Measurements of the differential jet cross section as a function of the jet mass in dijet events from proton-proton collisions at $\sqrt{s} =$ 13 TeV

Measurements of the differential jet cross section are presented as a function of jet mass in dijet events, in bins of jet transverse momentum, with and without a jet grooming algorithm. The data have been recorded by the CMS Collaboration in proton-proton collisions at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 2.3 fb$^{-1}$. The absolute cross sections show slightly different jet transverse momentum spectra in data and Monte Carlo event generators for the settings used. Removing this transverse momentum dependence, the normalized cross section for ungroomed jets is consistent with the prediction from Monte Carlo event generators for masses below 30% of the transverse momentum. The normalized cross section for groomed jets is measured with higher precision than the ungroomed cross section. Semi-analytical calculations of the jet mass beyond leading logarithmic accuracy are compared to data, as well as predictions at leading order and next-to-leading order, which include parton showering and hadronization. Overall, in the normalized cross section, the theoretical predictions agree with the measured cross sections within the uncertainties for masses from 10 to 30% of the jet transverse momentum.


Introduction
The understanding of the evolution of jets in quantum chromodynamics (QCD) is important to the understanding of physics at hadron colliders. Jets are involved in nearly every final state in proton-proton (pp) collisions. In the past, most predictions of jet properties did not focus on the jet mass m, defined as the mass of the sum of the four-momenta of the constituents inside the jet. However, the jet mass is the simplest observable that is nonzero only beyond leading order (LO) in perturbation theory for dijet production. Thus, it is more sensitive to the internal structure and evolution of jets than the jet transverse momentum p T . The evolution of jets is theoretically described by parton showering as reviewed in Refs. [1,2]. Experimental measurements of jet mass provide an important test of these theoretical concepts.
Jet mass has been used extensively to investigate signals of physics beyond the standard model (BSM) that are reviewed in Refs. [3][4][5]. In particular, jet mass generated by QCD radiation is typically lower than that generated by heavy hadronically decaying standard model (SM) particles that have 2-and 3-prong decays, such as top quarks, W bosons, Z bosons, or Higgs (H) bosons. This observation can be exploited to identify BSM particles that decay into highly Lorentz-boosted SM particles (boosted objects).
The jet mass generated by QCD arises from the radiation of gluons from the higher-energy (hard) portion of the jet. The probability that a gluon is radiated increases as its energy or angle of emission decreases (soft or collinear radiation, respectively). Hence, the probability of having m = 0 vanishes since many soft and/or collinear gluons will be radiated. Above m/p T ≈ 0.1, there is an overall decrease in the jet mass spectrum as the dominant contributions come from gluon emissions with high energy or at large angles. The distribution terminates around m/p T ≈ 0.3, where the jets become wide enough to start splitting into two separate jets (the splitting threshold). The appearance of a large peak at low mass is described in Ref. [6] as a "Sudakov peak". The jet mass is sensitive to soft QCD effects and to additional pp interactions in the same bunch crossing (pileup) [7]. There is further sensitivity in hadron colliders to correlations among soft gluon emissions from underlying event interactions, and wide-angle emissions among different jets. While the impacts on global event-wide observables (such as the event thrust) have been understood for some time [8][9][10][11], the impact on nonglobal jet observables, such as mass, are difficult to calculate. The technical difficulty arises from the treatment of nonglobal logarithms (NGLs) in the perturbative next-to-leading logarithmic (NLL) order calculations of the jet mass that arise from radiation that exits the jet re-radiating soft gluons back into the jet. It is currently unknown how to fully account for these NGLs in the perturbative integrals.
