Abstract

The production of 4 jets has been measured in pp collisions at s = 7 TeV using a luminosity of 36 pb−1 with the CMS detector at the LHC. The jets are reconstructed with the anti-kt jet algorithm in a range of |eta| < 2.5. The two leading jets are required to have a transverse momentum pt > 50 GeV and the two soft jets to have pt > 20 GeV. The cross section is measured as a function of the transverse momentum and the pseudorapidity of each of the four jets. The measured cross sections agree within uncertainties with predictions of LO and NLO dijet calculations matched with parton showers. Correlations between the four jets are measured which are useful for future studies to investigate contributions from double parton scattering.

Introduction

The production of jets with large transverse momenta pT in high energy pp collisions is believed to originate from a scattering of partons which can be described within the theory of strong interactions, Quantum Chromodynamics (QCD). The partonic process is convoluted with the density of partons inside the protons. The inclusive cross section for high pt jets has been measured by CMS and ATLAS and is in good agreement with predictions obtained at next-to-leading order QCD. However, the production of a forward jet in association with a jet in the central region of the detector is not very well described. The production of 4 jets at large transverse momenta provides additional and new information of the production process as it involves terms of alpha_s^4. Measurements with jets in the final state are needed to investigate and study the features of Quantum Chromodynamics (QCD). By requiring pairs of jets at different thresholds in transverse momentum, two processes at different scales are naturally selected: the hard scattering producing a pair of partons at high p T , and their evolution resulting in additional jets at lower momenta. This 2 -> 4 partonic process, (single parton scattering SPS), is a crucial test for higher order QCD calculations as well as for the description of high pT jets within a parton shower formalism. At high centre-of-mass energies the parton densities become large and the probability to have more than one partonic interaction becomes non-negligible, such that the pair of hard jets and the pair of softer jets can be produced via a double parton scattering (DPS). SPS and DPS processes result in different distributions of angular correlations. A final state arising from SPS tends to have a strongly correlated configuration in the azimuthal angle and p T -balance between the two jet systems, while a DPS event has a preferred back-to-back topology. Four-jet production at large transverse momenta pT is measured at s = 7 TeV using an integrated luminosity of 36 pb−1 recorded with the CMS detector at the LHC. The jets are reconstructed with the anti-k T algorithm in the pseudorapidity range of |eta| < 2.5. The two leading must have a transverse momentum pt > 50 GeV while the two other jets must have pT > 20 GeV. The cross section as a function of the transverse momenta and the pseudorapidity eta of the four jets is presented. In addition, the cross section is measured as a function of correlation variables, defined from the hard and soft pair of jets: the difference in azimuthal angle of the jet pair with small and large transverse momenta, DeltaPhi , the normalized sum of transverse momenta of the different jet pairs, Delta_rel pT, as well as the difference in pseudorapidity of the four jets. Distributions normalized to the visible cross section are also presented, since there some of the systematic uncertainties cancel, and thus allow a detailed comparison with the shape of the predicted distributions and eventually allow to tune free parametrs in the Monte Carlo event generator simulations. The measurements are compared to predictions from Monte Carlo event generators using O(α2 ) matrix elements improved with parton showers and DPS, which can be used in future to study a DPS contribution in four jet events. The measurements are also compared to predictions for dijet production at NLO matched to parton showers.

The discriminating observables

In order to separate the contributions of SPS and DPS, some discriminating variables were used. These were chosen based on the study described in arXiv: 0911.5348v1, defined in such a way to exploit the different behaviours of the two processes. In fact, a final state arising from a single chain tends to have a strongly correlated configuration in the azimuthal angle and $p_{T}$-balance distribution between the two jet systems, while a DPS event has a preferred back-to-back topology for the separated systems that are not correlated. Thus, intererting observables to look at to separate the two processes are:

