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| CMS-PAS-SMP-24-010 | ||
| Triple-differential measurement of Z+jet production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-03-02 | ||
| Abstract: A measurement is presented of the differential production cross section of $ \mathrm{Z}(\to\mu\mu) $+jet events using proton-proton collision data recorded at a center-of-mass energy of 13 TeV by the CMS experiment at the CERN LHC. The data, collected in the years 2016--2018, correspond to an integrated luminosity of 138 fb$ ^{-1} $. The cross section is measured triple-differentially as a function of the transverse momentum of the muon pair, half of the absolute rapidity separation between the muon pair and the leading jet, and the boost in rapidity of their center-of-mass system in the laboratory frame. This choice of observables ensures sensitivity to the scattering angle in the center-of-mass system and the fractional momenta of the interacting partons. After unfolding for detector effects in all three dimensions simultaneously, the results are compared with predictions at next-to-next-to-leading order in perturbative quantum chromodynamics corrected for electroweak and nonperturbative effects. The presented measurement provides valuable information towards the partonic structure of the proton. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Illustration of the $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ event topology and the phase space binning in the $ (y_\text{b},y^*) $ kinematic plane. The Z boson and the leading jet are represented in the laboratory frame. Illustration courtesy of [16]. |
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Figure 2:
Comparison of data and simulation at reconstruction level for the whole unrolled three-dimensional phase space in $ p_{\mathrm{T}}^\mathrm{Z} $, $ y_\text{b} $, and $ y^* $. The lower panel shows the ratio of data to simulation. The error bars on the data points represent the statistical uncertainties, while the gray band indicates the total uncertainty in the simulation. The gray dotted and black dashed vertical lines indicate the bin borders in $ y_\text{b} $ and $ y^* $, respectively. The unrolling in $ (y_\text{b},y^*) $ is illustrated below the plot. Each bin in $ (y_\text{b},y^*) $ contains the respective series of $ p_{\mathrm{T}}^\mathrm{Z} $ bins. |
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Figure 2-a:
Comparison of data and simulation at reconstruction level for the whole unrolled three-dimensional phase space in $ p_{\mathrm{T}}^\mathrm{Z} $, $ y_\text{b} $, and $ y^* $. The lower panel shows the ratio of data to simulation. The error bars on the data points represent the statistical uncertainties, while the gray band indicates the total uncertainty in the simulation. The gray dotted and black dashed vertical lines indicate the bin borders in $ y_\text{b} $ and $ y^* $, respectively. The unrolling in $ (y_\text{b},y^*) $ is illustrated below the plot. Each bin in $ (y_\text{b},y^*) $ contains the respective series of $ p_{\mathrm{T}}^\mathrm{Z} $ bins. |
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Figure 2-b:
Comparison of data and simulation at reconstruction level for the whole unrolled three-dimensional phase space in $ p_{\mathrm{T}}^\mathrm{Z} $, $ y_\text{b} $, and $ y^* $. The lower panel shows the ratio of data to simulation. The error bars on the data points represent the statistical uncertainties, while the gray band indicates the total uncertainty in the simulation. The gray dotted and black dashed vertical lines indicate the bin borders in $ y_\text{b} $ and $ y^* $, respectively. The unrolling in $ (y_\text{b},y^*) $ is illustrated below the plot. Each bin in $ (y_\text{b},y^*) $ contains the respective series of $ p_{\mathrm{T}}^\mathrm{Z} $ bins. |
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Figure 3:
Detector response matrix for the unrolled three-dimensional phase space of $ p_{\mathrm{T}}^\mathrm{Z} $, $ y_\text{b} $, and $ y^* $. The $ x $- and $ y $-axes correspond to the global bin indices $ i^\text{gen} $ at particle and $ i^\text{rec} $ at reconstruction level, respectively. The colored boxes indicate the probability to reconstruct an event in the reconstruction bin number $ i^\text{rec} $, given it had been generated in the generation bin number $ i^\text{gen} $. Everything not on the principal diagonal corresponds to event migrations. |