The hard part of the jet can be separated from the soft parts using jet-grooming techniques [3][4][5]. These techniques also reduce the effects of pileup, which is not correlated with the hard part of the jet. The earliest grooming techniques were unable to completely remove the soft parts of a jet systematically. More recently, major improvements have been made to separate the hard and soft parts of the jet without contamination from NGLs [6,8,[12][13][14][15]. The "mass drop" (MD) procedure [16] has been modified into such a theoretically controlled jet-grooming algorithm [6]. Its generalization, the "soft drop" (SD) algorithm [12], has similar properties. By applying the SD algorithm, soft parts of a jet are removed, resulting in a dramatically reduced Sudakov peak in the jet mass distribution. This also systematically removes the effects that cause NGLs in the calculation, allowing for direct comparisons of the semi-analytical NLL resummation calculations (in particular, from the authors of Refs. [17] and [18]) to Monte Carlo (MC) simulated predictions and data. We therefore apply the SD procedure to groom the jets in this paper. A similar analysis has been published by the ATLAS Collaboration in Ref. [19].
Understanding the behavior of the jet mass and the grooming techniques from first principles is important to further develop boosted object identification algorithms, to gain confidence in the tools should they uncover BSM physics, and to check that parton showering algorithms are correct.
In this paper, we present a measurement of the differential jet production cross section as a function of jet mass in bins of p T from dijet events, before and after the jets are groomed with the SD procedure (for our choice of parameters the SD and MD procedures are identical). Comparing the production cross section with respect to the groomed (m g ) and ungroomed (m u ) jet mass separately allows us to gain insight into both the hard and soft physics.
This analysis is similar to that of Ref. [7], except we correct both the jet p T and m for detector effects, and the SD algorithm is used. We present the double-differential production cross section of dijet events with respect to the jet p T and jet mass m (where m = m u or m g ): In addition, we define a normalized distribution: In both cases, the two jets in the dijet system are included in the distributions.

Theoretical predictions
There are five theoretical calculations used in this study: three MC event generator predictions, and two predictions using analytic resummation merged with fixed order MC simulations.
The three MC event generators used in this study are PYTHIA8, HERWIG++, and POWHEG. Version 8.212 of PYTHIA8 [20] is used with underlying event tune CUETP8M1 [21] and NNPDF 3.0 parton distribution functions (PDFs) NNPDF30 lo as 0130 [22]. The PDF4LHC15 NLO 100 meta-PDF set is used for uncertainty estimation, along with the PYTHIA8 generator. We use the LHAPDF [23] software package for this purpose, following the recommendations of Ref. [24]. The HERWIG++ version 2.7.0 generator [25] is used with tune CUETHS1 [21]. The HERWIG++ simulation sample is used for systematic uncertainty estimation and for generator-level comparisons, as it has a physics model that is different from PYTHIA8 in various aspects like parton showering, hadronisation, multiple-parton interactions, and the set of model parameters tuned to data. Finally, the POWHEG 2.0 [26][27][28][29] generator interfaced with PYTHIA8 is used as a next-toleading order (NLO) perturbative dijet event generator, supplemented with parton showering and multiparton interactions. The same underlying event tune CUETP8M1 [21] is used.
Two semi-analytical resummation-based calculations merged with fixed-order MC simulation are also used. The authors of Ref. [17] have provided a prediction of the groomed jet mass distribution for dijet events at LO using MADGRAPH v2.4.2 [30] and NNPDF 3.0 LO PDFs [22], resummed at NLL accuracy using soft collinear effective theory. Nonperturbative effects are included as an uncertainty in their prediction. The authors of Ref. [18] have provided a prediction of the groomed jet mass distribution for dijet events at NLO using NLOJET++ [31] and CT14NLO PDFs [32] with NLL resummation using perturbative QCD. They include an estimate of the nonperturbative effects directly, using PYTHIA8.
The semi-analytical predictions are expected to be accurate for intermediate masses 0.1 < m/p T < 0.3, since at low mass nonperturbative effects are large. Moreover, at high mass the resummed predictions are matched to fixed-order predictions at LO and NLO, which cannot account for more than one or two additional gluons, respectively, as would occur within genuine jets. For a single gluon emission, there is a kinematic upper limit at m = p T R/2 (where R = √ (∆η) 2 + (∆φ) 2 is the distance parameter for the jet clustering), from the relativistic kinematics of a 1 → 2 decay. However, in the all-orders limit, the approximate kinematic limit is closer to m = p T R/ √ 2. Consider a particle of energy E and mass m decaying to two massless particles, each with an energy E/2 and separated by an angle θ. The mass must satisfy m 2 < E 2 (1 − cos θ) /2. In the small-angle limit, this would be m 2 < E 2 θ 2 /4, or m < Eθ/2. With more particles, the stochastic nature of the shower increases this cutoff point. Thus, a single emission (1 → 2) decay will have a lower approximate kinematic limit than an all-orders (1 → many) decay. Reference [18] calculates these thresholds to be m/E ≈ 0.28 at LO and m/E ≈ 0.45 at NLO.