• Delta_{p_T}^{hard} = (p_T^(hard1)+p_T^(hard2)/(|p_T^(hard1)|+|p_T^(hard2)|
• Delta_{p_T}^{soft} = (p_T^(soft1)+p_T^(soft2)/(|p_T^(soft1)|+|p_T^(soft2)|

where p_T^(hard1) and p_T^(hard2) are the vectorial momenta for the two hard-jets and p_T^(soft1) and p_T^(soft2) are the ones for the soft-jets. Delta_{p_T}^{hard} and Delta_{p_T}^{soft} are defined as the normalized p_T balances for the hard- and soft-jets, respectively. In particular, a back-to-back topology for the two separate jet-systems contribute at low values of Delta_{p_T}^{soft}, Delta_{p_T}^{hard} while correlated pairs of jets bring to a broader distribution over the whole phase space. Going further, it is possible to combine the information from the two sets of jets, by building a new variable:

The different configurations for the jets in the final state translate also in different regions for angular variables. It is important to study the phase space for variables defined by the azimuthal angles of separate and combined jet pairs. In particular, these two variables

• Delta_phi_{hard}=phi_{hard-jet 1}-phi_{hard-jet 2}
• Delta_phi_{soft}=phi_{soft-jet 1}-phi_{soft-jet 2}

have a good distinguishing power. Delta_phi_{hard} and \Delta_phi_{soft} compute the angle between the two jet-systems. SPS events lead to a broad distribution for these quantities, while DPS events contribute most at values close to 3.1415, meaning an uncorrelation for the jets of the same type. Recently, also the configuration of the jet pairs in pseudorapidity came up into the discussion since it can be also interesting for the signal discrimination. The difference in eta between the hard jets and the soft jets has been studied and the following observables have been defined:

• Delta_eta_{hard}=eta_{hard-jet 1}-eta_{hard-jet 2}
• Delta_eta_{soft}=eta_{soft-jet 1}-eta_{soft-jet 2}

In particular, some differences between the two processes are mainly expected for Delta_eta_{hard}: a SPS process presents a longer tail towards high values due to the randomization introduced from the emitted radiation, while DPS should be more relevant at low values. Even for Delta_eta_{soft}, the same behaviour can be exhibited and is worthy to be checked.

Study at the generator level

A study at the generator level for these observables is shown in https://twiki.cern.ch/twiki/bin/view/Sandbox/AnalysisBBbarJetEventsPlusTwoLightJets

The experimental measurement

Three different runs from the 2010 data taking were used for the measurement. They are listed in the table below, along with the run ranges and the integrated luminosity for each of them. They correspond to different pile-up conditions with a mean value of the pile-up interactions ranging from 1.5 to 2.8. The treatment of the pile-up is shown in section 5. Data from the early stages of the LHC can give reasonable statistics for the applied selection and have been chosen in order not to have a high contribution on the jet spectrum coming from the pile up.

Data Sample Run range Trigger Integrated luminosity (pb^(-1)
JETMET 141950-144114 HLT_Jet30U 0.192895
141950-144114 HLT_Jet50U 2.896
JETMETTAU 135821-141887 HLT_Jet30U 0.117223
135821-141887 HLT_Jet50U 0.278789
JET 146240-149711 HLT_Jet30U 0.026783
146240-149711 HLT_Jet50U 0.239874

Different MC generators were used to compare predictions at the detector level and to correct at the generator level. Two samples generated respectively with Pythia6 tune Z2 and Herwig++ from a central CMS production and another one generated with Pythia8 tune 4C from a private production are compared. The first two were generated with a flat distribution in p_T_hat of the outgoing interacting partons between 15 and 3000 GeV while the third one used a generation in p_T_hat slices with a cut at the generator level for at least 4 jets in the central region (|eta|<2.5) with a p_T>15 GeV in order to increase the statistics for the applied selection. The first two include pile-up events while the third one is generated without it. The detector behaviour is simulated through a full simulation performed with Geant4. The details of the MC samples can be read in table below.

Montecarlo sample DBS location Number of gen events Cross section (pb)
Pythia6 Tune Z2 QCD_Pt-15to3000_TuneZ2star 9982400 2.21268193 x 10^{10}
Herwig++ Tune 2.3 QCD_Pt-15To3000_Tune23 9971200 2.30854004 x 10^{10}

Data and MC have been analyzed inside the CMSSW framework with the release 4_2_4_patch2, with the recommended global tags (respectively GR_R_42_V19::All and START42_V19B::All).

