cms physics analysis summary -...
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Available on the CERN CDS information server CMS PAS TOP-16-008
CMS Physics Analysis Summary
Contact: [email protected] 2016/03/23
Measurement of differential tt production cross sections inlepton + jets final states at 13 TeV
The CMS Collaboration
Abstract
The differential cross section for the production of top quark pairs in proton-protoncollisions at 13 TeV is measured as a function of various kinematic variables of the topquarks and the top quark-antiquark system as well as jet multiplicities. This analyisis based on data collected by the CMS experiment at the LHC corresponding to anintegrated luminosity of 2.3 fb−1. The measurements are performed in the lepton +jets decay channel with an electron or a muon in the final state. The differential crosssections are presented at particle level, within a phase space close to the experimentalacceptance, and at parton level in the full phase space. The measured cross sectionsare compared to several theoretical calculations. No significant deviation from thestandard model prediction is observed.
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1 IntroductionA measurement of the top quark pair (tt) differential production cross section as a functionof various kinematic observables of the tt event and jet multiplicities is performed based onan integrated luminosity of 2.3 fb−1 [1] of proton-proton collision data at 13 TeV. Studying theproduction cross section of top quarks at high energies is a crucial ingredient in testing thestandard model and searching for new physics that may alter the production rate. In particular,the differential tt cross section as a function of tt kinematic variables probes QCD predictionsand facilitates the comparison of the data with state-of-the-art calculations.
This measurement updates the earlier parton level result [2] with the full integrated luminosityrecorded in 2015 and extends the tt differential cross section measurements, that have beenmeasured in the dilepton channel [3], to the `+jets channel.
The differential cross sections are presented in two different ways, at particle level and at partonlevel. For the particle level measurements a proxy of the top quark is defined based on exper-imentally accessible quantities like jets, which consist of quasi-stable particles as described bytheoretical calculations that, in contrast to pure matrix element calculations, involve a partonshower and hadronization model. These objects are required to match closely the experimentalacceptance. A detailed definition is given in Section 3. Such an approach has the advantageto reduce theoretical uncertainties since it avoids theory based extrapolations from the experi-mental to the full phase space and from jets to partons.
For the parton level measurement the reconstructed distributions are unfolded to the top quarklevel without any phase space restrictions. Here the top quark level is defined by the top quarksdirectly before decaying into a bottom quark and a W boson. This includes the simulation ofinitial state parton showers. We consider only those cases where one of the W bosons decayshadronically and the other one leptonically excluding the tau decay mode.
The experimental signature is the same for both measurements and consists of two b jets, twojets from a W boson decay, missing transverse energy Emiss
T from the neutrino, and one isolatedelectron or muon.
We start with selected events that contain at least four jets and exactly one isolated electronor muon. Afterwards a reconstruction algorithm is used to identify the tt decay products andto reconstruct the top quarks or the top quark proxies. After subtracting the backgrounds ofsingle top, Drell-Yan, W boson, QCD, and non-signal tt events the spectra are unfolded.
2 Signal and background modelingThe Monte-Carlo programs POWHEG (v2) [4–7] and MG5 AMC@NLO (2.2.2) [8] are used tosimulate tt events. They include next-to-leading order NLO QCD matrix element calculationsthat are combined with the parton shower simulation of PYTHIA8.205 [9, 10] using the tuneCUETP8M1 [11]. In addition, MG5 AMC@NLO is used to produce tt multijet simulationsof tt plus up to 3(2) additional partons, each process at LO(NLO). These are combined withthe PYTHIA8 parton shower simulation using the MLM [8](FXFX [12]) algorithm. The defaultparton distribution function PDF used in all simulations is NNPDF30 nlo as 0118 [13]. A topquark mass of 172.5 GeV is used as default. In all samples, additional event weights are cal-culated that represent the usage of other PDF sets or its uncertainty eigenvector sets. Thereare also event weights available that represent the change of factorization and renormaliza-tion scale by a factor of two or one half. These additional weights allow for the calculationof PDF and scale uncertainties. When compared to the data all samples are normalized to the
2 3 Top quark proxy definition at particle level
NNLO cross section calculation [14] of 832 pb. For uncertainty estimations we use POWHEG
simulations with top quark masses of 169.5 GeV and 175.5 GeV and a simulation with POWHEG
combined with HERWIG++ [15] tune EE5C [16].
