CMS-SMP-20-011 ; CERN-EP-2021-221 | ||
Measurement and QCD analysis of double-differential inclusive jet cross sections in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
CMS Collaboration | ||
19 November 2021 | ||
JHEP 02 (2022) 142 [Addendum] | ||
Abstract:
A measurement of the inclusive jet production in proton-proton collisions at the LHC at $ \sqrt{s}= $ 13 TeV is presented. The double-differential cross sections are measured as a function of the jet transverse momentum $ p_{\mathrm{T}} $ and the absolute jet rapidity $ |y| $. The anti-$ k_{\mathrm{T}} $ clustering algorithm is used with distance parameter of 0.4 (0.7) in a phase space region with jet $ p_{\mathrm{T}} $ from 97 GeV up to 3.1 TeV and $ |y| < $ 2.0. Data collected with the CMS detector are used, corresponding to an integrated luminosity of 36.3 fb$ ^{-1} $ (33.5 fb$ ^{-1} $). The measurement is used in a comprehensive QCD analysis at next-to-next-to-leading order, which results in significant improvement in the accuracy of the parton distributions in the proton. Simultaneously, the value of the strong coupling constant at the Z boson mass is extracted as $ \alpha_\mathrm{S}(m_\mathrm{Z})= $ 0.1170 $ \pm $ 0.0019. For the first time, these data are used in a standard model effective field theory analysis at next-to-leading order, where parton distributions and the QCD parameters are extracted simultaneously with imposed constraints on the Wilson coefficient $ c_1 $ of 4-quark contact interactions. Note added: in the Addendum to this paper JHEP 12 (2022) 035, available as Appendix B in this document, an improved value of $ \alpha_\mathrm{S}(m_\mathrm{Z}) = $ 0.1166 $ \pm $ 0.0017 has been extracted. This result supersedes the number in the above abstract of the original publication, JHEP 02 (2022) 142. | ||
Links: e-print arXiv:2111.10431 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; |
Figures | |
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Figure 1:
The probability matrix, estimated with a simulated sample based on PYTHIA 8, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R = $ 0.7. The horizontal (vertical) axis corresponds to jets at the particle (detector) level. The global 5 $ \times $ 5 structure corresponds to the bins of rapidity $ y $ of the jets, indicated by the labels in the uppermost row and rightmost column; the horizontal and vertical axes of each cell correspond to the transverse momentum $ p_{\mathrm{T}} $ of the jets. The colour range covers a range from $ 10^{-6} $ to 1 and the rows are normalised to unity, indicating the probability for a particle-level jet generated with values of $ p_{\mathrm{T}}^\text{gen} $ and $ |y|^\text{gen} $ to be reconstructed at the detector level with values of $ p_{\mathrm{T}}^\text{rec} $ and $ |y|^\text{rec} $. Migrations outside of the phase space are not included; migrations across rapidity bins only occur among adjacent rapidity bins. The dashed lines indicate the diagonal bins in each rapidity cell. |
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Figure 2:
Relative uncertainties in the double-differential cross section, as functions of jet transverse momentum ($ x $ axis) and rapidity (cells), for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R = $ 0.7. The systematic uncertainties are shown in different, noncumulative colour bands: the red bands correspond to JES uncertainties, the yellow bands to the JER uncertainties, and the blue bands to all other sources, including the integrated luminosity uncertainty, the model uncertainty, uncertainties in the migrations in and out of the phase space, and uncertainties in various inefficiencies and backgrounds. The vertical error bars include the statistical uncertainties from the data and from the PYTHIA 8 simulated sample used for the unfolding, as well as the binwise systematic uncertainties, all summed in quadrature. The total uncertainty, shown in green, includes all systematic and statistical uncertainties summed in quadrature. |
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Figure 3:
The correlation matrix at the particle level, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R = $ 0.7. It contains contributions from the data and from the PYTHIA 8 sample used to perform the unfolding. The global 4 $ \times $ 4 structure corresponds to the bins of rapidity $ y $ of the jets, indicated by the labels in the uppermost row and rightmost column; the horizontal and vertical axes of each cell correspond to the transverse momentum $ p_{\mathrm{T}} $ of the jets. The colour range covers a range from-1 to 1 and indicates correlations in blue shades and anti-correlations in red shades, except for values between-0.1 and 0.1. Correlations across rapidity bins reach significant values mostly at the edges of the $ p_{\mathrm{T}} $ range. |
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Figure 4:
The EW corrections for inclusive jet cross sections, as reported in Ref. [62]. The values for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4 (0.7) are shown on the left (right); each curve corresponds to a rapidity bin. |