Trigger selection

The CMS trigger system is designed to control event rates consistent with available bandwidth. It consists of two parts, the Level-1 Trigger (L1) and High-Level Trigger (HLT), where the former one is mainly a hardware based trigger, where as the later one is a software based trigger. In this analysis, the trigger paths which were used are single jet triggers: L1SingleJet and HLTJet which combinedly forms the HLTJet trigger path. It is to be noted that jets used in the trigger paths are corrected AK5 calorimeter jets. Two different trigger paths were used from the data samples. In particular, the phase space was divided in three different regions as a function of the leading jet p_T selected in the central region corresponding to |eta|<2.5 and in each of these regions, only one trigger was used for each data sample. The regions were characterized by:

• 50 < leading jet p_T < 80 GeV
• 80 < leading jet p_T < 140 GeV
• leading jet p_T > 140 GeV

A schematic picture that explains the idea of the separation of the phase space in regions, can be found in the picture.

For the first two regions, the HLT_Jet30U trigger was used, while the third one was triggered by the HLT_Jet50U trigger. This analysis strategy allows to avoid double counting of events that triggered two different triggers and to reach significant statistics for the applied selection.

Trigger efficiency

The behaviour of the used triggers as a function of the leading jet p_T was studied in order to correct for possible inefficiencies in the different regions of the phase space. In order to do this, turn on curves for each HLT trigger paths were produced. The trigger efficiency was studied in two different ways and the results were compared for cross-check. The first method uses and the trigger efficiency for HLT_JetY is defined as:

Here the denominator is the number of events for which the trigger path HLT_JetX has fired. Here the value of X is chosen previous to that of Y in p_T ordering from the trigger list so that the higher trigger condition can be emulated from the lower trigger path. The numerator is the number of events for which HLT_JetX has fired and the p_T of HLTObject corresponding to the trigger path HLT_JetX is > Y. This efficiency is plotted against the corrected inclusive leading RecoJet p_T. For example, in order to obtain turn on curve for HLT_Jet30U, the immediately HLT path of lower threshold HLT_Jet15U is chosen, the p_T cut on L1Object corresponding to the trigger path HLT_Jet15U is 15 GeV. In figure below, we display the trigger turn on curve for HLT_Jet30 and HLT_Jet50 trigger paths for the inclusive central region |eta|< 2.5, as a function of the leading jet p_T. The dependence of the trigger efficiency on the pseudorapidity was also investigated and found to be negligible. In fig. below, the trigger efficiency is shown as a function of the pseudorapidity of the leading jet and it appears to be flat.

At the thresholds used for each trigger, there is no need to correct for the L1 trigger efficiencies in the second and third region, while the first region has been corrected by using the fit represented in fig. below for HLT_Jet30U, since it is not 100% efficient in that p_T range as seen in table below. The best fit to the curve was found to be a 8-degree polynomial function.

Pile-up reweighting

In order to study the pile-up contribution for each data sample, a pile-up reweighting has been applied to the MC samples. A pile-up event is defined as an additional interaction inside the same bunch crossing. The pile-up in the MC samples has been implemented by adding at the hard scattering, several additional interactions, recorded from data as Minimum Bias events. By reweighting the pile-up, it is possible to study its contribution to the measured observables.

The reweight procedure is based on an iterative process: the absolute reconstructed vertex distribution is extracted from data and MCs. The MCs are then reweighted according to this ratio as a function of the number of pile-up interactions for each event. The absolute reconstructed vertex distribution obtained after the reweighting is then considered, a new ratio with the vertex distribution in the data is evaluated and the MC sample is again reweighted as before. An iteration of 4 reweights was found to be satisfying and, as shown in figure \ref{vertexreweight} for the JETMET data sample, a nice agreement for Pythia and Herwig++ has been found.

Jet Selection

In both data and MC, a request for a good quality of at least one reconstructed vertex was applied. It implies the presence of a vertex with number of degrees of freedom greater than 4 and a distance to the beam spot in the longitudinal coordinate smaller than 10 cm.