The main backgrounds are produced using the same techniques. MG5 AMC@NLO withPYTHIA8 is used for the simulation of W boson production in association with jets, t-channelsingle top, and Drell-Yan in association with jets. POWHEG with PYTHIA8 is used for the simula-tion of single top associated production (tW) and PYTHIA8 is used for QCD multijet production.The W boson and Drell-Yan backgrounds are normalized to their NNLO cross sections [17]. Thesingle top processes are normalized to NLO calculations [18] and the QCD multijet sample isnormalized to the LO calculation [10].
The effects of the detector are simulated using GEANT4 [19]. Afterwards, the same reconstruc-tion algorithms as in the data are used. To correct the simulation to be in agreement withthe pileup conditions observed during the data taking the average number of pileup eventsper bunch crossing is calculated from the measured instantaneous luminosity. The simulatedevents are reweighted to follow this distribution.
3 Top quark proxy definition at particle levelThe following list describes the definition of objects constructed from quasi-stable particles atgenerator level and further used to construct the top quark proxies. In general, these objectsare constructed in a way that there is a corresponding measurable quantity.
• Electrons and muons that do not have their origin in a decay of a hadron are selectedand corrected for final state radiation. The anti-kt jet algorithm [20] with a distanceparameter of 0.1 is used to cluster these leptons and photons. Those photons thatare clustered together with a selected lepton are assumed to be radiative losses ofthe lepton and their momenta are added to the lepton momentum. However, thelepton is only selected if the contribution of the original pT is at least half of thecorrected pT.
• All neutrinos that do not have their origin in a decay of a hadron are selected.
• Jets are clustered by the anti-kt jet algorithm with a distance parameter of 0.4. Allstable particles excluding all neutrinos and the selected leptons together with theirradiative correction are considered.
• b jets are those jets that contain a b hadron. Although unstable, b hadrons are in-cluded during the jet clustering, but their momenta are scaled down to a negligiblevalue. These preserves the information of their direction, but they have no impacton the jet clustering itself.
Based on the invariant masses M of these objects we construct a pair of top quark proxies in the`+jets channel. Events with exactly one electron or muon with pT(`) > 30 GeV and |η(`)| < 2.5are selected. We sum the momenta of all selected neutrinos pN and find the permutation ofjets that minimizes Eq. 1 where pj1/2 are two light jet candidates, pb1/2 two b jet candidates. Alljets with pT > 25 GeV and |η| < 2.5 are considered. At least two b jets and a total numberof at least four jets are required. If there are more than two b jets, we allow b jets as decayproduct of the proxy for the hadronically decaying W boson. The values of mt = 172.5 GeVand mW = 80.4 GeV are used.
K2 = [M(pN + p` + pb1)−mt]2 + [M(pj1 + pj2)−mW]2 + [M(pj1 + pj2 + pb2)−mt]
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Figure 1: Relation between the pT of the hadronically top quark proxy at particle level and thetop quark at parton level extracted from the POWHEG plus PYTHIA8 simulation. Left: (yellow)fraction of events with a top quark proxy pair that are not `+jets events at parton level, (green)ratio of particle and parton level top quarks, (blue) fraction of parton level top quarks in thesame bin at particle level, (red) fraction of particle level top quarks in the same bin at partonlevel. Right: bin migrations between particle and parton level. Each column is normalized tothe number of events at parton level in the full phase space.
It should be remarked that events with a hadronic and a leptonic top quark proxy are notrequired to be `+jets events at parton level. As an example, in Fig. 1 the relation between thepT of the hadronically decaying top quark proxy at particle level and the top quark at partonlevel is shown.