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Figure 4:
Systematic uncertainties of the unfolded $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ cross section as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper plot shows the uncertainties for a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. In the lower row the uncertainties are presented for a boosted (large $ y_\text{b} $, left) and a forward-backward topology (large $ y^* $, right) of the 2 $ \to $ 2 scattering process. Labels for the various uncertainty components are explained in the text. |
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Figure 4-a:
Systematic uncertainties of the unfolded $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ cross section as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper plot shows the uncertainties for a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. In the lower row the uncertainties are presented for a boosted (large $ y_\text{b} $, left) and a forward-backward topology (large $ y^* $, right) of the 2 $ \to $ 2 scattering process. Labels for the various uncertainty components are explained in the text. |
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Figure 4-b:
Systematic uncertainties of the unfolded $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ cross section as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper plot shows the uncertainties for a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. In the lower row the uncertainties are presented for a boosted (large $ y_\text{b} $, left) and a forward-backward topology (large $ y^* $, right) of the 2 $ \to $ 2 scattering process. Labels for the various uncertainty components are explained in the text. |
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Figure 4-c:
Systematic uncertainties of the unfolded $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ cross section as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper plot shows the uncertainties for a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. In the lower row the uncertainties are presented for a boosted (large $ y_\text{b} $, left) and a forward-backward topology (large $ y^* $, right) of the 2 $ \to $ 2 scattering process. Labels for the various uncertainty components are explained in the text. |
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Figure 5:
Subprocess decomposition at NNLO (left) and ratios ($ K $ factors, right) of the cross-section predictions from NNLOJET at NLO (green) and NNLO (blue) to LO (red) in perturbative QCD as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for two phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper row corresponds to a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. The lower row presents the results for a forward-backward topology with large rapidity separation $ y^* $ between the Z boson and the balancing jet. All predictions are based on the PDF4LHC21 PDF set at NNLO\@. The colored areas on the left correspond to the fractional cross sections with initial parton-parton combinations as given in the legend. Interference terms appearing in calculations beyond tree level can lead to negative parton-parton cross sections. The colored bands on the right indicate the uncertainty in a prediction based on scale variations as further described in the text. |
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Figure 5-a:
Subprocess decomposition at NNLO (left) and ratios ($ K $ factors, right) of the cross-section predictions from NNLOJET at NLO (green) and NNLO (blue) to LO (red) in perturbative QCD as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for two phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper row corresponds to a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. The lower row presents the results for a forward-backward topology with large rapidity separation $ y^* $ between the Z boson and the balancing jet. All predictions are based on the PDF4LHC21 PDF set at NNLO\@. The colored areas on the left correspond to the fractional cross sections with initial parton-parton combinations as given in the legend. Interference terms appearing in calculations beyond tree level can lead to negative parton-parton cross sections. The colored bands on the right indicate the uncertainty in a prediction based on scale variations as further described in the text. |
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Figure 5-b:
Subprocess decomposition at NNLO (left) and ratios ($ K $ factors, right) of the cross-section predictions from NNLOJET at NLO (green) and NNLO (blue) to LO (red) in perturbative QCD as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for two phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper row corresponds to a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. The lower row presents the results for a forward-backward topology with large rapidity separation $ y^* $ between the Z boson and the balancing jet. All predictions are based on the PDF4LHC21 PDF set at NNLO\@. The colored areas on the left correspond to the fractional cross sections with initial parton-parton combinations as given in the legend. Interference terms appearing in calculations beyond tree level can lead to negative parton-parton cross sections. The colored bands on the right indicate the uncertainty in a prediction based on scale variations as further described in the text. |
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Figure 5-c:
Subprocess decomposition at NNLO (left) and ratios ($ K $ factors, right) of the cross-section predictions from NNLOJET at NLO (green) and NNLO (blue) to LO (red) in perturbative QCD as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for two phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper row corresponds to a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. The lower row presents the results for a forward-backward topology with large rapidity separation $ y^* $ between the Z boson and the balancing jet. All predictions are based on the PDF4LHC21 PDF set at NNLO\@. The colored areas on the left correspond to the fractional cross sections with initial parton-parton combinations as given in the legend. Interference terms appearing in calculations beyond tree level can lead to negative parton-parton cross sections. The colored bands on the right indicate the uncertainty in a prediction based on scale variations as further described in the text. |
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Figure 5-d:
Subprocess decomposition at NNLO (left) and ratios ($ K $ factors, right) of the cross-section predictions from NNLOJET at NLO (green) and NNLO (blue) to LO (red) in perturbative QCD as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for two phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane. The upper row corresponds to a central back-to-back topology, where the Z boson and the balancing jet are scattered in opposite directions perpendicularly to the beam. The lower row presents the results for a forward-backward topology with large rapidity separation $ y^* $ between the Z boson and the balancing jet. All predictions are based on the PDF4LHC21 PDF set at NNLO\@. The colored areas on the left correspond to the fractional cross sections with initial parton-parton combinations as given in the legend. Interference terms appearing in calculations beyond tree level can lead to negative parton-parton cross sections. The colored bands on the right indicate the uncertainty in a prediction based on scale variations as further described in the text. |
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Figure 6:
Approximate EW corrections derived with SHERPA as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The corrections are calculated for pQCD at LO (blue) and including corrections for pQCD at NLO (orange). |
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Figure 6-a:
Approximate EW corrections derived with SHERPA as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The corrections are calculated for pQCD at LO (blue) and including corrections for pQCD at NLO (orange). |
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Figure 6-b:
Approximate EW corrections derived with SHERPA as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The corrections are calculated for pQCD at LO (blue) and including corrections for pQCD at NLO (orange). |
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Figure 6-c:
Approximate EW corrections derived with SHERPA as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The corrections are calculated for pQCD at LO (blue) and including corrections for pQCD at NLO (orange). |
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Figure 7:
Non-perturbative correction factors obtained from MC simulations using HERWIG 7 or SHERPA on top of LO or NLO pQCD predictions as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The NP correction factors with their respective uncertainties are obtained as described in the text from NLO-based MC simulations. |
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Figure 7-a:
Non-perturbative correction factors obtained from MC simulations using HERWIG 7 or SHERPA on top of LO or NLO pQCD predictions as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The NP correction factors with their respective uncertainties are obtained as described in the text from NLO-based MC simulations. |
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Figure 7-b:
Non-perturbative correction factors obtained from MC simulations using HERWIG 7 or SHERPA on top of LO or NLO pQCD predictions as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The NP correction factors with their respective uncertainties are obtained as described in the text from NLO-based MC simulations. |
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Figure 7-c:
Non-perturbative correction factors obtained from MC simulations using HERWIG 7 or SHERPA on top of LO or NLO pQCD predictions as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The NP correction factors with their respective uncertainties are obtained as described in the text from NLO-based MC simulations. |
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Figure 8:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the MC prediction of AMC@NLO FXFX+PYTHIAviii as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The alternative signal MC sample based on POWHEG MINNLOPS+PYTHIAviii is shown as well. |
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Figure 8-a:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the MC prediction of AMC@NLO FXFX+PYTHIAviii as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The alternative signal MC sample based on POWHEG MINNLOPS+PYTHIAviii is shown as well. |
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Figure 8-b:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the MC prediction of AMC@NLO FXFX+PYTHIAviii as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The alternative signal MC sample based on POWHEG MINNLOPS+PYTHIAviii is shown as well. |
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Figure 8-c:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the MC prediction of AMC@NLO FXFX+PYTHIAviii as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. The alternative signal MC sample based on POWHEG MINNLOPS+PYTHIAviii is shown as well. |
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Figure 9:
Unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production for each $ (y_\text{b},y^*) $ bin as a function of $ p_{\mathrm{T}}^\mathrm{Z} $. The data points are compared with predictions at NNLO accuracy corrected for EW and NP effects. For improved visibility the points and curves are shifted by constant factors as indicated in the legend. |
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Figure 10:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the prediction at NNLO accuracy corrected for EW and NP effects as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for each $ (y_\text{b},y^*) $ bin. For improved visibility the points and curves are offset by constant values as indicated in the legend. |
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Figure 11:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the prediction at NNLO accuracy corrected for EW and NP effects as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. Predictions using alternative PDF sets are shown as well. |
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Figure 11-a:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the prediction at NNLO accuracy corrected for EW and NP effects as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. Predictions using alternative PDF sets are shown as well. |
png pdf |
Figure 11-b:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the prediction at NNLO accuracy corrected for EW and NP effects as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. Predictions using alternative PDF sets are shown as well. |
png pdf |
Figure 11-c:
Ratio of the unfolded cross section of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production to the prediction at NNLO accuracy corrected for EW and NP effects as a function of $ p_{\mathrm{T}}^\mathrm{Z} $ for the same three phase space intervals in the $ (y_\text{b},y^*) $ kinematic plane as described in Fig. 4. Predictions using alternative PDF sets are shown as well. |