The same jet selection described in section 3 in the phenomenological study was applied at the detector level. In particular, 4 jets in the central region, corresponding to |eta|<2.5, were requested exclusively. Two of them were requested to have a corrected transverse momentum above 50 GeV and the other two a corrected transverse momentum greater than 20 GeV. A tight selection was applied for the selected jets: this is required in order to suppress non physical jets, i.e. jets resulting from noise in the electromagnetic and/or hadronic calorimeters. Each jet should contain at least two particles, one of which is a charged hadron and the jet energy fraction carried by neutral hadrons, photons, muons and electrons should be less than 90%. These tight criteria have an efficiency greater than 99$\%$ for physical jets. For the jet p_T correction, the L1 (Offset) + L2(Relative) + L3 (Absolute) + Residual jet energy correction were applied on the data. On Monte Carlo L1 (Offset) + L2 (Residual) + L3 (Absolute) corrections have been applied.

Results of the selection

A table with the total number of events and with the number of selected events progressively after each applied cut can be found in tables below for each data and MC sample.

DATA sample Total Number of Events Trigger requirement Good Vertex requirement Number of events in the trigger region Number of Selected Events
JETMET 20350952 50-80 6730757 1168570 17125
20350952 80-140 6730757 232628 19198
20350952 >140 6730757 283420 57318
JETMETTAU 4887422 50-80 1728630 722490 10647
4887422 80-140 1728630 143640 5431
4887422 >140 1728630 27606 11785
JET2010B 11234922 50-80 408361 165592 2624
11234922 80-140 408361 33016 4958
11234922 >140 408361 24902 2784

Montecarlo Sample Total Number of events Number of Triggered events Good Vertex requirement Number of selected events
Pythia6 9982400 7128229 7127080 1130589
Herwig++ 9971200 6732445 6731530 1125835

Results at the detector level

The observables defined in section 3 have been measured for data and MC and are shown in this section. These plots are referred to the JETMET sample and the MCs have been reweighted with the corresponding reconstructed vertex distribution. The trigger efficiency correction is here applied, as described before.

First of all, it is worthy to look at the distributions of the jet multiplicity in order to check the agreement between data and MC. In figures below, three different p_T thresholds have been applied at the jets in the central region: in (a), all the jets with p_T greater than 20 GeV have been selected, in (b), the number of hard jets (p_T > 50 GeV) is shown while in (c), only the soft jets (20 < p_T < 50 GeV) are taken into account.

The following figures represent the absolute cross sections and the shapes for the same observables. Both the figure sets deal with data at detector level, i.d. uncorrected data.

There is an overall agreement in all the distributions, both in the absolute cross sections and in the shapes. For the cross sections, in particular, both the MC samples predict a slightly bigger (~10%) total number of events that makes the distributions a little shifted up. The comparison between data from the other samples and MC brings to the same conclusions.

Purity, stability, background and acceptance

\subsubsection{Purity, stability, background and acceptance} \addcontentsline{toc}{subsubsection}{Purity, stability, background and acceptance} In order to study the reliability of the measured observables, the migration effects inside and outside the phase space need to be studied. In particular, events selected at the detector level may not have a corresponding event at the generator level under detector effects like inefficiencies or resolution, or in the same way events at the generator level may not be selected at the detector level for the same reasons. On the other hand, it may occur that events selected in both generator and detector level can belong to different bins for the same observables, again under the effect of the resolution. The former type of events is labelled as migration outside the phase space, while the latter one is identified as migration inside the phase space. The events that were selected in both detector and generator level are labelled as "matched events'' but no eta-phi matching was applied in order not to introduce a bias in the study of the migration effects. A correction for the migration effects, both inside and outside the phase space, is needed and this is done by evaluating some quantities, defined in the following.

