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CMS-PAS-SMP-16-010
Measurement of the differential jet production cross section with respect to jet mass and transverse momentum in dijet events from pp collisions at $\sqrt{s}= $ 13 TeV
Abstract: A measurement of the differential jet production cross section as a function of the jet mass and transverse momentum is presented in events with a dijet topology, with and without a jet grooming algorithm applied that selectively removes low-energy portions from a jet. For ungroomed jets, all Monte Carlo event generators are found to predict the jet mass spectrum within uncertainties in the data for intermediate masses of about 10-30% of the jet transverse momentum. Outside of this range, some disagreement is observed. For groomed jets, the jet mass peak is suppressed and the precision in the low and intermediate regions improves, since the grooming algorithm removes the portions of the jet arising from soft radiation that are difficult to model. Semi-analytical calculations beyond next-to-leading logarithmic accuracy of the groomed jet mass are also compared to the data for the first time at a hadron collider. These calculations are found to predict the data within their uncertainties below a jet mass of about 30% of a jet's transverse momentum, where wide jets start to be split into two. Below jet masses of 20 GeV the predicted cross sections tend to be somewhat smaller than measured in data.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Comparison of data to MC simulation for ungroomed jets for various $ {p_{\mathrm {T}}} $ bins at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 1-a:
Comparison of data to MC simulation for ungroomed jets for $ {p_{\mathrm {T}}} $ bin 260 $ < {p_{\mathrm {T}}} < $ 350 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 1-b:
Comparison of data to MC simulation for ungroomed jets for $ {p_{\mathrm {T}}} $ bin 650 $ < {p_{\mathrm {T}}} < $ 760 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 1-c:
Comparison of data to MC simulation for ungroomed jets for $ {p_{\mathrm {T}}} $ bin 900 $ < {p_{\mathrm {T}}} < $ 1000 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 1-d:
Comparison of data to MC simulation for ungroomed jets for $ {p_{\mathrm {T}}} $ bin 1200 $ < {p_{\mathrm {T}}} < $ 1300 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 2:
Comparison of data to MC simulation for groomed jets for various $ {p_{\mathrm {T}}} $ bins at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 2-a:
Comparison of data to MC simulation for groomed jets for $ {p_{\mathrm {T}}} $ bin 260 $ < {p_{\mathrm {T}}} < $ 350 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 2-b:
Comparison of data to MC simulation for groomed jets for $ {p_{\mathrm {T}}} $ bin 650 $ < {p_{\mathrm {T}}} < $ 760 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 2-c:
Comparison of data to MC simulation for groomed jets for $ {p_{\mathrm {T}}} $ bin 900 $ < {p_{\mathrm {T}}} < $ 1000 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 2-d:
Comparison of data to MC simulation for groomed jets for $ {p_{\mathrm {T}}} $ bin 1200 $ < {p_{\mathrm {T}}} < $ 1300 GeV at the detector level. The data are shown in black points along with their statistical uncertainties and the experimental systematic uncertainties. The PYTHIA8 results before unfolding are shown as a blue histogram, including systematic uncertainties from the simulation before unfolding in the hatched blue area. The HERWIG++ results before unfolding are shown without uncertainties as a dashed red histogram.

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Figure 3:
Results of unfolding ungroomed jets for all $ {p_{\mathrm {T}}} $ bins. Bins with total uncertainty larger than 60% are not shown. The data are shown in markers for each $ {p_{\mathrm {T}}} $ bin, scaled by a factor for better visibility. The total uncertainties (statistical added to systematic in quadrature) are shown in grey bands. The predictions from PYTHIA8 are shown as a dashed red line.

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Figure 4:
Results of unfolding groomed jets for all $ {p_{\mathrm {T}}} $ bins. Bins with total uncertainty larger than 60% are not shown. The data are shown in markers for each $ {p_{\mathrm {T}}} $ bin, scaled by a factor for better visibility. The total uncertainties (statistical added to systematic in quadrature) are shown in grey bands. The predictions from PYTHIA8 are shown as a dashed red line.

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Figure 5:
Results of unfolding the ungroomed jets for various $ {p_{\mathrm {T}}} $ bins. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown.

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Figure 5-a:
Results of unfolding the ungroomed jets for $ {p_{\mathrm {T}}} $ bin 260 $ < {p_{\mathrm {T}}} < $ 350 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown.

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Figure 5-b:
Results of unfolding the ungroomed jets for $ {p_{\mathrm {T}}} $ bin 650 $ < {p_{\mathrm {T}}} < $ 760 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown.

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Figure 5-c:
Results of unfolding the ungroomed jets for $ {p_{\mathrm {T}}} $ bin 900 $ < {p_{\mathrm {T}}} < $ 1000 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown.

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Figure 5-d:
Results of unfolding the ungroomed jets for $ {p_{\mathrm {T}}} $ bin 1200 $ < {p_{\mathrm {T}}} < $ 1300 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown.

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Figure 6:
Results of unfolding groomed jets for various $ {p_{\mathrm {T}}} $ bins. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref. [11] (Frye et. al.) are shown in blue hatched histograms with $+45^\circ $ hatching. The uncertainties include scale variations and an estimate of nonperturbative effects. The predictions from Ref. [12] (Marzani et. al.) are shown in an orange hatched histogram with $-45^\circ $ hatching. The uncertainties only include effects from scale variations, since nonperturbative corrections have been considered directly in the calculation.