| Tables | |
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Table 1:
The bin borders in $ p_{\mathrm{T}}^\mathrm{Z} $. The central binning scheme (C) is used in the central rapidity regions. At the edge of the $ (y_\text{b},y^*) $ plane, the edge binning scheme (E) is used, merging bins due to limited statistical precision. An extra wide binning scheme (X) is used for the highest $ y^* $ bin. Due to the limited number of events, the extra binning truncates the binning at 250 GeV. |
| Summary |
| A first measurement of $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ production cross sections is presented, where the data, recorded in the years 2016--2018 and corresponding to an integrated luminosity of 138 fb$ ^{-1} $, have been unfolded for detector effects simultaneously in three dimensions. The three observables were chosen to be the transverse momentum of the Z boson, $ p_{\mathrm{T}}^\mathrm{Z} $, as reconstructed from the decay muons, the boost of the center-of-mass system, $ y_\text{b} $, of the 2 $ \to $ 2 scattering process with the Z boson and a balancing jet in the final state, and half of their absolute separation in rapidity. These quantities correlate with the energy scale of the collision process, the initial-state parton momenta $ x_1 $ and $ x_2 $, and the scattering angle in the partonic center-of-mass system and hence are very advantageous for comparisons to theory. For $ p_{\mathrm{T}}^\mathrm{Z} > $ 50 GeV up to 1 TeV the $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ cross section has been measured with a total experimental uncertainty ranging from 1.5% in the central detector region up to 5% in the boosted regime of $ y_\text{b} > $ 1. The uncertainty is limited by multiple different systematic effects in the central region, while at larger $ p_{\mathrm{T}}^\mathrm{Z} $ or $ y_\text{b} $ the largest contributions stems from limited event counts. For $ p_{\mathrm{T}}^\mathrm{Z} < $ 50 GeV the dominant uncertainty is always given by the jet energy scale that comes into play through the minimum jet $ p_{\mathrm{T}} $ requirement when defining the leading-$ p_{\mathrm{T}} $ jet in the event. Going to larger rapidity separations $ y^* $, event numbers drop dramatically and the reach in $ p_{\mathrm{T}}^\mathrm{Z} $ is much more limited. The experimental uncertainty, combined from the statistical uncertainty and the jet energy scale and luminosity determination, doubles to 10% or more. Within uncertainties, the $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ triple-differential production cross section is well described, in particular by the Monte Carlo event generator POWHEG MINNLOPS+PYTHIAviii. In comparison with accurate predictions at next-to-next-to-leading order in perturbative quantum chromodynamics, complemented with electroweak and nonperturbative corrections, an overall agreement is found, including the strong decrease in cross section for larger $ y^* $. This suppression can be traced back to effects of the initial parton distributions in the proton disfavoring this kinematic regime for all the parton-parton processes available already at leading order. Quark-quark scattering becomes possible only at next-to-leading order. Remaining differences provide valuable input to further constrain the partonic structure of the proton. Notably, the very different parton-parton luminosities in the triple-differential $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ as compared with dijet production is very promising with regards to future combined determinations of parton distributions and the strong coupling constant from fits to LHC dijet and $ \mathrm{Z}/\gamma^*(\to\mu\mu)+\text{jet} $ data. |
| References | ||||
| 1 | D0 Collaboration | Measurement of differential $ \mathrm{Z} /\gamma^{*} $ + jet + $ X $ cross sections in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at $ \sqrt{s}= $ 1.96 TeV | PLB 669 (2008) 278 | 0808.1296 |
| 2 | D0 Collaboration | Measurements of differential cross sections of $ \mathrm{Z} /\gamma^{*} $ + jets + $ X $ events in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at $ \sqrt{s}= $ 1.96 TeV | PLB 678 (2009) 45 | 0903.1748 |
| 3 | D0 Collaboration | Measurement of $ {\mathrm{Z}}/\gamma^* $ + jet + $ x $ angular distributions in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at $ \sqrt{s}= $ 1.96 TeV | PLB 682 (2010) 370 | 0907.4286 |
