CMS-TOP-18-014

CMS-TOP-18-014 ; CERN-EP-2021-222
Combination of inclusive top-quark pair production cross-section measurements using ATLAS and CMS data at $\sqrt{s}=$ 7 and 8 TeV
ATLAS and CMS Collaborations
25 May 2022
JHEP 07 (2023) 213
Abstract: A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron-muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb $^{-1}$ at $\sqrt{s}=$ 7 TeV and about 20 fb $^{-1}$ at $\sqrt{s}=$ 8 TeV for each experiment. The combined cross-sections are determined to be 178.5 $\pm$ 4.7 pb at $\sqrt{s}=$ 7 TeV and 243.3 $^{+6.0}_{-5.9}$ pb at $\sqrt{s}=$ 8 TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be $R_{8/7}=$ 1.363 $\pm$ 0.032. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are $m_t^\text{pole} =$ 173.4 $^{+1.8}_{-2.0}$ GeV and $\alpha_\text{s}(m_Z)=$ 0.1170 $^{+ 0.0021}_{-0.0018}$ .
Links: e-print arXiv:2205.13830 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Measured $\mathrm{t\bar{t}}$ production cross-sections at $\sqrt {s}=$ 7 and 8 TeV compared with predictions using different PDF sets. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The shaded bands represent the total uncertainties in the predictions.
png pdf	Figure 2: Measured ratios of the $\mathrm{t\bar{t}}$ production cross-sections at $\sqrt {s}=$ 7 and 8 TeV compared with predictions using different PDF sets. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The shaded bands represent the total uncertainties in the predictions.
png pdf	Figure 3: Dependence of the predicted cross-section and the combined measured cross-section on (left) the top-quark pole mass ${{m_{\mathrm {t}}^{\text {pole}}}}$ and (right) the strong coupling ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ . The prediction is evaluated for three different PDF sets and assumes (left) ${\alpha _{\text {S}}} (m_{\mathrm{Z}})=$ 0.118 $\pm$ 0.001 or (right) ${m_{\mathrm {t}}^{\text {pole}}} =$ 172.5 $\pm$ 1.0 GeV. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The uncertainty bands include the effects of the uncertainties in the combined cross-sections and of the factorisation and renormalisation scale and PDF uncertainties in the predicted cross-sections.
png pdf	Figure 3-a: Dependence of the predicted cross-section and the combined measured cross-section on the top-quark pole mass ${{m_{\mathrm {t}}^{\text {pole}}}}$ . The prediction is evaluated for three different PDF sets and assumes ${\alpha _{\text {S}}} (m_{\mathrm{Z}})=$ 0.118 $\pm$ 0.001. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The uncertainty bands include the effects of the uncertainties in the combined cross-sections and of the factorisation and renormalisation scale and PDF uncertainties in the predicted cross-sections.
png pdf	Figure 3-b: Dependence of the predicted cross-section and the combined measured cross-section on the strong coupling ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ . The prediction is evaluated for three different PDF sets and assumes ${m_{\mathrm {t}}^{\text {pole}}} =$ 172.5 $\pm$ 1.0 GeV. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The uncertainty bands include the effects of the uncertainties in the combined cross-sections and of the factorisation and renormalisation scale and PDF uncertainties in the predicted cross-sections.
png pdf	Figure 4: Dependence of the top-quark pole mass, ${m_{\mathrm {t}}^{\text {pole}}}$ , on the assumed value for the strong coupling, ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ , including constraints from the combined measured cross-sections for three different PDF sets. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements. The shaded band represents the 68% CL uncertainty on the extracted ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ when fixing ${m_{\mathrm {t}}^{\text {pole}}}$ and on ${m_{\mathrm {t}}^{\text {pole}}}$ when fixing ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ . The uncertainty bands include the effects of the uncertainties in the combined cross-sections and of the renormalisation and factorisation scale and PDF uncertainties in the predicted cross-sections.