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Figure 6-a:
Results of unfolding groomed jets for $ {p_{\mathrm {T}}} $ bin 260 $ < {p_{\mathrm {T}}} < $ 350 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref. [11] (Frye et. al.) are shown in blue hatched histograms with $+45^\circ $ hatching. The uncertainties include scale variations and an estimate of nonperturbative effects. The predictions from Ref. [12] (Marzani et. al.) are shown in an orange hatched histogram with $-45^\circ $ hatching. The uncertainties only include effects from scale variations, since nonperturbative corrections have been considered directly in the calculation.

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Figure 6-b:
Results of unfolding groomed jets for $ {p_{\mathrm {T}}} $ bin 650 $ < {p_{\mathrm {T}}} < $ 760 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref. [11] (Frye et. al.) are shown in blue hatched histograms with $+45^\circ $ hatching. The uncertainties include scale variations and an estimate of nonperturbative effects. The predictions from Ref. [12] (Marzani et. al.) are shown in an orange hatched histogram with $-45^\circ $ hatching. The uncertainties only include effects from scale variations, since nonperturbative corrections have been considered directly in the calculation.

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Figure 6-c:
Results of unfolding groomed jets for $ {p_{\mathrm {T}}} $ bin 900 $ < {p_{\mathrm {T}}} < $ 1000 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref. [11] (Frye et. al.) are shown in blue hatched histograms with $+45^\circ $ hatching. The uncertainties include scale variations and an estimate of nonperturbative effects. The predictions from Ref. [12] (Marzani et. al.) are shown in an orange hatched histogram with $-45^\circ $ hatching. The uncertainties only include effects from scale variations, since nonperturbative corrections have been considered directly in the calculation.

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Figure 6-d:
Results of unfolding groomed jets for $ {p_{\mathrm {T}}} $ bin 1200 $ < {p_{\mathrm {T}}} < $ 1300 GeV. The data are shown in black points, with dark grey bands for the statistical uncertainty (Stat. Unc.) and in light grey bands for the total uncertainty (Stat. + Sys. Unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG+PYTHIA are shown in dashed black, dash-dot-dotted red, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref. [11] (Frye et. al.) are shown in blue hatched histograms with $+45^\circ $ hatching. The uncertainties include scale variations and an estimate of nonperturbative effects. The predictions from Ref. [12] (Marzani et. al.) are shown in an orange hatched histogram with $-45^\circ $ hatching. The uncertainties only include effects from scale variations, since nonperturbative corrections have been considered directly in the calculation.

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Figure 7:
Alternative display of Fig. 6 showing only the MC predictions and data.

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Figure 7-a:
Alternative display of Fig. 6-a showing only the MC predictions and data.

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Figure 7-b:
Alternative display of Fig. 6-b showing only the MC predictions and data.

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Figure 7-c:
Alternative display of Fig. 6-c showing only the MC predictions and data.

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Figure 7-d:
Alternative display of Fig. 6-d showing only the MC predictions and data.

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Figure 8:
Alternative display of Fig. 6 showing only the predictions from Refs. [11] and [12], and data.

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Figure 8-a:
Alternative display of Fig. 6-a showing only the predictions from Refs. [11] and [12], and data.

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Figure 8-b:
Alternative display of Fig. 6-b showing only the predictions from Refs. [11] and [12], and data.

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Figure 8-c:
Alternative display of Fig. 6-c showing only the predictions from Refs. [11] and [12], and data.

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Figure 8-d:
Alternative display of Fig. 6-d showing only the predictions from Refs. [11] and [12], and data.
Tables

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Table 1:
List of trigger thresholds used for each high-level trigger path. The $ {p_{\mathrm {T}}} $ ranges are shown in the second column. Events are selected such that exactly one trigger is used for each $ {p_{\mathrm {T}}} $ bin.
Summary
A double-differential jet cross section has been presented in bins of the ungroomed jet $p_{\mathrm{T}}$ in conjunction with the ungroomed and groomed jet mass using the "soft drop'' grooming algorithm, which is the same as the "mass drop'' grooming algorithm for our choice of parameters.

This observable is sensitive to the physics modeling, and could be used in future global fits for parameter tuning. This analysis improves over previous results [49] by using a more theoretically controlled jet grooming algorithm, as well as by unfolding in both transverse momentum and mass.

For ungroomed jets, all Monte Carlo event generators investigated were found to predict the jet mass spectrum within uncertainties in the data for intermediate masses (0.1 $ < m/p_{\mathrm{T}} < $ 0.3). For $m/p_{\mathrm{T}} < $ 0.1, large variations (above 20%) were observed between the predictions from the PYTHIA8 and HERWIG++ generators. The PYTHIA8 generator was observed to predict the data slightly better in this regime. For $m/p_{\mathrm{T}} > $ 0.3, the predictions from PYTHIA8 and HERWIG++ agree with each other, but overpredict the data by 20-50%. There is no significant difference observed when POWHEG+PYTHIA8 is used compared to PYTHIA8 alone.

For groomed jets, the Sudakov peak is suppressed and the precision in the intermediate mass region (0.1 $ < m/p_{\mathrm{T}} < $ 0.3) improves, since the grooming algorithm removes the portions of the jet arising from soft radiation. At low masses ($m/p_{\mathrm{T}} < $ 0.1), disagreement was observed between PYTHIA8 and HERWIG++. As in the case for ungroomed jets, PYTHIA8 was observed to predict the data slightly better for groomed jets.

Semi-analytical calculations beyond next-to-leading logarithmic accuracy of the groomed jet mass were also compared to the data for the first time at a hadron collider. These calculations agree with each other, and were found to also predict the data within their uncertainties for masses lower than 30% of the transverse momentum.
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Compact Muon Solenoid
LHC, CERN