| 4 | CDF Collaboration | Measurement of differential production cross sections for $ {\mathrm{Z}}/\gamma^* $ bosons in association with jets in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at $ \sqrt{s}= $ 1.96 TeV | PRD 91 (2015) 012002 | 1409.4359 |
| 5 | CMS Collaboration | Measurements of jet multiplicity and differential production cross sections of Z+jets events in proton-proton collisions at $ \sqrt{s}= $ 7 TeV | PRD 91 (2015) 052008 | CMS-SMP-12-017 1408.3104 |
| 6 | CMS Collaboration | Measurements of differential production cross sections for a Z boson in association with jets in $ {\mathrm{p}\mathrm{p}} $ collisions at $ \sqrt{s}= $ 8 TeV | JHEP 04 (2017) 022 | CMS-SMP-14-013 1611.03844 |
| 7 | CMS Collaboration | Measurement of differential cross sections for Z boson production in association with jets in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | EPJC 78 (2018) 965 | CMS-SMP-16-015 1804.05252 |
| 8 | ATLAS Collaboration | Measurement of the inclusive cross-section for the production of jets in association with a Z boson in proton-proton collisions at 8 TeV using the ATLAS detector | EPJC 79 (2019) 847 | 1907.06728 |
| 9 | ATLAS Collaboration | Cross-section measurements for the production of a Z boson in association with high-transverse-momentum jets in pp collisions at $ \sqrt{s}= $ 13 TeV with the ATLAS detector | JHEP 06 (2023) 080 | 2205.02597 |
| 10 | CMS Collaboration | Measurement of differential cross sections for the production of a Z boson in association with jets in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | PRD 108 (2023) 052004 | CMS-SMP-19-009 2205.02872 |
| 11 | ATLAS Collaboration | Simultaneous unbinned differential cross-section measurement of twenty-four Z+jets kinematic observables with the ATLAS detector | PRL 133 (2024) 261803 | 2405.20041 |
| 12 | T.-J. Hou et al. | New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC | PRD 103 (2021) 014013 | 1912.10053 |
| 13 | ATLAS Collaboration | Determination of the parton distribution functions of the proton from ATLAS measurements of differential $ \mathrm{W}^{\pm} $ and Z boson production in association with jets | JHEP 07 (2021) 223 | 2101.05095 |
| 14 | NNPDF Collaboration | The path to proton structure at 1\% accuracy | EPJC 82 (2022) 428 | 2109.02653 |
| 15 | T. Cridge, L. A. Harland-Lang, and R. S. Thorne | The impact of LHC jet and $ \mathrm{Z} p_\mathrm{T} $ data at up to approximate N$ ^3 $LO order in the MSHT global PDF fit | EPJC 84 (2024) 446 | 2312.12505 |
| 16 | M. J. Schnepf | Dynamic Provision of Heterogeneous Computing Resources for Computation- and Data-intensive Particle Physics Analyses | PhD thesis, Karlsruhe Institute of Technology (KIT), 2022 link |
|
| 17 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | |
| 18 | CMS Collaboration | Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | JINST 15 (2020) P10017 | CMS-TRG-17-001 2006.10165 |
| 19 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 20 | CMS Collaboration | Performance of the CMS high-level trigger during LHC \mboxRun 2 | JINST 19 (2024) P11021 | CMS-TRG-19-001 2410.17038 |
| 21 | J. Alwall et al. | The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations | JHEP 07 (2014) 079 | 1405.0301 |
| 22 | P. Artoisenet, R. Frederix, O. Mattelaer, and R. Rietkerk | Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations | JHEP 03 (2013) 015 | 1212.3460 |
| 23 | S. Frixione and B. R. Webber | Matching NLO QCD computations and parton shower simulations | JHEP 06 (2002) 029 | hep-ph/0204244 |
| 24 | R. Frederix and S. Frixione | Merging meets matching in MC@NLO | JHEP 12 (2012) 061 | 1209.6215 |
| 25 | K. Melnikov and F. Petriello | Electroweak gauge boson production at hadron colliders through $ \mathcal{O}({\alpha_\mathrm{S}^2}) $ | PRD 74 (2006) 114017 | hep-ph/0609070 |
| 26 | R. Gavin, Y. Li, F. Petriello, and S. Quackenbush | FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order | Comput. Phys. Commun. 182 (2011) 2388 | 1011.3540 |
| 27 | R. Gavin, Y. Li, F. Petriello, and S. Quackenbush | W physics at the LHC with FEWZ 2.1 | Comput. Phys. Commun. 184 (2013) 208 | 1201.5896 |
| 28 | Y. Li and F. Petriello | Combining QCD and electroweak corrections to dilepton production in FEWZ | PRD 86 (2012) 094034 | 1208.5967 |
| 29 | P. Nason | A new method for combining NLO QCD with shower Monte Carlo algorithms | JHEP 11 (2004) 040 | hep-ph/0409146 |