4 Object selectionThe Particle Flow (PF) algorithm [21] is used to combine the information of all subdetectorsand to categorize reconstructed objects as photons, muons, electrons, charged hadrons, andneutral hadrons. A detailed description of the CMS detector can be found in Ref. [22]. Thisanalysis depends on the reconstruction and identification of muons, electrons, jets, and missingtransverse energy Emiss
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Leptons from tt decays are typically isolated, i.e., separated in ∆R =√(∆φ)2 + (∆η)2 from
other particles. A requirement on the lepton isolation is used to reject leptons produced indecays of hadrons. The muon isolation variable is defined as the pT sum of all tracks, exceptfor the muon track, originating from the tt interaction vertex within a cone of ∆R < 0.3. Itis required to be less than 5% of the muon pT. For electrons the isolation variable is the pTsum of neutral hadrons, charged hadrons, and photon-like PF objects in a cone of ∆R < 0.3around the electron. Contributions of the electron to the isolation variables are suppressed us-ing a veto region. This isolation variable is required to be smaller than 7% of the electron pT.An event-by-event correction is applied, which keeps the electron isolation efficiency constantwith respect to pileup interactions [23]. Reconstruction and identification efficiencies for elec-trons and muons are measured with tag and probe techniques and scale factors are obtained tocorrect the simulation.
Jets are reconstructed from PF objects clustered by the anti-kt jet algorithm with a distanceparameter of 0.4 using the FASTJET package [24]. The total energy of the jets is corrected forenergy depositions from pileup. In addition η and pT dependent corrections are applied tocorrect for detector response effects.
4 6 Reconstruction of the top quark-antiquark system
The missing transverse momentum~pmissT is calculated as the negative vectorial sum of all PF ob-
jects. Its magnitude is referred to as missing transverse energy EmissT . The jet energy corrections
are used to improve the ~pmissT measurement.
5 Event selectionEvents are selected if they pass single lepton triggers. These require a minimum pT > 22 GeVfor electrons and muons as well as various quality and isolation criteria.
Events with exactly one electron or muon with pT > 30 GeV and |η| < 2.1 are selected. Noadditional electrons or muons with pT > 15 GeV and |η| < 2.4 are allowed. In addition to thelepton, at least four jets with pT > 30 GeV and |η| < 2.4 are required. At least two of thesejets are required to be tagged as b jet [25]. At least one has to fulfill a tight b jet criterion withan efficiency of about 70% with a light jet rejection of 95%. For a second b jet a looser selectionrequirement with an efficiency of about 80% and a light jet rejection of 85% is applied. At leastone of the two jets with the highest value of the b tagging discriminant and at least one of theremaining jets are required to have pT > 35 GeV.
We compare several kinematic distributions of electrons and muons to verify that there is nounexpected difference between the two channels. The relative normalization of the two chan-nels is in agreement and in the remaining steps of the analysis the two channels are combined.
6 Reconstruction of the top quark-antiquark systemThe goal of the tt reconstruction is the correct identification of the top quark or top quark proxydecay products. To test the performance of the reconstruction algorithm an assignment be-tween reconstructed and generator level objects is needed. For the particle level measurementthis relation is straightforward. Reconstructed leptons and jets can spatially be matched to cor-responding objects at particle level. For the parton level measurement we need a definitionhow to match the four initial quarks of a tt decay with reconstructed jets. This is not free ofambiguities since a quark does generally not lead to a single jet. One quark might shower intoseveral jets or several quarks are clustered into one jet if they are not well separated. We intro-duce an unambiguous matching criterion, which matches the reconstructed jet with the highestpT within ∆R < 0.4 to a quark from the tt decay. If two quarks are matched with the same jet,the event is not reconstructible according to our definition.
The same matching criterion is also used to identify particle level jets as tt decay products. Forboth kind of measurements we define as additional jets all particle level jets with pT > 25 GeVand |η| < 2.5 that are not assigned to the respective tt decay products.
All possible assignments of reconstructed jets to tt decay products are tested and a likelihoodthat a certain permutation is correct is evaluated. In each event the permutation with the high-est probability is selected. However, only permutations where the two jets with the highestb tagging probabilities are the two b jet candidates are considered. In addition, the pT of atleast one b jet candidate and at least on jet candidate from the W boson decay have to be above35 GeV. The same algorithm is used either to reconstruct the parton level top quarks or thetop quark proxies. Only the likelihood distributions taken as input differ for the particle andparton level measurements.