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Figure 4-a:
The EW corrections for inclusive jet cross sections, as reported in Ref. [62]. The values for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4 are shown; each curve corresponds to a rapidity bin. |
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Figure 4-b:
The EW corrections for inclusive jet cross sections, as reported in Ref. [62]. The values for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7 are shown; each curve corresponds to a rapidity bin. |
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Figure 5:
The values for NP corrections for inclusive jet cross sections. The values for jets with $ R= $ 0.4 (0.7) are shown on the left (right); each curve corresponds to a rapidity bin. The values correspond to the average of the corrections obtained with PYTHIA 8 and with HERWIG++. |
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Figure 5-a:
The values for NP corrections for inclusive jet cross sections. The values for jets with $ R= $ 0.4 are shown; each curve corresponds to a rapidity bin. The values correspond to the average of the corrections obtained with PYTHIA 8 and with HERWIG++. |
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Figure 5-b:
The values for NP corrections for inclusive jet cross sections. The values for jets with $ R= $ 0.7 are shown; each curve corresponds to a rapidity bin. The values correspond to the average of the corrections obtained with PYTHIA 8 and with HERWIG++. |
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Figure 6:
The inclusive jet production cross sections as a function of the jet transverse momentum $ p_{\mathrm{T}} $ measured in intervals of the absolute rapidity $ |y| $. The cross section obtained for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4 (0.7) is shown on the upper (lower) plot. The results in different $ |y| $ intervals are scaled by a constant factor for presentation purpose. The data in different $ |y| $ intervals are shown by markers of different style. The statistical uncertainties are too small to be visible; the systematic uncertainties are not shown. The measurements are compared with fixed-order NNLO QCD predictions (solid line) using CT14nnlo PDF and corrected for EW and NP effects. |
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Figure 6-a:
The inclusive jet production cross sections as a function of the jet transverse momentum $ p_{\mathrm{T}} $ measured in intervals of the absolute rapidity $ |y| $. The cross section obtained for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4 is shown. The results in different $ |y| $ intervals are scaled by a constant factor for presentation purpose. The data in different $ |y| $ intervals are shown by markers of different style. The statistical uncertainties are too small to be visible; the systematic uncertainties are not shown. The measurements are compared with fixed-order NNLO QCD predictions (solid line) using CT14nnlo PDF and corrected for EW and NP effects. |
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Figure 6-b:
The inclusive jet production cross sections as a function of the jet transverse momentum $ p_{\mathrm{T}} $ measured in intervals of the absolute rapidity $ |y| $. The cross section obtained for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7 is shown. The results in different $ |y| $ intervals are scaled by a constant factor for presentation purpose. The data in different $ |y| $ intervals are shown by markers of different style. The statistical uncertainties are too small to be visible; the systematic uncertainties are not shown. The measurements are compared with fixed-order NNLO QCD predictions (solid line) using CT14nnlo PDF and corrected for EW and NP effects. |
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Figure 7:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4, presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistic uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. In the upper panel, the data are divided by the NNLO prediction, corrected for NP and EW effects, using CT14nnlo PDF and with renormalisation and factorisation scales jet $ p_{\mathrm{T}} $ and, alternatively $ H_{\mathrm{T}} $ (blue solid line). In the lower panel, the data are shown as ratio to NLO+NLL prediction, calculated with CT14nlo PDF, and corrected for NP and EW effects. The scale (PDF) uncertainties are shown by red solid (dashed) lines. NLO+NLL predictions obtained with alternative PDF sets are displayed in different colours as a ratio to the central prediction using CT14nlo. |
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Figure 7-a:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4, presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistic uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. The data are divided by the NNLO prediction, corrected for NP and EW effects, using CT14nnlo PDF and with renormalisation and factorisation scales jet $ p_{\mathrm{T}} $ and, alternatively $ H_{\mathrm{T}} $ (blue solid line). |