| 30 | S. Frixione, P. Nason, and C. Oleari | Matching NLO QCD computations with parton shower simulations: the POWHEG method | JHEP 11 (2007) 070 | 0709.2092 |
| 31 | S. Alioli, P. Nason, C. Oleari, and E. Re | A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG box | JHEP 06 (2010) 043 | 1002.2581 |
| 32 | E. Re | Single-top $ {\mathrm{W}\mathrm{t}} $-channel production matched with parton showers using the POWHEG method | EPJC 71 (2011) 1547 | 1009.2450 |
| 33 | S. Alioli, P. Nason, C. Oleari, and E. Re | NLO single-top production matched with shower in POWHEG: $ s $- and $ t $-channel contributions | JHEP 09 (2009) 111 | 0907.4076 |
| 34 | S. Frixione, G. Ridolfi, and P. Nason | A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction | JHEP 09 (2007) 126 | 0707.3088 |
| 35 | M. Czakon and A. Mitov | TOP++: a program for the calculation of the top-pair cross-section at hadron colliders | Comput. Phys. Commun. 185 (2014) 2930 | 1112.5675 |
| 36 | J. Campbell, T. Neumann, and Z. Sullivan | Single-top-quark production in the $ t $-channel at NNLO | JHEP 02 (2021) 040 | 2012.01574 |
| 37 | N. Kidonakis | Two-loop soft anomalous dimensions for single top quark associated production with a $ \mathrm{W^-} $ or $ \mathrm{H}^{-} $ | PRD 82 (2010) 054018 | 1005.4451 |
| 38 | N. Kidonakis | Top quark production | in Proc. Helmholtz International Summer School on Physics of Heavy Quarks and Hadrons (): Dubna, Russia, July 15--28,.. [DESY-PROC-2013-03], 2013 HQ 201 (2013) 3 |
1311.0283 |
| 39 | T. Melia, P. Nason, R. Röntsch, and G. Zanderighi | $ {\mathrm{W^+}\mathrm{W^-}} $, $ {\mathrm{W}\mathrm{Z}} $ and $ {\mathrm{Z}\mathrm{Z}} $ production in the POWHEG box | JHEP 11 (2011) 078 | 1107.5051 |
| 40 | T. Sjöstrand et al. | An introduction to PYTHIA8.2 | Comput. Phys. Commun. 191 (2015) 159 | 1410.3012 |
| 41 | CMS Collaboration | Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements | EPJC 80 (2020) 4 | CMS-GEN-17-001 1903.12179 |
| 42 | J. Butterworth et al. | PDF4LHC recommendations for LHC \mboxRun 2 | JPG 43 (2016) 023001 | 1510.03865 |
| 43 | S. Dulat et al. | New parton distribution functions from a global analysis of quantum chromodynamics | PRD 93 (2016) 033006 | 1506.07443 |
| 44 | L. A. Harland-Lang, A. D. Martin, P. Motylinski, and R. S. Thorne | Parton distributions in the LHC era: MMHT 2014 PDFs | EPJC 75 (2015) 204 | 1412.3989 |
| 45 | NNPDF Collaboration | Parton distributions for the LHC run II | JHEP 04 (2015) 040 | 1410.8849 |
| 46 | GEANT4 Collaboration | GEANT 4---a simulation toolkit | NIM A 506 (2003) 250 | |
| 47 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 48 | M. Cacciari, G. P. Salam, and G. Soyez | The anti-$ k_{\mathrm{T}} $ jet clustering algorithm | JHEP 04 (2008) 063 | 0802.1189 |
| 49 | M. Cacciari, G. P. Salam, and G. Soyez | FASTJET user manual | EPJC 72 (2012) 1896 | 1111.6097 |
| 50 | CMS Collaboration | Pileup mitigation at CMS in 13 TeV data | JINST 15 (2020) P09018 | CMS-JME-18-001 2003.00503 |
| 51 | CMS Collaboration | Jet energy scale and resolution in the CMS experiment in $ {\mathrm{p}\mathrm{p}} $ collisions at 8 TeV | JINST 12 (2017) P02014 | CMS-JME-13-004 1607.03663 |
| 52 | A. Bodek et al. | Extracting muon momentum scale corrections for hadron collider experiments | EPJC 72 (2012) 2194 | 1208.3710 |
| 53 | CMS Collaboration | Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV | JINST 13 (2018) P06015 | CMS-MUO-16-001 1804.04528 |
| 54 | Particle Data Group , R. L. Workman et al. | Review of particle physics | Prog. Theor. Exp. Phys. 2022 (2022) 083C01 | |
| 55 | CMS Collaboration | Performance of CMS muon reconstruction in $ {\mathrm{p}\mathrm{p}} $ collision events at $ \sqrt{s}= $ 7 TeV | JINST 7 (2012) P10002 | CMS-MUO-10-004 1206.4071 |
| 56 | CMS Collaboration | Performance of the CMS muon trigger system in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | JINST 16 (2021) P07001 | CMS-MUO-19-001 2102.04790 |
| 57 | S. Schmitt | TUnfold, an algorithm for correcting migration effects in high energy physics | JINST 7 (2012) T10003 | 1205.6201 |
| 58 | J. Alwall et al. | Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions | EPJC 53 (2008) 473 | 0706.2569 |
| 59 | J. Bellm et al. | HERWIG 7.0/ HERWIG++ 3.0 release note | EPJC 76 (2016) 196 | 1512.01178 |
| 60 | CMS Collaboration | Development and validation of HERWIG 7 tunes from CMS underlying-event measurements | EPJC 81 (2021) 312 | CMS-GEN-19-001 2011.03422 |