Experimental setup
The central feature of the CMS detector [33] is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each split in the barrel and two endcap sections. In the region |η| < 1.74, the HCAL cells have widths of 0.087 in pseudorapidity (η) and 0.087 radians in azimuth (φ). In the η-φ plane, and for |η| < 1.48, the HCAL cells map onto 5×5 ECAL crystal arrays to form calorimeter towers projecting radially outwards from close to the nominal interaction point. At larger values of |η|, the size of the towers increases and the matching ECAL arrays contain fewer crystals. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. Electron momenta are estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. In this analysis, the jet rapidity (y) is used in the computation of jet quantities. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [33].
Events of interest are selected using a two-tiered trigger system [34]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz with a latency of less than 4 µs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage.
The event reconstruction is based on the CMS particle-flow (PF) algorithm [35], which includes information from all subdetectors, including charged-particle tracks from the tracking system, energy deposits in the ECAL and HCAL, and tracks reconstructed in the muon chambers. Particles in an event are reconstructed and identified as electrons, muons, photons, charged hadrons, or neutral hadrons. Charged hadrons associated with pileup vertices are removed from consideration. This method is referred to as "charged-hadron subtraction" (CHS) [36]. In our dataset, the average number of pileup interactions per beam crossing is 14.
Jets are clustered using the anti-k T algorithm [37] with the FASTJET 3.0 software package [38], with a distance parameter of R = 0.8 (AK8 jets). This distance parameter is chosen to coincide with the majority of CMS BSM searches using jet substructure techniques. To reconstruct the groomed jets, the constituents of the AK8 jets are reclustered using the Cambridge-Aachen algorithm [39,40] with the same characteristic radius (CA8) to retain substructure information. The hierarchical sequence of clustering is then reversed ("declustering"). The jet grooming algorithm used is the SD algorithm [12]. For each declustering step, the "soft-drop condition" is applied: where p T,i and p T,j are the transverse momenta of the ith and jth particle at each declustering step, ∆R ij is the distance between them, z cut corresponds to the threshold to separate the "soft" and "hard" parts of the jet, and β is an angularity exponent. We choose β = 0, z cut = 0.1 and hence R 0 is no longer a relevant parameter. For this choice of parameters, the SD algorithm is identical to the variant of the MD algorithm described in Ref. [6]. This is done for simplicity, while other values of β will be addressed in future work. If any declustering step does not satisfy the soft-drop condition, the softer constituent is removed from consideration by the jet algorithm.
For the reconstructed jets, all PF candidates that survive the CHS procedure are included. The same reconstruction criteria are also used to create generator-level jets using generated stable particles (mean path length cτ > 1 cm, no minimum p T requirement), removing neutrinos. Simulated pileup particles are not included in the generator-level jets. The ungroomed jet mass is taken as the mass of the four-momentum sum of the constituents of the AK8 jet without grooming applied. The groomed jet mass is taken as the mass of the four-momentum sum of the constituents of the AK8 jet with the SD algorithm applied. For this measurement, the p T of the ungroomed AK8 jet is used for both the groomed and ungroomed jet cross sections, since it has been shown that the groomed jet p T is not collinear-safe for the SD algorithm chosen [18].
Since only charged hadrons arising from pileup interactions are removed with the CHS procedure, corrections based on the jet area [41] are applied to the jet energies to remove the energy contribution of neutral hadrons from pileup. The area-based residual subtraction is not applied to the jet mass because it is observed [42] that this overcorrects the mass of hadronically decaying W bosons in a tt control sample. Further jet energy scale (JES) corrections are applied as functions of η and p T , derived from simulation. Data-to-simulation correction factors are also applied, using the methodology of Ref. [42]. These corrections are also applied to the jet mass by scaling the mass by the same factor used for the p T in the four-momentum of the jet.
