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| CMS-PAS-SMP-21-009 | ||
| Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $\sqrt{s} = $ 5.02 TeV | ||
| CMS Collaboration | ||
| July 2021 | ||
| Abstract: The inclusive jet cross section is differentially measured in bins 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 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, across the kinematic range 0.06 $ < p_{\mathrm{T}} < $ 1 TeV. The jet cross section is unfolded from detector-level to particle-level using the measured jet response and resolution. The measurement is compared with perturbative QCD predictions, calculated at both next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). The prediction is corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization and factorization scale $\mu$. The NNLO prediction reproduces the measured cross section better than NLO does, and the NNLO prediction is also significantly less dependent on the choice of $\mu$. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
The merged detector-level spectrum, with colors indicating which part of the spectrum comes from which trigger. The vertical axis is the number of observed jets divided by the product of effective luminosity and bin width. |
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Figure 2:
The ${p_{\mathrm {T}}}$ distribution at detector-level of the inclusive jet cross section, for the four rapidity bins, is shown for the data (points) and the PYTHIA 8 prediction (histogram) normalized to the total cross section of the data. The error bars show the statistical uncertainties on the data |
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Figure 3:
The nonperturbative corrections to the fixed-order QCD calculation of inclusive-jet cross section, as a function of jet ${p_{\mathrm {T}}}$, for the most central rapidity bin. Dashed lines show the prediction of corrections using HERWIG 7 (lower line) and PYTHIA 8 (higher 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 bin. The color scale reports the square of the effective number of jets in data. |
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Figure 4-a:
The covariance matrices of the observed detector-level jet ${p_{\mathrm {T}}}$ for the four rapidity bin. The color scale reports the square of the effective number of jets in data. |
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Figure 4-b:
The covariance matrices of the observed detector-level jet ${p_{\mathrm {T}}}$ for the four rapidity bin. The color scale reports the square of the effective number of jets in data. |
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Figure 4-c:
The covariance matrices of the observed detector-level jet ${p_{\mathrm {T}}}$ for the four rapidity bin. The color scale reports the square of the effective number of jets in data. |
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Figure 4-d:
The covariance matrices of the observed detector-level jet ${p_{\mathrm {T}}}$ for the four rapidity bin. The color scale reports the square of the effective number of jets in data. |
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Figure 5:
The response matrices, the number of jets in a bin of detector-level pt that originate from jets in a bin of particle-level ${p_{\mathrm {T}}}$, for the four rapidity bins. The color scale reports the square of the number of toy-MC jets. |
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Figure 5-a:
The response matrices, the number of jets in a bin of detector-level pt that originate from jets in a bin of particle-level ${p_{\mathrm {T}}}$, for the four rapidity bins. The color scale reports the square of the number of toy-MC jets. |
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Figure 5-b:
The response matrices, the number of jets in a bin of detector-level pt that originate from jets in a bin of particle-level ${p_{\mathrm {T}}}$, for the four rapidity bins. The color scale reports the square of the number of toy-MC jets. |
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Figure 5-c:
The response matrices, the number of jets in a bin of detector-level pt that originate from jets in a bin of particle-level ${p_{\mathrm {T}}}$, for the four rapidity bins. The color scale reports the square of the number of toy-MC jets. |
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Figure 5-d:
The response matrices, the number of jets in a bin of detector-level pt that originate from jets in a bin of particle-level ${p_{\mathrm {T}}}$, for the four rapidity bins. The color scale reports the square of the number of toy-MC jets. |
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Figure 6:
JEC, JER, and total systematic uncertainties in unfolded cross sections as a function of transverse momentum and rapidity. The total systematic uncertainty includes also the luminosity, jet identification and trigger turn-on uncertainties. |
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Figure 7:
The unfolded measured particle-level inclusive jet cross sections as a function of jet ${p_{\mathrm {T}}}$ for the four rapidity regions, overlaid with the NLO perturbative QCD prediction, using the CT14nlo PDF set, with $\mu _R=\mu _F=H_{\mathrm{T}}$, and corrected for nonperturbative effects. The yellow band shows the experimental systematic uncertainty and the red band shows the theoretical systematic uncertainty. |
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Figure 8:
Ratio of cross sections to the NLO theoretical prediction, using the CT14nlo PDF set, with $\mu = p_{\mathrm{T}}$. The yellow band shows the total experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and individual sources of theoretical uncertainty are shown with lines. |
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Figure 9:
Ratio of cross sections to the NLO theoretical prediction, using the CT14nlo PDF set, with $\mu = H_{\mathrm{T}}$. The yellow band shows the total experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and individual sources of theoretical uncertainty are shown with lines. |
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Figure 10:
Ratio of cross sections to the NNLO theoretical prediction, using the CT14nnlo PDF set, with $\mu = H_{\mathrm{T}}$. The yellow band shows the total experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and individual sources of theoretical uncertainty are shown with lines. |
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Figure 11:
Ratio of cross sections to the NNLO theoretical prediction, using the NNPDF31nnlo PDF set, with $\alpha _S(M_{\mathrm{Z}}) = $0.120 and $\mu = H_{\mathrm{T}}$. The yellow band shows the total experimental uncertainty, the hashed red band shows the total theoretical uncertainty, and individual sources of theoretical uncertainty are shown with lines. |
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Figure 12:
The effect of $\alpha _S$ variation. The NNLO theoretical cross section predictions using the NNPDF31nnlo PDF with $\mu =H_{\mathrm{T}}$, calculated for different choices of $\alpha _S$, are divided by the benchmark NNLO prediction for $\alpha _S = $0.118 and the same choice of PDF set and renormalization and factorization scales. Also shown is the experimental unfolded measurement divided by the same benchmark prediction. |
| Tables | |
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Table 1:
The ${p_{\mathrm {T}}}$ binning for the detector-level spectra (all rapidities) and the particle-level spectra. |
| Summary |
| The measurement of the double-differential inclusive jet cross section in proton-proton collisions at 5.02 TeV has been presented. The measurements agree well with standard model predictions. The best agreement is found when the prediction is a NNLO QCD calculation with the renormalization and factorization scale choice $\mu = \mu_R = \mu_F = H_{\mathrm{T}}$, and using the NNPDF31nnlo PDF set with $\alpha_S(M_{\mathrm{Z}})=$ 0.120. Going from the NLO to NNLO prediction reduces the scale systematic uncertainty at high ${p_{\mathrm{T}}}$, but increases it at low ${p_{\mathrm{T}}}$. The scale systematic uncertainty also increases when going from $\mu = {p_{\mathrm{T}}}$ to $\mu = H_{\mathrm{T}}$ in the NLO case. The effect of changing the scale is not very large for the NNLO calculation, and the scale systematic decreases at low-${p_{\mathrm{T}}}$ going from $\mu = {p_{\mathrm{T}}}$ to $\mu = H_{\mathrm{T}}$. The uncertainty on the cross section due to PDFs is significantly reduced by choosing the NNPDF31nnlo family of PDF sets. For this PDF set, the choice of strong coupling constant $\alpha_S(M_{\mathrm{Z}})=$ 0.120 gives a cross section that is closer to the experimental results, compared to a benchmark of $\alpha_S(M_{\mathrm{Z}})=$ 0.118. The demonstrated sensitivity of the comparisons to the different values of $\alpha_S$ could lead to a measurement of the strong coupling constant based on these results. |
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