For the migration outside the phase space, acceptance and background are defined respectively as the fraction of events at the detector level that have a corresponding event at the generator level and the fraction of events at the generator level that have a corresponding one at the detector level. These quantities are evaluated for each bin of the measured observables. It is worthy to remind that the same binning has to be used for the detector and the generator level. In a compact way, acceptance and background can be expressed as:

• B_{i}^{MC}=1- N^{MC}_{matched jets} E^{MC}_{det} bin i) / N_{all jets}^{MC(E_{det}^{MC} bin i)

For the migration inside the phase space, it is useful to study the purity and the stability of the observables. In particular, the purity is defined as the fraction of the matched events that remain in the same bin as the detector level selection, while the stability is the fraction of the matched events that stay in the same bin as the generator level selection. Again, in formulas, they can be defined as:

• P_{i}^{MC}=N^{MC}_{matched jets}(E^{MC}_{det} bin i && E^{MC}_{had} bin i) / N_{matched jets}^{MC}(E_{det}^{MC} bin i)
• S_{i}^{MC}=N^{MC}_{matched jets}(E^{MC}_{det} bin i && E^{MC}_{had} bin i) / N_{matched jets}^{MC}(E_{had}^{MC} bin i)

In the following figures purity, stability, acceptance and background are shown for the whole set of the measured observables, using Pythia6. A high value of purity and stability is required, as well as high acceptance and low background, over the whole phase space.

Purity and stability are overall for each measured variable above 0.6. For the angular variables, i.e. Delta_phi^{hard}, Delta_phi^{soft}, Delta_eta^{hard} and Delta_eta^{soft}, they are around 0.8-0.9, while for the p_T balance observables, i.e. S_{p_T}^{hard} and S_{p_T}^{soft}, purity and stability decreases at low values under the effect of the p_T resolution.The leading jet p_T and eta distributions have again high values of purity and stability above 0.7. The acceptance is around 0.5-0.6 without any big fluctuations, while the background curves are fluctuating a bit more and again around 0.6. Background events are due both to not matched events, in particular to events at the detector level that are not present at the generator level because of reconstruction inefficiencies or migration effects, or to pile-up events, where one or more jets at the detector level come from pile-up interactions; such event can not be matched at the generator level because there is no information of gen-jets coming from the pile-up.

Bin-by-bin correction factors

Since the migration effects inside the phace space are not relevant for the measured observables, as shown in the previous section, a bin-by-bin correction can be applied in order to extract the distributions at the generator level. The bin-by-bin correction factors are computed by using both MC samples and they are defined as the bin-by-bin ratio between the distributions at the generator level and the ones at the detector level:

• C_{i}^{MC}=N_{all jets}^{MC}(E_{had}^{MC} bin i) / N_{all jets}^{MC}(E_{det}^{MC} bin i}

In the figures below, the correction factors are shown for each measured quantity. Three MC samples are here shown: the usual Pythia6 and Herwig are the ones that are taken into account for the evaluation of the final correction factors and in addition the correction factor from a sample generated with Pythia8 tune 4C without pile-up is also plotted. This can help to understand the effect of the pile-up in the correction factors, but the values of this sample are not considered for the final correction.

Systematic uncertainties

Some additional uncertainties due to systematic effects were also evaluated. Analyses using jets have to consider in particular the impact of the jet energy scale and the jet energy resolution. The uncertainty on the luminosity and a study on the model dependence has to be also performed. All these effects that can play a role and can affect the measurements are described and treated in the following sections and they are evaluated both for the absolute cross section measurements and for the shape distributions.

Jet energy scale uncertainty

The applied jet energy correction carries a defined uncertainty whose effect has to be evaluated when dealing with jets. Since this analysis is based on the selection of a quite high number of jets, it is expected that this is the major factor that affects the total systematic uncertainty. The effect of the jet energy scale has been evaluated by varying up and down the jet transverse momentum by the uncertainty; the observables obtained with these changes are then compared to the nominal distributions, by evaluating the ratios between them. The maximum discrepancy between the nominal distributions and the ones got from the modified jet scale is referred as the jet energy scale uncertainty. The results show a contribution around 20-25% for the absolute cross section and less than 5% for the shape distributions.

Model dependence uncertainty

Different MC generators were used to compute the uncertainty due to the physics models. In particular, the half discrepancy between Pythia and Herwig samples at the detector level is referred as the model dependence uncertainty. They are using different models for MPI and hadronization and it is important to study the effect of the different physics used by the generators on the measured observables. The results show a contribution around 5-10$\%$ for the absolute cross section and around 5% for the shape distributions.