To account for the poorer jet energy resolution (JER) in the data and MC simulation, the reconstructed simulated jets are smeared compared to generator-level jets by the amounts listed in Ref. [42]. The typical values of the JER are around 5-8%. After these corrections, the JES and JER in MC simulation agree with those in data for both groomed and ungroomed jets.
The jet mass can also have different scales and resolutions in experimental data and in MC simulation. The jet mass scale (JMS) and jet mass resolution (JMR) are respectively determined by comparing the means and widths of distributions of the jet mass at the reconstructed and generator levels (m reco /m gen ). The JMSs in MC simulation for groomed and ungroomed jets are shown in Fig. 1 as a function of jet mass for various p T bins, and similar distributions are shown for the JMR in Fig. 2. The JMS and JMR are accounted for directly in a detector response parameterization along with corrections to the MC simulation to match data by using the approach outlined in Ref.
[43], except we use the SD algorithm to groom the jets. We fit the jet mass from hadronically decaying W bosons in tt events where one W boson decays hadronically and the other decays leptonically (the "lepton plus jets" channel). The ratio of the fitted means in data and in MC simulation is the correction to the JMS, and the ratio of the fitted widths is the correction to the JMR. This estimate assumes that detector-related uncertainties will be the same for jets from W boson decays and jets initiated by quarks and gluons. The remaining differences are effects from the physics model, and are thus accounted for with our physics model uncertainty. The JMS correction in the 2015 run of the LHC ("Run 2") is measured to be nearly unity. In the 2010-2012 run of the LHC ("Run 1"), the JMR and JMS corrections were observed to be 1.11 ± 0.09 and 1.017 ± 0.006, respectively [44]. In Run 2, these corrections are 1.07 ± 0.12 and 0.98 ± 0.01, respectively (using the methods of Ref. [43]). In addition to smearing the entire four-vector (including the p T and the mass) of the jet by the JER, we also correct the jet mass distribution in the MC simulation to match the data in the W reference sample.  . As in that paper, the ensemble of events is constructed such that any given trigger only contributes to a specific p T region, where it is fully efficient. However, since we are using a different R-parameter for the jet clustering algorithm (we use R = 0.8 as opposed to R = 0.4 and 0.7), our thresholds, shown in Table 1, are slightly different than those from the inclusive jet analysis [45]. The same p T thresholds are used for both 50 and 25 ns data. In the collisions with 50 ns bunch spacing, the trigger prescales were lower, and thus this dataset increases the number of events collected for p T < 460 GeV by 10% compared to the 25 ns run alone, where the prescales are considerably higher. There are 43.9 million events in the 25 ns sample and 4.4 million events in the 50 ns sample.

Analysis strategy
The measurement of the dijet cross section is corrected for detector effects using an unfolding technique. The detector response is parameterized as a four-dimensional response matrix representing the migrations from reconstructed m and p T to simulated m and p T . This response matrix is used to correct the measured distribution, and the resulting unfolded distribution is compared to various theoretical models.
The events are required to have at least two jets, without an explicit third jet veto, which allows for an easier comparison to semi-analytical calculations. To ensure a high-purity dijet-like sample, we require that the asymmetry between the leading and subleading jet transverse momenta, defined as p T 1 and p T 2 respectively, satisfies (p T 1 − p T 2 )/(p T 1 + p T 2 ) < 0.3 and the difference in azimuthal angles satisfies ∆(φ 1 − φ 2 ) > π/2. In addition to ensuring a dijet topology, these criteria reduce the number of jets from detector noise. Both jets in the dijet system are included in the measurement.
