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| CMS-SMP-21-009 ; CERN-EP-2023-219 | ||
| Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $ \sqrt{s} = $ 5.02 TeV | ||
| CMS Collaboration | ||
| 21 January 2024 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: The inclusive jet cross section is measured as a function of jet transverse momentum $ p_{\mathrm{T}} $ and rapidity $ y $. The measurement is performed using proton-proton collision data at $ \sqrt{s} = $ 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4$\,\text{pb}^{-1}$. The jets are reconstructed with the anti-$ k_{\mathrm{T}} $ algorithm using a distance parameter of $ R= $ 0.4, within the rapidity interval $ |y| < $ 2, and across the kinematic range 0.06 $ < p_{\mathrm{T}} < $ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $ \alpha_\mathrm{S} $. | ||
| Links: e-print arXiv:2401.11355 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Detector-level cross section obtained after merging the contributions from the three triggers, normalized to their respective integrated luminosities. |
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Figure 2:
Detector-level inclusive jet cross section, differential in $ p_{\mathrm{T}} $, for the four rapidity bins, for the data (points) and the PYTHIA8 prediction (line) normalized to the total cross section of the data. The lower panels show the ratio of the two distributions. The error bars show the statistical uncertainties in the data. |
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Figure 3:
Nonperturbative correction to the fixed-order QCD calculation of inclusive jet cross section, as a function of jet $ p_{\mathrm{T}} $, for the $ |y| < $ 0.5 rapidity bin. Dashed lines show the prediction of corrections using HERWIG 7 (lower line) and PYTHIA8 (upper line). The central solid line shows the average NP correction used in this analysis, with an uncertainty defined by the extreme predictions. The NP corrections are similar in shape and value for the other rapidity bins. |
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Figure 4:
The covariance matrices of the observed detector-level jet $ p_{\mathrm{T}} $ for the four rapidity bins. The color scale reports the product of the effective number of jets in the respective $ p_{\mathrm{T}} $ bin combinations. |
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Figure 4-a:
The covariance matrices of the observed detector-level jet $ p_{\mathrm{T}} $ for the four rapidity bins. The color scale reports the product of the effective number of jets in the respective $ p_{\mathrm{T}} $ bin combinations. |
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Figure 4-b:
The covariance matrices of the observed detector-level jet $ p_{\mathrm{T}} $ for the four rapidity bins. The color scale reports the product of the effective number of jets in the respective $ p_{\mathrm{T}} $ bin combinations. |
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Figure 4-c:
The covariance matrices of the observed detector-level jet $ p_{\mathrm{T}} $ for the four rapidity bins. The color scale reports the product of the effective number of jets in the respective $ p_{\mathrm{T}} $ bin combinations. |
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Figure 4-d:
The covariance matrices of the observed detector-level jet $ p_{\mathrm{T}} $ for the four rapidity bins. The color scale reports the product of the effective number of jets in the respective $ p_{\mathrm{T}} $ bin combinations. |
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Figure 5:
The response matrices for the four rapidity bins. Each 2D-histogram bin contains the number of pseudo-experiment jets that are generated in the particular particle-level $ p_{\mathrm{T}} $ bin and that are reconstructed in the corresponding detector-level $ p_{\mathrm{T}} $ bin. |
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Figure 5-a:
The response matrices for the four rapidity bins. Each 2D-histogram bin contains the number of pseudo-experiment jets that are generated in the particular particle-level $ p_{\mathrm{T}} $ bin and that are reconstructed in the corresponding detector-level $ p_{\mathrm{T}} $ bin. |
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Figure 5-b:
The response matrices for the four rapidity bins. Each 2D-histogram bin contains the number of pseudo-experiment jets that are generated in the particular particle-level $ p_{\mathrm{T}} $ bin and that are reconstructed in the corresponding detector-level $ p_{\mathrm{T}} $ bin. |
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Figure 5-c:
The response matrices for the four rapidity bins. Each 2D-histogram bin contains the number of pseudo-experiment jets that are generated in the particular particle-level $ p_{\mathrm{T}} $ bin and that are reconstructed in the corresponding detector-level $ p_{\mathrm{T}} $ bin. |
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Figure 5-d:
The response matrices for the four rapidity bins. Each 2D-histogram bin contains the number of pseudo-experiment jets that are generated in the particular particle-level $ p_{\mathrm{T}} $ bin and that are reconstructed in the corresponding detector-level $ p_{\mathrm{T}} $ bin. |
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Figure 6:
The JEC, JER, and total systematic uncertainties in unfolded cross sections as functions of transverse momentum and rapidity. The total systematic uncertainty includes also the luminosity, jet identification and trigger efficiency uncertainties. |
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Figure 7:
The unfolded measured particle-level inclusive jet cross sections as functions of jet $ p_{\mathrm{T}} $ in the four rapidity bins (markers), compared to the NLO perturbative QCD prediction (red histogram), using the CT14NLO PDF set, with $ \mu_\mathrm{R}=\mu_\mathrm{F}=H_{\mathrm{T}} $, and corrected for the NP effects. The yellow (red) band shows the experimental (theoretical) systematic uncertainty. Statistical uncertainties are included but are barely visible. |
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Figure 8:
Ratios (points) of the unfolded measured cross sections to the NLO theoretical predictions, using the CT14NLO PDF set, with $ \mu = p_{\mathrm{T}} $. The vertical error bars show the statistical experimental uncertainty, the yellow band shows the systematic experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and the individual sources of theoretical uncertainty are shown with colored lines. |
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Figure 9:
Ratios (points) of the unfolded measured cross sections to the NLO theoretical predictions, using the CT14NLO PDF set, with $ \mu= H_{\mathrm{T}} $. The vertical error bars show the statistical experimental uncertainty, the yellow band shows the systematic experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and the individual sources of theoretical uncertainty are shown with colored lines. |
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Figure 10:
Ratios (points) of the unfolded measured cross sections to the NNLO theoretical predictions, using the CT14NNLO PDF set, with $ \mu=H_{\mathrm{T}} $. The vertical error bars show the statistical experimental uncertainty, the yellow band shows the systematic experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and the individual sources of theoretical uncertainty are shown with colored lines. |
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Figure 11:
Ratios (points) of the unfolded measured cross sections to the NNLO theoretical predictions, using the NNPDF31NNLO PDF set, with $ \alpha_\mathrm{S}(m_{{\mathrm{Z}} })= $ 0.118 and $ \mu=H_{\mathrm{T}} $. The vertical error bars show the statistical experimental uncertainty, the yellow band shows the systematic experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and the individual sources of theoretical uncertainty are shown with colored lines. |
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Figure 12:
The effect of $ \alpha_\mathrm{S}(m_{{\mathrm{Z}} }) $ variation. The NNLO theoretical cross section predictions using the NNPDF31NNLO PDF with $ \mu=H_{\mathrm{T}} $, calculated for different choices of $ \alpha_\mathrm{S} $ (0.108, 0.110, 0.112, 0.114, 0.116, 0.117, 0.118, 0.119, 0.120, 0.122, and 0.124), are divided by the benchmark NNLO prediction for $ \alpha_\mathrm{S} = $ 0.118 and the same choice of PDF set, $ \mu_\mathrm{R} $, and $ \mu_\mathrm{F} $. Also shown is the experimental unfolded measurement divided by the same benchmark prediction. The width of the unity line corresponds to the statistical uncertainty from the MC integration for the determination of the NNLO prediction. The error bars on the unfolded data correspond to the total experimental statistical and systematic uncertainty added in quadrature. |
| Tables | |
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Table 1:
The edges of the $ p_{\mathrm{T}} $ bins for the detector-level spectra (all rapidities) and for the particle-level spectra (per rapidity bin). |
| Summary |
| The double-differential inclusive jet cross section in proton-proton collisions at 5.02 TeV was measured in the rapidity interval $ |y| < $ 2, and for the transverse momentum range 0.06 $ < p_{\mathrm{T}} < $ 1 TeV. The achieved experimental systematic uncertainty is about 5% across most $ p_{\mathrm{T}} $ ranges for all $ |y| $. The next-to-leading order (NLO) perturbative quantum chromodynamics calculations agree better with the observations if the renormalization and factorization scales ($ \mu $) equal $ H_{\mathrm{T}} $, the scalar sum of the transverse momentum ($ p_{\mathrm{T}} $) of the partons in each event. The energy scale systematic uncertainty also increases when the scale is changed from $ \mu=p_{\mathrm{T}} $ of each jet to $ \mu=H_{\mathrm{T}} $ in the NLO case. Changing the order of the perturbative calculation from the NLO to next-to-NLO (NNLO) reduces the scale systematic uncertainty at high $ p_{\mathrm{T}} $, but increases it at low $ p_{\mathrm{T}} $. The effect of changing the scale is not very large for the NNLO calculation, and the scale systematic decreases at low $ p_{\mathrm{T}} $ when the scale is changed from $ \mu=p_{\mathrm{T}} $ to $ \mu=H_{\mathrm{T}} $. The uncertainty in the predicted cross section due to the parton distribution functions is significantly reduced by choosing the NNPDF31NNLO set. The measurement is consistent with the standard model expectation, even when the latter is determined with the low uncertainty provided by the NNLO calculation. |
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