The first reconstruction step is the determination of the neutrino momentum p(ν). This is doneusing the algorithm described in Ref. [26]. The idea of this algorithm is to find all possible
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solutions for the three components of the neutrino momentum using the two mass constraints[p(ν) + p(`)]2 = m2
W and [p(ν) + p(`) + p(b`)]2 = m2t , where p(`) and p(b`) are the four-
momenta of the lepton and the b jet in the leptonic top quark decay. Each equation describesan ellipsoid in the three dimensional momentum space of the neutrino. The intersection ofthese two ellipsoids is usually an ellipse that can be parametrized as (Ex(t), Ey(t), Ez(t)). Todetermine the best point on this ellipse we minimize Dν = |(Ex(t)− ~pmiss
T,x , Ey(t)− ~pmissT,y )|. The
values of mt = 172.5 GeV and mW = 80.4 GeV are used. This algorithm leads to a uniquesolution for the longitudinal neutrino momentum pz(ν) and an improved resolution of thetransversal component pT(ν) compared to the Emiss
T . The minimum distance Dν,min can alsobe used to identify the correct b`. In the cases with an invariant mass of the lepton and the b`candidate above mt no solution can be found and we continue with the next permutation.
The likelihood λ, which is maximized to select the best permutation of jets, uses the constraintsof the top quark and W boson masses at the hadronic side and the Dν,min from the neutrinoreconstruction,
− log(λ) =− log(λm)− log(λν), (2)λm =Pm(m2, m3),λν =Pν(Dν,min),
where Pm is the two dimensional probability distribution of the invariant mass of the two jetstested as W boson decay products m2 =
√(p(jW1) + p(jW2))
2 and the invariant mass of alltested th decay products m3 =
√(p(jW1) + p(jW2) + p(bh))2. These distributions, taken from
the POWHEG simulation and normalized to unity, are shown in Fig. 2 for the parton and particlelevel measurements. Permutations with λm smaller than Pm,max/1000 are rejected. This part ofthe likelihood λm is sensitive to the correct reconstruction of the hadronically decaying topmodulo a permutation of the two jets from the W boson, jW1 and jW2 , but none of the measuredkinematic variables will be affected by this ambiguity.
The probability distribution Pν describes the Dν,min of the neutrino reconstruction for a correctlyselected b`. In Fig. 2 the normalized distributions of Dν,min for b` and for other jets are shown. Inaverage the distance Dν,min for correctly selected b` is smaller and with a lower tail compared tothe distance obtained for other jets. Permutations with values of Dν,min > 150 GeV are rejectedsince they are very unlikely to originate from a correct b` association. This part of the likelihoodλν is sensitive to the correct reconstruction of the leptonically decaying top quark.
The likelihood λ, which is the combination of λm and λν as defined in Eq. 2, gives a handleto reconstruct both sides of the tt system. The performance of the reconstruction algorithmis tested using the three tt signal samples generated with POWHEG combined with PYTHIA8and HERWIG++, and MG5 AMC@NLO where we use the input distribution Pm and Pν fromPOWHEG-PYTHIA8. The efficiency of the reconstruction algorithm is defined as the probabilitythat the most likely permutation, as identified by the likelihood λ, is the correct one, giventhat all decay products from the tt decay are reconstructed and selected. These efficiencies as afunction of the jet multiplicity are shown in Fig. 3. Since the number of permutations increasesdrastically with the number of jets it is more likely to select a wrong permutation if there areadditional jets. The performance observed in the various samples is similar. The deviationsare taken into account for the uncertainty estimations. We observe a lower reconstruction ef-ficiency for the particle level measurement. This is caused by the weaker mass constraints fora top quark proxy, which is in contrast to the parton level top quark not required to match
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Figure 2: Top: normalized two dimensional mass distribution of m2 and m3 for the parton (left)and the particle (right) level measurements. Bottom: normalized distributions of Dν,min forcorrectly and wrongly selected b jets of the leptonically decaying top quarks. The distributionsare taken from the POWHEG simulation.
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Figure 3: Reconstruction efficiency of the tt system as function of number of additional jets forthe parton (left) and particle (right) level measurements using different simulations.