Tables
png pdf	Table 1: Predicted $\mathrm{t\bar{t}}$ production cross-sections at different centre-of-mass energies and for different PDF sets. The uncertainties comprise PDF and ${\alpha _{\text {S}}}$ uncertainties as well as uncertainties in the renormalisation and factorisation scales. The ratio of the predicted $\mathrm{t\bar{t}}$ production cross-sections at $\sqrt {s}=$ 8 TeV and 7 TeV, $R_{8/7}$ , is also shown. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements.
png pdf	Table 2: Summary of the relative statistical, systematic and total uncertainties in the ATLAS measurements of the $\mathrm{t\bar{t}}$ production cross-section, ${\sigma _{\mathrm{t\bar{t}}}}$ , at $\sqrt {s}=$ 7 and 8 TeV from Ref. [15], where ID stands for identification and JES for jet-energy scale, and the grouping is modified to allow for the combination with the CMS measurements.
png pdf	Table 3: Illustrative summary of the individual contributions to the total uncertainty in the CMS $\mathrm{t\bar{t}}$ cross-section measurements from Ref. [19], where ID stands for identification, JES for jet-energy scale, ME for matrix element and PS for parton shower.
png pdf	Table 4: Assumed correlations between ATLAS and CMS systematic uncertainties. The assigned sign is based on the nature of the systematic uncertainty (e.g., minus for an `up' variation in the ATLAS measurement that corresponds to a `down' variation in the CMS measurement due to conventions within the collaborations). If the sign is ambiguous, the sign maximising the total uncertainty in the combined cross-section is chosen. Any uncertainties not included in the table are considered uncorrelated.
png pdf	Table 5: Illustration of the impact $\Delta \sigma _{{\mathrm {\mathrm{t\bar{t}}}}}/\sigma _{{\mathrm {\mathrm{t\bar{t}}}}}$ of the dominant groups of systematic uncertainties on the combined cross-sections at $\sqrt {s}=$ 7 and 8 TeV.
png pdf	Table 6: Measured ${m_{\mathrm {t}}^{\text {pole}}}$ and ${\alpha _{\text {S}}} (m_{\mathrm{Z}})$ values for each PDF set using the measured 7 and 8 TeV combined cross-sections. NNPDF3.1_a is a version of this PDF set containing no top-quark measurements.

Summary

A combination of measurements of the inclusive

$\mathrm{t\bar{t}}$ production cross-section performed by the ATLAS and CMS experiments at

$\sqrt{s} =$ 7 and 8 TeV is presented, accounting for correlations between the measurements from different experiments as well as correlations within the ATLAS and CMS measurements.

The resulting cross-sections are

$\sigma_{\mathrm{t\bar{t}}}( \sqrt{s} = \text{7 TeV}) = 178.5 \pm 4.7\, \text{pb}$ ,

$\sigma_{\mathrm{t\bar{t}}}( \sqrt{s} = \text{8 TeV}) = 243.3\,{}^{+6.0}_{-5.9}\, \text{pb}$ .
The combined results improve on the precision of the most precise individual results by 25% at

$\sqrt{s} =$ 7 TeV, and by 28% at

$\sqrt{s} =$ 8 TeV, making these combined results the most precise measurements of the inclusive

$\mathrm{t\bar{t}}$ cross-section to date at those respective centre-of-mass energies. The correlation between the combined cross-sections values is 0.41, and their ratio is determined to be

$R_{8/7} = 1.363 \pm 0.032$ .
Furthermore, the combined values for

$\sigma_{\mathrm{t\bar{t}}}$ are used to determine the top-quark pole mass and the strong coupling by comparing them with the predicted evolution of

$\sigma_{\mathrm{t\bar{t}}}$ as a function of

$m_{\mathrm{t}}^{\text{pole}}$ and

$\alpha_{S}(m_{\mathrm{Z}})$ , for different PDF sets. The measurement yields the most precise values,

$m_{\mathrm{t}}^{\text{pole}} =$ 173.4

$^{+1.8}_{-2.0}$ GeV (1.2% relative uncertainty) and

$\alpha_{S}(m_{\mathrm{Z}}) =$ 0.1170

$^{+0.0021}_{-0:0018}$ (1.8% relative uncertainty), when using the NNPDF3.1_a PDF set. The extracted

$\alpha_{S}(m_{\mathrm{Z}})$ value is more precise than previous measurements performed using top-quark event.

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