All reconstructed AK8 jets are required to have p T > 200 GeV and rapidity |y| < 2.4, and jet identification requirements that remove detector noise outlined in Ref. [46]. After these criteria, the number of jets from detector noise in this sample is negligible. Generator-level AK8 jets are required to have |y| < 2.4 and a very low p T selection (>50 GeV) to ensure an accurate estimate of the migration of events between p T bins, but the measurement is presented only for p T > 200 GeV at the generator level. The p T asymmetry and ∆φ selections are also applied at the generator level.
The bins in ungroomed jet p T are chosen so that each bin is populated by exactly one trigger, with binning as shown in Table 1 (i.e., the trigger with a threshold of 80 GeV will be used to populate the 200-260 GeV bin, etc). Above the threshold of the lowest unprescaled trigger at p T = 760 GeV, more uniform p T binning is used. The lower bin boundaries are 200, 260, 350, 460, 550, 650, 760, 900, 1000, 1100, 1200, >1300 GeV. The choice of jet mass bins is a trade-off among the approximate detector resolution of ∼10 GeV [42], the purity (the fraction of events in a reconstructed bin that are generated in the same bin), and the stability (the fraction of events in a generated bin that are reconstructed in the same bin). The lower bin boundaries are 10, 20, 40, 60, 80, 100 GeV and then increase by 50 GeV beyond 100 GeV. The same binning is used for both the reconstructed and generated jet mass. There are, however, kinematic regions that have insufficient accuracy for the jet mass measurement. This inaccuracy can arise from the finite spatial resolution of the detector or from excessive pileup contamination. These regions in p T and m are removed by requiring that the uncertainty in a Gaussian fit to the distribution of m reco /m gen in MC simulation is less than 50% for that region. We do not consider the measurements below those thresholds. For ungroomed jets, the dominant effect is pileup contamination, and we do not consider jet masses below 20 GeV when p T < 760 GeV, or below 40 GeV when p T > 760 GeV. For groomed jets, the dominant effect is the finite spatial resolution of the detector, and we do not consider jet masses below 10 GeV for all p T bins.
The unfolding procedure of D'Agostini with early stopping is applied [47][48][49]. The detector response is from MC simulation, and parameterized in bins of ungroomed jet p T and ungroomed jet mass for the ungroomed case, and in bins of ungroomed jet p T and groomed jet mass for the groomed case. The central value of the response matrix is constructed using PYTHIA8. The uncertainty in the response matrix is estimated by varying the systematic uncertainties described below, rederiving the matrix for each case, and applying the modified response matrix to the reconstructed data, taking the difference in the unfolded distribution as the resultant uncertainty.
The number of iterations in the early stopping procedure has been optimized as follows. The response matrix is used to unfold the PYTHIA8 MC simulation varying the number of iterations in the regularization. A simple matrix multiplication is then used to refold the unfolded MC simulation. The resulting refolded distribution is compared to the original reconstructed distribution and a χ 2 probability is calculated. The optimal number of iterations is determined as the lowest number such that the χ 2 probability exceeded 99%. We found n = 3 to be optimal.
The uncertainties in the unfolded result due to statistical uncertainties in the MC simulation are nontrivial to estimate in the unfolding procedure because the events have different weights, so the statistical uncertainty is not correctly estimated by simply adding the uncertainties from weighted events in quadrature. Instead of standard methods, we employ a "jackknife resampling" technique (a linear bootstrapping method) [50,51], where we create 10 samples, each with 90% of the MC events (such that each event is excluded from exactly one resampling), and unfold the spectrum. The root-mean-square of this ensemble of distributions, multiplied by 10/9 to account for using 90% of the events per iteration, is taken as the statistical uncertainty in the MC simulation.
There are both theoretical and experimental systematic uncertainties that affect this measurement, along with uncertainties from the unfolding procedure. The uncertainties are estimated by creating response matrices with the systematic effect applied, and unfolding the reconstructed data to account for systematic migrations. Unless otherwise specified, the difference between the systematically varied output and the nominal output is taken to be the systematic uncertainty for that source. The uncertainties from different sources are then added together in quadrature.
The experimental uncertainties that affect the measurement are the JES, JER, JMS, JMR, pileup, and luminosity. The theoretical uncertainties include uncertainties on the physics model PDFs.