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Figure 4: Distribution of the negative log-likelihood for the selected best permutation in theparton (left) and the particle (right) level measurements in data and simulation. The simula-tion of POWHEG together with PYTHIA8 is used to describe the tt production. Experimentaland statistical uncertainties are shown for the simulation that is normalized to the measuredintegrated luminosity.
the top quark and W boson masses as shown in the mass distributions of Fig. 2. This becomesalso visible in the likelihood distributions in Fig. 4. Here the signal sample is divided into thefollowing categories: correctly reconstructed tt systems (tt right reco), events where all decayproducts are available, but the algorithm failed to identify the correct permutation (tt wrongreco), `+jets tt events where at least one decay product is missing (tt not reconstructible), andnon `+jets tt events (tt background). However, the lower reconstruction efficiency of the topquark proxy is compensated by the higher number of reconstructible events.
In Fig. 5 the distributions of pT and |y| of the reconstructed hadronically decaying top quarksfor the parton and particle level measurements are compared to the simulation. In Fig. 6 thedistributions of pT(tt), |y(tt)|, M(tt), and jet multiplicities are shown. In general, a good agree-ment between the data and the simulation is observed though the overall yield in the data isslightly lower. The observed jet multiplicities are lower than predicted.
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Figure 5: Comparisons of the reconstructed top quark pT (top) and |y| (bottom) in the data andthe simulation for the parton (left) and the particle (right) level. The simulation of POWHEG to-gether with PYTHIA8 is used to describe the tt production. Experimental and statistical uncer-tainties are shown for the simulation that is normalized according to the measured integratedluminosity.
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Figure 6: Comparisons of the reconstructed distributions of pT(tt) (top) and |y(tt)| (middle)for the parton (left) and the particle (right) level measurements in the data and the simulation.Bottom: distributions of M(tt) (left) and jet multiplicities (right). The simulation of POWHEG
together with PYTHIA8 is used to describe the tt production. Experimental and statistical uncer-tainties are shown for the simulation that is normalized according to the measured integratedluminosity.
10 8 Unfolding
7 Background subtractionThe backgrounds from single top quark production are subtracted based on the predictions ofthe simulations. Its overall contribution is 4%. Since the calculations have a limited reliabilityafter tt selection we assume an overall uncertainty of 50%. However, this conservative estimatehas negligible impact on the final results.
The simulation of QCD, Drell-Yan, and W boson production, have a limited number of eventsafter the full selection. We extract this background shape from a b tagging sideband, requiringthat there is no b-tagged jet in the event. In this selection the contribution of tt events is about15%. The remaining part consists of QCD, Drell-Yan, and W boson events. The reconstructionalgorithm is exactly the same as for the signal selection. To estimate the shape dependencyfrom this sideband selection we vary the selection threshold of the b tagging discriminant. Thischanges the top quark contribution and the flavor composition. However, we find the observedshape variation to be negligible. For the background subtraction the side band shapes arenormalized to the predicted event yield of the of QCD, Drell-Yan, and W boson simulation. Inthe sideband region we observe a 8% deficit in the data compared to the simulation. This andthe statistical uncertainty of the normalization factor of 15% are considered as uncertainties.The overall contribution of this background is about 5%.
Special care has to be taken on the contribution of non signal tt events, i.e., dileptonic, fullyhadronic, and `+jets events with an intermediate tau for the parton level measurement andall tt events for which no pair of top quark proxies exists for the particle level measurement.The behavior of this background is not independent from the tt cross section and a subtrac-tion according to the expectation can result in a bias of the measurement, especially if largedifferences between the simulation and the data are observed. However, we observe a goodagreement between the data and simulation and we subtract the predicted relative fractionsfrom the remaining event yields. The related bias is estimated in Section 8.
8 UnfoldingFor the unfolding of the differential distributions the iterative D’Agostini method [27] is used.The migration matrix and the truth distribution are needed as input. In the parton level mea-surement the truth distribution is based on the top quark in the full phase space, while in theparticle level measurement it is based on the top quark proxies in the restricted phase space.
The migration matrix shows the relation between the truth and the reconstructed quantities ifan event fulfills all selection criteria and passes the tt reconstruction algorithm. It accounts forthe effects from the parton shower and hadronization as well as the detector response wherethe former has a large impact on the parton level measurement. We also rely on the predictionof additional jets that might allow non-reconstructible events to pass the selection and canspuriously be selected as a jet from tt decay. These input distributions are taken from thePOWHEG simulation and other simulations are used to estimate uncertainties. The binning forthe unfolding is chosen in a way that there are about 50% of the entries in each row and columnof the migration matrix in the diagonal elements.