| 61 | P. F. Monni et al. | MiNNLO\textsubscriptps: a new method to match NNLO QCD to parton showers | JHEP 05 (2020) 143 | 1908.06987 |
| 62 | P. F. Monni, E. Re, and M. Wiesemann | MiNNLO\textsubscriptps: optimizing 2 $ \to $ 1 hadronic processes | EPJC 80 (2020) 1075 | 2006.04133 |
| 63 | E. Barberio and Z. Wcas | photos---a universal Monte Carlo for QED radiative corrections: version 2.0 | Comput. Phys. Commun. 79 (1994) 291 | |
| 64 | CMS Collaboration | Precision luminosity measurement in proton-proton collisions at $ \sqrt{s}= $ 13 TeV in 2015 and 2016 at CMS | EPJC 81 (2021) 800 | CMS-LUM-17-003 2104.01927 |
| 65 | CMS Collaboration | Precision luminosity measurement in proton-proton collisions at $ \sqrt{s}= $ 13 TeV with the CMS detector | CMS Physics Analysis Summary, 2025 CMS-PAS-LUM-20-001 |
CMS-PAS-LUM-20-001 |
| 66 | J. Gao and P. Nadolsky | A meta-analysis of parton distribution functions | JHEP 07 (2014) 035 | 1401.0013 |
| 67 | S. Carrazza et al. | An unbiased Hessian representation for Monte Carlo PDFs | EPJC 75 (2015) 369 | 1505.06736 |
| 68 | G. Watt and R. S. Thorne | Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs | JHEP 08 (2012) 052 | 1205.4024 |
| 69 | R. Boughezal et al. | Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD | PRL 116 (2016) 152001 | 1512.01291 |
| 70 | A. Gehrmann-De Ridder et al. | Precise QCD predictions for the production of a Z boson in association with a hadronic jet | PRL 117 (2016) 022001 | 1507.02850 |
| 71 | A. Gehrmann-De Ridder et al. | The NNLO QCD corrections to Z boson production at large transverse momentum | JHEP 07 (2016) 133 | 1605.04295 |
| 72 | T. Gehrmann et al. | Jet cross sections and transverse momentum distributions with NNLOJET | in the International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) --- PoS(RADCOR), volume 290, 2017 Proceedings of 1 (2017) 074 |
1801.06415 |
| 73 | D. Britzger et al. | NNLO interpolation grids for jet production at the LHC | EPJC 82 (2022) 930 | 2207.13735 |
| 74 | D. Britzger, K. Rabbertz, F. Stober, and M. Wobisch | New features in version 2 of the fastNLO project | fastNLO Collaboration, in th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS): Bonn, Germany, March 26--30,, 2012 Proc. 2 (2012) 0 |
1208.3641 |
| 75 | CMS Collaboration | Measurement of the triple-differential dijet cross section in proton-proton collisions at $ \sqrt{s}= $ 8 TeV and constraints on parton distribution functions | EPJC 77 (2017) 746 | CMS-SMP-16-011 1705.02628 |
| 76 | CMS Collaboration | Measurement of multidifferential cross sections for dijet production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | EPJC 85 (2025) 72 | CMS-SMP-21-008 2312.16669 |
| 77 | P. Ciafaloni and D. Comelli | Sudakov effects in electroweak corrections | PLB 446 (1999) 278 | hep-ph/9809321 |
| 78 | V. V. Sudakov | Vertex parts at very high energies in quantum electrodynamics | Sov. Phys. JETP 3,4,5,6 65, 1956 | |
| 79 | Sherpa Collaboration | Event generation with Sherpa 3 | JHEP 12 (2024) 156 | 2410.22148 |
| 80 | A. Denner and S. Pozzorini | One-loop leading logarithms in electroweak radiative corrections: I. Results | EPJC 18 (2001) 461 | hep-ph/0010201 |
| 81 | A. Denner and S. Pozzorini | One-loop leading logarithms in electroweak radiative corrections: II. Factorization of collinear singularities | EPJC 21 (2001) 63 | hep-ph/0104127 |
| 82 | E. Bothmann and D. Napoletano | Automated evaluation of electroweak Sudakov logarithms in SHERPA | EPJC 80 (2020) 1024 | 2006.14635 |
| 83 | S. Kallweit et al. | NLO electroweak automation and precise predictions for W+multijet production at the LHC | JHEP 04 (2015) 012 | 1412.5157 |
| 84 | J. M. Lindert et al. | Precise predictions for V+jets dark matter backgrounds | EPJC 77 (2017) 829 | 1705.04664 |
| 85 | S. Gieseke et al. | Nonperturbative effects in triple-differential dijet and Z+jet production at the LHC | Gieseke 202 (1900) 4 | 2412.19694 |
| 86 | PDF4LHC Working Group , R. D. Ball et al. | The PDF4LHC21 combination of global PDF fits for the LHC \mboxRun 3 | JPG 49 (2022) 080501 | 2203.05506 |
| 87 | NNPDF Collaboration | Parton distributions from high-precision collider data | EPJC 77 (2017) 663 | 1706.00428 |
| 88 | S. Bailey et al. | Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs | EPJC 81 (2021) 341 | 2012.04684 |
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