Jet energy resolution uncertainty

One of the most important detector effects on a jet measurement is the energy resolution. The jet energy response is not exactly corresponding to the true value of the measured physical quantity but it results in a gaussian distribution around it. The wider the distribution is, the less accurate the measurement is. The width of this distribution is called resolution. While the angular resolutions in eta and in phi were found to have negligible effect for the described measurement, the resolution in the transverse momentum (equivalent to the one in the energy) is more relevant and its effect needs to be taken into account. In order to do this, the p_T of the jets was smeared out around its true value by matching every jet at the detector level to the closest one at the generator level. The match is performed through an angular cone algorithm with an aperture \Delta R=sqrt{(Delta eta)^2+(Delta phi)^2} = 0.3. The smearing procedure is summarized by the formula:

• p_{T}^{smeared}=p_T^{true} +/- a x (p_T^{true}-p_T^{det level})

with a = official parameters of the detector resolution for the 2010 data and p_T^{true}, p_T^{det level} transverse momenta of the two matched jets, respectively the generator and the detector level one. The uncertainty due to this effect was computed by taking the ratios of the samples with the sign plus and the sign minus with the nominal sample. These values for each bin are taken as uncertainties. The results show a contribution aroundless than 5% for both the absolute cross section and the shape distributions.

Total uncertainty

The previous uncertainties are finally combined in order to get the total systematic uncertainty. For 2010 data, the official uncertainty on the luminosity is around 4% and this value was taken for this analysis and included in the combination. The combination of the uncertainties has been evaluated by summing in quadrature the single contributions, assuming absence of correlation among the different sources. The final results are shown in figures in the AN.

Results

The distributions corrected at the stable particle level are presented in this section. The data from each sample were corrected and combined. The combination of the data and of the systematics was performed by weighting every sample according to the fraction of selected events with respect to the total number. In the following figures, the absolute cross sections and the shapes are presented. The different data samples have been combined by correcting each of them with the corresponding correction factors and then by weighting every sample according to the fraction of selected events. In particular, the JETMET sample is the one that gets the higher weight while the JET sample is the less relevant.

By looking at the shapes, the picture is more clear since the systematic uncertainty is much lower than the previous case. For the basic distributions related to p_T and eta of the selected jets, a nice agreement is obtained among all the predictions and the data. By looking at the discriminating observables, some slight discrepancies are observed: mainly for Pythia6, a lack of events of the order of 10% is present at low values of S_{p_T}^{hard}, S_{p_T}^{soft} and S_{p_T}', and at high values of Delta phi^{hard}, Delta phi^{soft} and S_{phi}. The agreement for Herwig++ seems to be the best for all the discriminating variables. Pythia8 slightly fails to describe the overall shape of the data both in the signal and in the background regions for S_{p_T}^{hard}, S_{p_T}^{soft}, \Delta\phi^{hard} and \Delta\phi^{soft}. All the Monte Carlo generators provide a nice description of the \Delta\eta observables. It will be very interesting to add to the comparison more Monte Carlo generators and also to study different samples for background and signal in order to check the room left for DPS.

Conclusions

A measurement of exclusive four jets has been performed using data collected with the CMS experiment in 2010 and corresponding to 36 pb−1 . The cross section of a final state with a pair of hard jets with pt > 50 GeV and another pair with pT > 20 GeV within a range in pseudorapidity of the jets |eta | < 2.5 has been measured to σ (4 jet) = 201 ± 3stat ± 34syst . The cross section as a function of pt and eta of each of the four jets together with the cross section as a function of correlation variables Delta phi, Delta_rel pT and Delta eta are presented and compared to several the- oretical predictions. The theoretical predictions agree essentially with the measurements. The NLO dijet calculation matched with parton showers (POWHEG) agrees with the measurement for specific tunes used in the simulation of multiparton interactions, however, the sensitivity to the parameters used in the parton shower simulation is significant.
Topic revision: r7 - 2013-05-31 - PaoloGunnellini

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