A cross check of the unfolding procedure with modified spectra is performed to estimate thebias. The modified spectra are obtained by reweighting pT(t), |y(t)|, or pT(tt) in the simulation.The reweighted spectra are chosen in a way that they cover the differences observed betweenthe data and the unmodified simulation, i.e., the bias observed for the modified spectra shouldreflect the bias expected in the unfolded data.
11
The iterative D’Agostini method takes the number of iterations as input parameter. To optimizethis number we test the unfolding procedure using a large number of pseudo experiments forwhich the measured distributions of the reweighted simulations are varied within their statisti-cal uncertainties. These distributions are unfolded and for each bin the mean and the standarddeviation are calculated. As a figure of merit we add in quadrature the relative difference be-tween the mean and the expected value (bias) and the relative standard deviations of all bins.A very large number of iterations corresponds to an inversion of the response matrix. Thisminimizes the bias, but results in large variances and large fluctuations in the unfolded distri-butions. To minimize the variance the algorithm should be stopped as fast as possible. After6–8 iterations the bias has already reached the minimum and we use these for the unfolding.
The unfolded spectra are compared to their corresponding truth distributions after 6–8 itera-tions and the unfolded spectra are in good agreement with the expected truth distributions.Finally, the data is unfolded using these optimized number of iterations. However, the un-folded spectra do not strongly depend on the number of iterations.
9 Systematic uncertaintiesWe study several sources of experimental and theoretical uncertainties. Uncertainties in the jetand Emiss
T calibrations, in the b tagging and lepton selection efficiencies, and in the luminosityfall into the first category.
Uncertainties in the jet energy calibration are estimated by shifting the energy of jets in the sim-ulation up and down by their pT and η dependent uncertainties of 3–7%. At the same time theEmiss
T is recalculated according to the rescaled jet energies. The recomputed response matricesare used to unfold the data. The observed differences between these and the original resultsare taken as uncertainty in the unfolded event yields. The same technique is used to calculatethe uncertainties caused by the jet resolution uncertainty and the remaining uncertainty in theEmiss
T that is not due to jet energy calibrations.
The trigger, reconstruction, and identification efficiencies of leptons are evaluated with tagand probe techniques at the Z boson peak. The uncertainties in the scale factors, which areused to correct the simulation, take into account the different lepton selection efficiencies inenvironments with high jet multiplicities. The overall uncertainty in the lepton reconstructionand selection efficiencies is 3%.
The b tagging efficiency in the simulation is corrected using scale factors determined from thedata [28]. These have an uncertainty of about 2–5% depending on the pT of the b jets.
The effect on the measurement due to the uncertainty in the pileup condition and modeling isestimated by a variation of the minimum bias cross section by 5% and, accordingly, reweightingof the simulation.
The uncertainty in the luminosity measurement is 2.7%.
Into the second category of theoretical uncertainties fall uncertainties in the PDFs, in the choiceof factorization and renormalization scales, in the modeling of the parton shower and the had-ronization, the effect of different NLO calculation methods, and in the top quark mass. Theeffects of these uncertainties are estimated either by reweighting the simulation, e.g., in thecase of PDF, factorization scale, and renormalization scale, or by using a different simulation.The POWHEG simulation combined with HERWIG++ is used to estimate the effect of differentparton shower and hadronization models. In addition, POWHEG-PYTHIA8 samples with a par-
12 10 Cross section results
Table 1: Overview on uncertainties in the differential cross section measurement. Typicalranges of uncertainties in the bins are shown.
source particle [%] parton [%]statistical uncertainty 1–5 1–5b tagging 2–3 2–3jet energy scale 5–7 6–8jet energy resolution < 1 < 1lepton selection 3 3Emiss
T (non jet) < 1 < 1pileup < 1 < 1background 1–3 1–3PDF < 1 < 1fact./ren. scale < 1 < 1NLO generator 1–6 1–10parton shower scale 1–5 2–9POWHEG + PYTHIA8 vs. HERWIG++ < 3 1–12
ton shower scale, varied by a factor of two, are used to study the parton shower uncertainties.The result obtained with MG5 AMC@NLO is used to estimate the effect of different NLO sim-ulations. The effect due to uncertainties in the top quark mass is estimated using simulationswith altered top quark masses.