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Figure 7-b:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4, presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistic uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. The data are shown as ratio to NLO+NLL prediction, calculated with CT14nlo PDF, and corrected for NP and EW effects. The scale (PDF) uncertainties are shown by red solid (dashed) lines. NLO+NLL predictions obtained with alternative PDF sets are displayed in different colours as a ratio to the central prediction using CT14nlo. |
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Figure 8:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7, presented as ratios to the QCD predictions. The notations are identical to those of Fig. 7. |
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Figure 8-a:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7, presented as ratios to the QCD predictions. The notations are identical to those of Fig. 7-a. |
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Figure 8-b:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7, presented as ratios to the QCD predictions. The notations are identical to those of Fig. 7-b. |
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Figure 9:
Fractional uncertainties in the u-valence (upper left), d-valence (upper right), gluon (lower left), and the sea quark (lower right) distributions, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NLO+NLL. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 9-a:
Fractional uncertainties in the u-valence distribution, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NLO+NLL. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 9-b:
Fractional uncertainties in the d-valence distribution, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NLO+NLL. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 9-c:
Fractional uncertainties in the gluon distribution, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NLO+NLL. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 9-d:
Fractional uncertainties in the sea quark distribution, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NLO+NLL. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 10:
Fractional uncertainties in the u-valence (upper left), d-valence (upper right), gluon (lower left), and the sea quark (lower right) distributions, shown as functions of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nnlo PDF at NNLO, by using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NNLO. The original uncertainty is shown in red, while the profiled result is shown in blue. |
png pdf |
Figure 10-a:
Fractional uncertainties in the u-valence distribution, shown as functions of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nnlo PDF at NNLO, by using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NNLO. The original uncertainty is shown in red, while the profiled result is shown in blue. |
png pdf |
Figure 10-b:
Fractional uncertainties in the d-valence distribution, shown as functions of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nnlo PDF at NNLO, by using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NNLO. The original uncertainty is shown in red, while the profiled result is shown in blue. |
png pdf |
Figure 10-c:
Fractional uncertainties in the gluon distribution, shown as functions of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nnlo PDF at NNLO, by using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NNLO. The original uncertainty is shown in red, while the profiled result is shown in blue. |
png pdf |
Figure 10-d:
Fractional uncertainties in the sea quark distribution, shown as functions of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nnlo PDF at NNLO, by using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV, implying the theoretical prediction for these data at NNLO. The original uncertainty is shown in red, while the profiled result is shown in blue. |
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Figure 11:
The $ \chi^2 $ obtained in profiling of CT14 PDF $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ series using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV at NLO (left) and NNLO (right). |
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Figure 11-a:
The $ \chi^2 $ obtained in profiling of CT14 PDF $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ series using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV at NLO. |
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Figure 11-b:
The $ \chi^2 $ obtained in profiling of CT14 PDF $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ series using the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV at NNLO. |
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Figure 12:
Fractional uncertainty in the gluon distribution (left), shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using the CMS inclusive jet and the triple-differential $ \mathrm{t} \overline{\mathrm{t}} $ cross sections at $ \sqrt{s}= $ 13 TeV. The original (profiled) uncertainty is shown in red (blue). The $ \chi^2 $ (right) obtained in profiling of CT14 PDF $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ series using the same data as in (left). |
