ extracted from individual ratios at $ \sqrt{s} = $ 7 and 8 TeV yield a combined value of $| f_{\rm LV} V_{\mathrm{tb}} | = $ 1.02 $\pm$ 0.04 (meas) $\pm$ 0.02 (theo). All combined measurements are consistent with their corresponding SM predictions. |
| Additional Figures | |
png pdf |
Additional Figure 1:
Single-top-quark cross-section measurements performed by ATLAS and CMS, together with the combined results. These measurements are compared with the theoretical predictions at NLO and NLO+NNLL for all three production modes and the prediction at NNLO for $t$-channel only. The corresponding theoretical uncertainties are also presented. The scale uncertainty for the NNLO prediction is small and is presented as a narrow band under the dashed line. |
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