The JES uncertainty is evaluated by varying the jet energy and mass up and down by the appropriate uncertainties for all of the JES uncertainty sources as described in Ref. [42]. The JER uncertainty is evaluated by smearing the jet energy and mass by an additional factor as described in Ref. [42]. The central value is determined by correcting the MC simulation to match the JER from data, and the uncertainties are evaluated by correcting the MC simulation by the JER systematic variations. This is also propagated to the jet mass because these effects are correlated for jets reconstructed from PF candidates. The uncertainty due to the finite resolution of the jet angle is found to be negligible compared to other uncertainties.
As mentioned in Section 3, the JMR in simulation is corrected by 1.07 ± 0.12 to match the measured difference between data and MC simulation for the mass of W boson jets in lepton+jets tt events [52]. The JMS in MC simulation is approximately unity for larger jet p T and masses. Deviations from unity are included directly in the response matrix, as described in Section 3.
The pileup uncertainty is estimated by reweighting the pileup distribution of the MC simulation up and down, assuming a change of the minimum bias cross section by 2.7% [53]. For the absolute cross section, the luminosity uncertainty itself is also taken as an additional systematic uncertainty.
The PDF uncertainty is taken from the PDF4LHC15 NLO 100 meta-PDF set using the PYTHIA8 generator. The physics model uncertainty is evaluated by comparing a response matrix derived from PYTHIA8 to a response matrix derived from HERWIG++. The difference between the two results for the two cases is taken as the systematic uncertainty.
The jet mass distributions in data before unfolding are compared to PYTHIA8

Results
The absolute cross sections as a function of jet mass are shown for two p T bins in Figs. 9 and 10 for the ungroomed and groomed jets, respectively. The cross sections are compared to PYTHIA8, POWHEG + PYTHIA8, and HERWIG++ predictions, which are scaled to match the number of events in the data.
The normalized cross sections are shown in Figs. 11 and 12. All p T bins of the normalized cross section are shown in Figs. 13 and 14. The lowest masses in the measurement are difficult to measure experimentally, as described in Section 4. As mentioned there, the mass measurements are presented for ungroomed jets for m > 20 GeV when p T < 760 GeV, and m > 40 GeV for jets with p T > 760 GeV. Results for groomed jets are presented for m > 10 GeV for all p T . The normalized results for the groomed jets are also compared to the calculation of the jet mass from Refs. [17] and [18]. The normalized results are scaled to unity for each individual jet p T bin for the unfolded data, for the PYTHIA8, HERWIG++, POWHEG + PYTHIA8 predictions, and for the results from the calculation from the authors of Ref. [18]. The calculation from Ref. [17], on the other hand, is normalized to match the data at 50 GeV, since the calculation does not consider nonperturbative corrections that are important below that value. As a reminder, the prediction from Ref. [17] includes nonperturbative effects as an uncertainty, while the prediction from Ref. [18] directly includes nonperturbative effects in the prediction, and has smaller systematic uncertainties in low-mass regions where nonperturbative effects are important.
Comparing the normalized ungroomed and groomed cross sections (Figs. 11-12), our results show that the grooming algorithm considerably lowers the jet mass and suppresses the Sudakov peak, as expected. The precision of the measurement improves, since the grooming algorithm removes the parts of the jet arising from soft radiation and the pileup contribution. Figures 7-8 show the reduced effect of the uncertainties from the physics model and pileup, decreasing the overall uncertainty from ∼8-12% at m = 100 GeV for ungroomed jets to ∼2-5% for groomed jets at the same mass. The absolute cross sections (Figs. 9-10) have increased uncertainties from jet energy uncertainties (JES and JER), as shown in Figs. 5-6.