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Figure 12-a:
Fractional uncertainty in the gluon distribution, shown as a function of $ x $ for the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The profiling is performed using CT14nlo PDF at NLO, by using the CMS inclusive jet and the triple-differential $ \mathrm{t} \overline{\mathrm{t}} $ cross sections at $ \sqrt{s}= $ 13 TeV. The original (profiled) uncertainty is shown in red (blue). |
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Figure 12-b:
The $ \chi^2 $ obtained in profiling of CT14 PDF $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ series using the same data as in Fig. 12-a. |
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Figure 13:
The profiled Wilson coefficient $ c_1 $ for the contact interaction models, assuming the left-handed, vector-like, and axial vector-like scenarios, as obtained in the profiling analysis using NLO+NLL calculation for the jet production and the CT14nlo PDF set. The value of $ \Lambda = $ 10 TeV is assumed. The results are obtained using the CMS measurements of inclusive jet cross section and of normalised triple-differential $ \mathrm{t} \overline{\mathrm{t}} $ cross section at $ \sqrt{s}= $ 13 TeV. The inner error bar shows the PDF uncertainty at 68% CL, while the outer error bar represents the total uncertainty, obtained from the PDF and scale uncertainties, added in quadrature. |
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Figure 14:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $, resulting from the NNLO fit using HERA DIS together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panels, the relative uncertainty contributions are presented. |
png pdf |
Figure 14-a:
The u-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $, resulting from the NNLO fit using HERA DIS together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 14-b:
The d-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $, resulting from the NNLO fit using HERA DIS together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 14-c:
The gluon distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $, resulting from the NNLO fit using HERA DIS together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 14-d:
The sea quark distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $, resulting from the NNLO fit using HERA DIS together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 15:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panels, the comparison of the relative PDF uncertainties is shown for each distribution. The dashed line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure 15-a:
The u-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The dashed line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure 15-b:
The d-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The dashed line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure 15-c:
The gluon distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The dashed line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure 15-d:
The sea quark distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_t^2 $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The dashed line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure 16:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t}^2 $, resulting from the SM fit using HERA DIS together with the CMS inclusive jet cross section and the normalised triple-differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panels, the relative uncertainty contributions are presented. |
png pdf |
Figure 16-a:
The u-valence distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t}^2 $, resulting from the SM fit using HERA DIS together with the CMS inclusive jet cross section and the normalised triple-differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 16-b:
The d-valence distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t}^2 $, resulting from the SM fit using HERA DIS together with the CMS inclusive jet cross section and the normalised triple-differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 16-c:
The gluon distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t}^2 $, resulting from the SM fit using HERA DIS together with the CMS inclusive jet cross section and the normalised triple-differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 16-d:
The sea quark distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t}^2 $, resulting from the SM fit using HERA DIS together with the CMS inclusive jet cross section and the normalised triple-differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV. Contributions of fit, model, and parameterisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure 17:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the fits with and without the CI terms. The SMEFT fit is performed with the left-handed CI model with $ \Lambda= $ 10 TeV. |