The background predictions, truth distributions, and response matrices as obtained from themodified simulations are used to unfold the data. The observed deviations with respect to theoriginal result are quoted as uncertainty in the unfolded event yield.
For the PDF uncertainty the variation of the acceptance according to the uncertainties in theNNPDF30 nlo as 0118 [13] parametrization is calculated. In addition, the uncertainties ob-tained using the PDF sets derived with varied values of αs = 0.117 and αs = 0.119 are con-sidered.
An overview on the uncertainties in the differential cross sections is given in Tab. 1 where thetypical ranges of uncertainties in the bins are shown.
10 Cross section resultsThe measured differential cross sections are compared to the predictions of POWHEG andMG5 AMC@NLO, each combined with parton shower simulations of PYTHIA8 andHERWIG++. In addition, the tt multijet simulations of MG5 AMC@NLO at LO(MLM) andNLO(FxFx) with a PYTHIA8 parton shower are shown in Fig. 7 and Fig. 9 as a function of the topquark pT and |y| at parton and particle level, respectively. In Fig. 8 pT and |y| of the top quarksat parton level are compared to an approximate NNNLO [29, 30] and a NLO+NNLL’ [31] calcu-lation. In Fig. 10 and Fig. 11 the differential cross sections are shown as a function of kinematicvariables of the tt system and the number of additional jets.
The precision of the measurement is limited by systematic uncertainties, dominated by jet en-ergy scale uncertainties on the experimental side and parton shower modeling uncertaintieson the theoretical side. Where the theoretical uncertainties are reduced in the particle levelmeasurement. In general, the observed cross section is slightly lower than expected. However,
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Figure 7: Differential cross sections at parton level as a function of pT(t) and |y(t)| comparedto the predictions of POWHEG and MG5 AMC@NLO plus PYTHIA8 (P8) or HERWIG++ (H++)and the multijet simulations MG5 AMC@NLO (MLM) and MG5 AMC@NLO (FxFx).
this effect is covered by both of these leading systematic uncertainties. As observed from theratio plots, the measured shapes are in agreement with all simulations. Only the measured jetmultiplicities are lower than predicted.
11 SummaryMeasurements of the differential tt production cross section in pp collisions at 13 TeV basedon an integrated luminosity of 2.3 fb−1 have been presented. The tt production cross sectionis measured as a function of pT and |y| of the top quarks and as a function of pT, |y|, and in-variant mass of the tt system, as well as the jet multiplicity. The measurement at parton level isdominated by uncertainties in the parton shower and hadronization model. The dependencyon these theoretical models is reduced for the particle level measurement, for which the exper-imental uncertainties of jet energy calibration and b tagging efficiency are the most dominant.The results are compared to several standard model calculations. All calculations are compati-ble with the measured results.
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14 References
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Figure 8: Differential cross sections at parton level as a function of pT(t), |y(t)|, and M(tt)compared to the predictions of an approximate NNNLO calculation [29, 30] and a NLO+NNLL’calculation [31].
References 15
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Figure 9: Differential cross sections at particle level as a function of pT(t) and |y(t)| comparedto the predictions of POWHEG and MG5 AMC@NLO plus PYTHIA8 (P8) or HERWIG++ (H++)and the multijet simulations MG5 AMC@NLO (MLM) and MG5 AMC@NLO (FxFx).
16 References
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Figure 10: Differential cross sections as a function of pT(tt), |y(tt)|, M(tt), and the num-ber of additional jets compared to the predictions of POWHEG and MG5 AMC@NLO plusPYTHIA8 (P8) or HERWIG++ (H++) and the multijet simulations MG5 AMC@NLO (MLM)and MG5 AMC@NLO (FxFx).
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Figure 11: Differential cross sections at particle level as a function of pT(tt), |y(tt)|, M(tt), andthe number of additional jets compared to the predictions of POWHEG and MG5 AMC@NLOplus PYTHIA8 (P8) or HERWIG++ (H++) and the multijet simulations MG5 AMC@NLO(MLM) and MG5 AMC@NLO (FxFx).
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