The LO theory predictions with a MC-based physics model are from PYTHIA8 and HERWIG++, and they predict the ungroomed jet mass measurement within uncertainties, although the experimental uncertainties are large. Above the splitting threshold (m/p T > 0.3), the prediction is slightly larger than the data. After grooming, the experimental precision improves, so some deviations from the data can be observed at very low jet masses. Some disagreements are observed between PYTHIA8 and HERWIG++. The PYTHIA8 generator tends to predict the data better, although for m/p T < 0.1, the agreement is worse than in the range 0.1 < m/p T < 0.3. The same disagreement above the splitting threshold is observed as in the ungroomed case. The NLO theory prediction with a MC-based physics model is from POWHEG + PYTHIA8, and is observed to have largely the same behavior as PYTHIA8 alone, so the largest effects are coming from the physics model.
The LO and NLO theory predictions with analytic resummation (Refs. [17] and [18], respectively) agree overall with the data, with some slight disagreements at very low masses. For m/p T > 0.3, the fixed-order matrix element merging is insufficient to capture the true dynamics due to kinematic effects, as described in Section 2, so the predictions diverge from the data. They agree with the predictions using MC-based physics models, although some disagreement is observed at very low masses. The resummed predictions are slightly closer to the PYTHIA8 prediction than to the HERWIG++ one.  Figure 9: Absolute cross section for ungroomed jets for two p T bins. The data are shown by the black points, with dark grey bands for the statistical uncertainty (Stat. unc.) and with light grey bands for the total uncertainty (Stat. + sys. unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG + PYTHIA are shown with dashed black, dash-dot-dotted magenta, and dash-dotted green histograms, respectively, with no uncertainties shown. The MC simulations are normalized to the data over the entire p T range.  Figure 10: Absolute cross section for groomed jets for two p T bins. The data are shown by the black points, with dark grey bands for the statistical uncertainty (Stat. unc.) and with light grey bands for the total uncertainty (Stat.+sys. unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG + PYTHIA are shown with dashed black, dash-dotdotted magenta, and dash-dotted green histograms, respectively, with no uncertainties shown. The MC simulations are normalized to the data over the entire p T range.  Figure 11: Normalized cross section for the ungroomed jets for two p T bins. The data are shown by the black points, with dark grey bands for the statistical uncertainty (Stat. unc.) and with light grey bands for the total uncertainty (stat.+sys. unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG + PYTHIA are shown with dashed black, dash-dotdotted magenta, and dash-dotted green histograms, respectively, with no uncertainties shown.  Figure 12: Normalized cross section for the groomed jets for two p T bins. The data are shown by the black points, with dark grey bands for the statistical uncertainty (Stat. unc.) and with light grey bands for the total uncertainty (stat.+sys. unc., added in quadrature). The predictions from PYTHIA8, HERWIG++, and POWHEG + PYTHIA are shown with dashed black, dash-dotdotted magenta, and dash-dotted green histograms, respectively, with no uncertainties shown. The predictions from Ref.   Figure 13: Normalized cross section for ungroomed jets for all p T bins. Bins with total uncertainty larger than 60% are not shown. The data are shown with markers for each p T bin, scaled by a factor for better visibility. The total uncertainties (statistical added to systematic in quadrature) are shown with grey bands. The predictions from PYTHIA8 are shown as a dashed red line.

Summary
The double-differential production cross section has been presented for dijet events in bins of ungroomed jet p T as a function of jet mass, with and without a jet grooming algorithm applied. The grooming algorithm is observed to decrease the jet mass overall, and reduce the sensitivity of the observable to details of the physics modeling and pileup effects. The data are compared to various theoretical predictions, including new calculations using analytical resummation. Overall, in the normalized cross section, the theoretical predictions agree with the measured cross sections within the uncertainties for masses from 10 to 30% of the jet transverse momentum. 2.3 fb Figure 14: Normalized cross section for groomed jets for all p T bins. Bins with total uncertainty larger than 60% are not shown. The data are shown with markers for each p T bin, scaled by a factor for better visibility. The total uncertainties (statistical added to systematic in quadrature) are shown with grey bands. The predictions from PYTHIA8 are shown as a dashed red line.

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies:  [45] CMS Collaboration, "Measurement of the double-differential inclusive jet cross section in proton-proton collisions at √ s = 13 TeV", Eur. Phys. J. C 76 (2016) 451, doi:10.1140/epjc/s10052-016-4286-3, arXiv:1605.04436.