png pdf |
Figure 17-a:
The u-valence distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the fits with and without the CI terms. The SMEFT fit is performed with the left-handed CI model with $ \Lambda= $ 10 TeV. |
png pdf |
Figure 17-b:
The d-valence distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the fits with and without the CI terms. The SMEFT fit is performed with the left-handed CI model with $ \Lambda= $ 10 TeV. |
png pdf |
Figure 17-c:
The gluon distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the fits with and without the CI terms. The SMEFT fit is performed with the left-handed CI model with $ \Lambda= $ 10 TeV. |
png pdf |
Figure 17-d:
The sea quark distribution, shown as functions of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the fits with and without the CI terms. The SMEFT fit is performed with the left-handed CI model with $ \Lambda= $ 10 TeV. |
png pdf |
Figure 18:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the SMEFT fit with the left-handed CI model with $ \Lambda= $ 10 TeV. The PDFs are shown with the fit uncertainties obtained by the Hessian (solid blue) and Monte Carlo (solid red) methods. |
png pdf |
Figure 18-a:
The u-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the SMEFT fit with the left-handed CI model with $ \Lambda= $ 10 TeV. The PDFs are shown with the fit uncertainties obtained by the Hessian (solid blue) and Monte Carlo (solid red) methods. |
png pdf |
Figure 18-b:
The d-valence distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the SMEFT fit with the left-handed CI model with $ \Lambda= $ 10 TeV. The PDFs are shown with the fit uncertainties obtained by the Hessian (solid blue) and Monte Carlo (solid red) methods. |
png pdf |
Figure 18-c:
The gluon distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the SMEFT fit with the left-handed CI model with $ \Lambda= $ 10 TeV. The PDFs are shown with the fit uncertainties obtained by the Hessian (solid blue) and Monte Carlo (solid red) methods. |
png pdf |
Figure 18-d:
The sea quark distribution, shown as a function of $ x $ at the scale $ \mu_\mathrm{f}^2=m_\mathrm{t}^2 $, resulting from the SMEFT fit with the left-handed CI model with $ \Lambda= $ 10 TeV. The PDFs are shown with the fit uncertainties obtained by the Hessian (solid blue) and Monte Carlo (solid red) methods. |
png pdf |
Figure 19:
The Wilson coefficients $ c_1 $ obtained in the SMEFT analysis at NLO, divided by $ \Lambda^2 $, for $ \Lambda= $ 50 TeV. The solid (dashed) lines represent the total uncertainty at 68 (95)% CL. The inner (outer) error bars show the fit (total) uncertainty at 68% CL. |
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Figure A1:
Cross sections of inclusive jet production for distance parameter $ R= $ 0.4 as a function of transverse momentum of the individual jet in bins of absolute rapidity $ |y| $, compared to the theoretical predictions at NLO, NLO+NLL, and NNLO. All results are normalised to the prediction at NLO. The measurement (solid symbols) is presented with the statistical uncertainties (vertical error bars), while the systematic uncertainty is represented by a yellow filled band, centered at 1. The NLO (black dashed line) and NLO+NLL (blue solid line) predictions are obtained using CT14nlo PDF. The PDF (dotted red line) and scale (solid red line) uncertainties are shown for the NLO prediction. The NNLO calculation (purple solid line) is obtained using CT14nnlo PDF. |
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Figure A2:
Cross sections of inclusive jet production for distance parameter $ R= $ 0.4 as a function of transverse momentum of the individual jet in bins of absolute rapidity $ |y| $, compared to the theoretical predictions at NLO using different PDFs (lines of different colors). All results are normalised to the prediction at NLO obtained using CT14nlo PDF (black dashed line). The measurement (solid symbols) is presented with the statistical uncertainties (vertical error bars), while the systematic uncertainty is represented by a yellow filled band, centered at 1. |
png pdf |
Figure A3:
Same as Fig. A1 for the distance parameter $ R= $ 0.7. |
png pdf |
Figure A4:
Same as Fig. A2 for the distance parameter $ R= $ 0.7. |
png pdf |
Figure B1:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4 (upper panel) and $ R= $ 0.7 (lower panel), presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistical uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. The data are divided by the NNLO prediction corrected for NP and EW effects, using CT14nnlo PDF and choosing jet $ p_{\mathrm{T}} $ as renormalisation and factorisation scale. NNLO predictions obtained with alternative PDF sets are displayed in different colours as a ratio to the central prediction using CT14nnlo. |
png pdf |
Figure B1-a:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.4, presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistical uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. The data are divided by the NNLO prediction corrected for NP and EW effects, using CT14nnlo PDF and choosing jet $ p_{\mathrm{T}} $ as renormalisation and factorisation scale. NNLO predictions obtained with alternative PDF sets are displayed in different colours as a ratio to the central prediction using CT14nnlo. |
png pdf |
Figure B1-b:
The double-differential cross section of inclusive jet production, as a function of $ p_{\mathrm{T}} $ and $ |y| $, for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ R= $ 0.7, presented as ratios to the QCD predictions. The data points are shown by filled circles, with statistical uncertainties shown by vertical error bars, while the total experimental uncertainty is centred at one and is presented by the orange band. The data are divided by the NNLO prediction corrected for NP and EW effects, using CT14nnlo PDF and choosing jet $ p_{\mathrm{T}} $ as renormalisation and factorisation scale. NNLO predictions obtained with alternative PDF sets are displayed in different colours as a ratio to the central prediction using CT14nnlo. |
png pdf |
Figure B2:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $, resulting from the NNLO fit using HERA DIS data together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. Contributions of the fit, model, and parametrisation uncertainties for each PDF are shown. In the lower panels, the relative uncertainty contributions are presented. |
png pdf |
Figure B2-a:
The u-valence distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $, resulting from the NNLO fit using HERA DIS data together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. Contributions of the fit, model, and parametrisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure B2-b:
The d-valence distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $, resulting from the NNLO fit using HERA DIS data together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. Contributions of the fit, model, and parametrisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure B2-c:
The gluon distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $, resulting from the NNLO fit using HERA DIS data together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. Contributions of the fit, model, and parametrisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure B2-d:
The sea quark distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $, resulting from the NNLO fit using HERA DIS data together with the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. Contributions of the fit, model, and parametrisation uncertainties for each PDF are shown. In the lower panel, the relative uncertainty contributions are presented. |
png pdf |
Figure B3:
The u-valence (upper left), d-valence (upper right), gluon (lower left), and sea quark (lower right) distributions shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. In the lower panels, the comparison of the relative PDF uncertainties is shown for each distribution. The line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure B3-a:
The u-valence distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure B3-b:
The d-valence distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure B3-c:
The gluon distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The line corresponds to the ratio of the central PDF values of the two variants of the fit. |
png pdf |
Figure B3-d:
The sea quark distribution shown as a function of $ x $ at the scale $ \mu_\mathrm{f}=m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s}= $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. The prediction for the inclusive jet cross section is obtained using NNLO interpolation grids. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The line corresponds to the ratio of the central PDF values of the two variants of the fit. |
Tables | |
png pdf |
Table 1:
Recent measurements of inclusive jet production, performed by the ATLAS and CMS Collaborations at different $ \sqrt{s} $, with the corresponding integrated luminosities. |
png pdf |
Table 2:
Description of the simulations used in the analysis. |
png pdf |
Table 3:
The HLT ranges and effective integrated luminosities used in the jet cross section measurement for $ R= $ 0.4. The first (second) row shows the $ p_{\mathrm{T}} $ threshold for the HLT (offline PF) reconstruction; the third row corresponds to the effective luminosity of each trigger $ \mathcal{L} $. |
png pdf |
Table 4:
The HLT ranges and effective integrated luminosities used in the jet cross section measurement for $ R= $ 0.7. The first (second) row shows the $ p_{\mathrm{T}} $ threshold for the HLT (offline PF) reconstruction; the third row corresponds to the effective luminosity of each trigger $ \mathcal{L} $. |
png pdf |
Table 5:
Partial $ \chi^2 $ per number of data points $ N_\mathrm{dp} $ and the global $ \chi^2 $ per degree of freedom, $ N_\mathrm{dof} $, as obtained in the QCD analysis at NNLO of HERA+CMS jet data and HERA-only data. In the DIS data, the proton beam energy is given as $ E_\mathrm{p} $ and the electron energy is 27.5 GeV. |
png pdf |
Table 6:
Partial $ \chi^2 $ per number of data points $ N_\mathrm{dp} $ and the global $ \chi^2 $ per degree of freedom, $ N_\mathrm{dof} $, as obtained in the QCD analysis of HERA DIS data and the CMS measurements of inclusive jet production and the normalised triple-differential $ \mathrm{t} \overline{\mathrm{t}} $ production at $ \sqrt{s}= $ 13 TeV, obtained in SM and SMEFT analyses. |
png pdf |
Table 7:
The values and uncertainties of the fitted Wilson coefficients $ c_1 $ for various scales $ \Lambda $. The fit uncertainties are obtained by using the Hessian method. |
png pdf |
Table B1:
Partial $ \chi^2 $ per number of data points, $ N_\mathrm{dp} $, and the global $ \chi^2 $ per degree of freedom, $ N_\mathrm{dof} $, as obtained in the QCD analysis at NNLO of HERA+CMS jet data, using NNLO interpolation grids for the 13 TeV inclusive jet cross section. In the DIS data, the proton beam energy is given as $ E_\mathrm{p} $ and the electron energy is 27.5 GeV. |
Summary |
In this paper, the measurement of the double-differential inclusive jet cross sections in proton-proton collisions at $ \sqrt{s}= $ 13 TeV is presented as a function of the jet transverse momentum $ p_{\mathrm{T}} $ and the jet rapidity $ |y| $ for jets reconstructed using the anti-$ k_{\mathrm{T}} $ clustering algorithm with a distance parameter $ R $ of 0.4 and 0.7. The phase space covers jet $ p_{\mathrm{T}} $ from 97 GeV up to 3.1 TeV and jet rapidity up to $ |y|= $ 2.0. The measured jet cross sections are compared with predictions of perturbative quantum chromodynamics (pQCD) at next-to-next-to-leading order (NNLO) and next-to-leading order (NLO) with the next-to-leading-logarithmic (NLL) resummation correction, using various sets of parton distribution functions (PDFs). A strong impact of the measurement on determination of the parton distributions is observed, expressed by significant differences among the theoretical predictions using different PDF sets, and by large corresponding uncertainties. To investigate the impact of the measurements on the PDFs and the strong coupling constant $ \alpha_\mathrm{S} $, a QCD analysis is performed, where the jet production cross section with $ R= $ 0.7 is used together with the HERA measurements of deep inelastic scattering. Significant improvement of the accuracy of the PDFs by using the present measurement in the QCD analysis is demonstrated in a profiling analysis using the CT14 PDF set and in the full PDF fit. The value of the strong coupling constant at the Z boson mass is extracted in a QCD analysis at NNLO using the inclusive jet cross sections in proton-proton collisions for the first time, and results in $ \alpha_\mathrm{S}(m_\mathrm{Z})= $ 0.1170 $ \pm $ 0.0014 (fit) $ \pm $ 0.0007 (model) $ \pm $ 0.0008 (scale) $ \pm $ 0.0001 (parametrisation). The QCD analysis is also performed at NLO, where the CMS measurement of the normalised triple-differential top quark-antiquark production cross section at $ \sqrt{s}= $ 13 TeV is used in addition. In this analysis, the PDFs, the values of the strong coupling constant, and of the top quark pole mass $ m_\mathrm{t}^{\text{pole}} $ are extracted simultaneously with $ \alpha_\mathrm{S}(m_\mathrm{Z}) = $ 0.1188 $ \pm $ 0.0017 (fit) $ \pm $ 0.0004 (model) $ \pm $ 0.0025 (scale) $ \pm $ 0.0001 (parameterisation), dominated by the scale uncertainty, and $ m_\mathrm{t}^{\text{pole}} = $ 170.4 $ \pm $ 0.6 (fit) $ \pm $ 0.1 (model) $ \pm $ 0.1 (scale) $ \pm $ 0.1 (parameterisation) GeV. The resulting values of $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ agree with the world average and the previous CMS results using the jet measurements. The value of $ m_\mathrm{t}^{\text{pole}} $ agrees well with the result of the previous CMS analysis using the triple-differential cross section of the top quark-antiquark pair production. Although the inclusive jet production is not directly sensitive to $ m_\mathrm{t}^{\text{pole}} $, the resulting value is improved by the additional constraint on the gluon distribution and on $ \alpha_\mathrm{S}(m_\mathrm{Z}) $ provided by the jet measurements. Furthermore, an alternative QCD analysis is performed with the same data, where the standard model Lagrangian is modified by the introduction of effective terms related to 4-quark contact interactions. In the analysis, the Wilson coefficients for the contact interactions are extracted for different values assumed for the scale $ \Lambda $ of the new interaction. The results are translated into a 95% confidence level exclusion limit for the left-handed model with constructive interference, corresponding to $ \Lambda > $ 24 TeV. These results are compatible with the standard model and the previous limits obtained at the LHC using jet production. The advantage of the present approach is the simultaneous extraction of PDFs, thereby mitigating possible bias in the interpretation of the measurements in terms of physics beyond the standard model. Tabulated results are provided in the HEPData record for this analysis [94]. |
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Compact Muon Solenoid LHC, CERN |