Measurement of the underlying event in jet events from 7 TeV proton-proton collisions with the ATLAS detector

Distributions sensitive to the underlying event in QCD jet events have been measured with the ATLAS detector at the LHC, based on 37/pb of proton-proton collision data collected at a centre-of-mass energy of 7 TeV. Charged-particle mean $p_T$ and densities of all-particle $E_T$ and charged-particle multiplicity and $p_T$ have been measured in regions azimuthally transverse to the hardest jet in each event. These are presented both as one-dimensional distributions and with their mean values as functions of the leading-jet transverse momentum from 20 GeV to 800 GeV. The correlation of charged-particle mean $p_T$ with charged-particle multiplicity is also studied, and the $E_T$ densities include the forward rapidity region; these features provide extra data constraints for Monte Carlo modelling of colour reconnection and beam-remnant effects respectively. For the first time, underlying event observables have been computed separately for inclusive jet and exclusive dijet event selections, allowing more detailed study of the interplay of multiple partonic scattering and QCD radiation contributions to the underlying event. Comparisons to the predictions of different Monte Carlo models show a need for further model tuning, but the standard approach is found to generally reproduce the features of the underlying event in both types of event selection.


Introduction
To perform precise measurements or search for new physics phenomena at hadron colliders it is essential to have a good understanding not only of the hard scattering process, but also of the accompanying interactions of the rest of the proton.The aspects of a given collider event not identified with the hard process are collectively termed the "underlying event" CERN, CH-1211 Geneva 23.Switzerland (UE).The UE can receive contributions not only from additional partonic scatters in the same proton-proton collision (multiple parton interactions, or MPI) and from quantum chromodynamics (QCD) colour connections between partons and beam remnants, but also from processes typically associated with the hard process, such as QCD initial-and final-state radiation (ISR, FSR).It is impossible, even in principle, to unambiguously separate the UE from the hard scattering process on an event-by-event basis.However, observables can be measured which are particularly sensitive to its properties.
The low-momentum QCD processes which dominate the UE are the main type of interaction in proton-proton collisions.The behaviour of such soft interactions cannot be calculated reliably with perturbative QCD methods, due to the divergence of the QCD coupling at low scales; it is therefore typically modelled in a phenomenological manner by Monte Carlo (MC) event generator programs.These models invariably contain parameters whose values are not a priori known or calculable and must instead be fitted ("tuned") to experimental data.Predictivity of UE modelling is important since the UE forms an irreducible background of particle activity in all hard-scale processes studied at the LHC.Most new-physics searches operate in event types with high momentum transfer where the UE has not yet been measured, hence extension of the measurements into these regions is important, as is testing the reliability of the UE modelling between hard process types with different QCD colour flows.
UE observables were previously measured by both the Tevatron and LHC experiments.The CDF experiment measured the UE with inclusive jet and Drell-Yan events in Tevatron proton-antiproton (p p) collision data, at centre-ofmass energies of √ s = 1.8 TeV [1] and 1.96 TeV [2].The ATLAS [3][4][5][6], ALICE [7] and CMS [8,9] experiments at the LHC have thus far measured observables sensitive to the UE in proton-proton (pp) collision data at √ s = 900 GeV and 7 TeV, using track-jets, leptonically decaying Z bosons, and the highest-p T charged particle to define the hard scattering direction in the event.This paper reports a measurement of UE observables in inclusive jet and exclusive dijet events, recorded by the ATLAS detector [10] at the LHC using proton-proton collisions at a centre-of-mass energy of 7 TeV, from the LHC 2010 run.This study extends the phase-space coverage of previous studies of the UE by probing a much higher jet-p T scale (up to 800 GeV), studying a subset of events with an exclusive dijet topology, and by measuring the sum of the transverse energy in the full range of the ATLAS calorimeter acceptance.This paper is organised according to the following structure.The ATLAS detector is described in Sect. 2. The observables sensitive to the underlying event are defined in Sect.3. In Sect.4, the QCD MC models used in this analysis are discussed.Sections 5-7 respectively describe the event selection, correction of the data back to particle level, and estimation of the systematic uncertainties.The results are discussed in Sect.8 and finally the conclusions are presented in Sect.9.

The ATLAS detector
The ATLAS detector is described in detail in Ref. [10].In this analysis, the trigger system, the tracking detectors, and the calorimeters are of particular relevance.
The ATLAS inner detector is immersed in the 2 T axial magnetic field of a superconducting solenoid, and measures the trajectories of charged particles in the pseudorapidity range |η| < 2.5 with full azimuthal coverage. 1The inner detector consists of a silicon pixel detector (pixel), a silicon microstrip detector (SCT) and a straw-tube transition radiation tracker (TRT).The inner detector barrel (endcap) detectors consist of 3 (2 × 3) pixel layers, 4 (2 × 9) layers of double-sided silicon strip modules, and 73 (2 × 160) layers of TRT straws.The pixel, SCT and TRT have r-φ position resolutions of 10 µm, 17 µm, and 130 µm respectively, and the pixel and SCT have z-coordinate (r-coordinate) resolutions of 115 µm and 580 µm respectively in the barrel (endcaps).A track traversing the barrel typically has 11 silicon hits (3 pixel clusters, and 8 strip clusters), and more than 30 straw tube hits.
Electromagnetic (EM) calorimetry is provided by liquidargon (LAr) calorimeters.The barrel (|η| < 1.475) and endcap (1.375 < |η| < 3.2) sections have lead absorbers, and the 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe.The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward.Cylindrical coordinates (r, φ ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe.The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ /2).forward (3.1 < |η| < 4.9) section (FCal) contains LAr/Cu modules.The hadronic calorimeter is divided into four sections: the barrel (|η| < 0.8) and extended barrel (0.8 < |η| < 1.7), both of which are scintillator/steel sampling calorimeters; the hadronic endcap (1.5 < |η| < 3.2), which has LAr/Cu modules; and the hadronic FCal, which has LAr/W modules and covers the same η range as the EM FCal.The total calorimeter coverage is |η| < 4.9.
The EM calorimeter has three longitudinal layers (called strip, middle and back) and a fine segmentation in the lateral direction of the showers within the inner detector coverage.At high energy, most of the EM shower energy is collected in the middle layer which has a η-φ granularity of η × φ = 0.025 × 0.025.The η-φ granularity in the hadronic endcap ranges from η × φ = 0.1 × 0.1 to 0.2 × 0.2.In the forward calorimeter, the cells are not arranged in projective towers but are instead aligned parallel to the beam axis.As such the readout granularity is not constant in η-φ .
The ATLAS detector has a three-level trigger system: level 1, level 2 and the event filter.Data were taken for this analysis using the single-arm minimum bias trigger scintillators (MBTS) and central jet-trigger, covering |η| < 3.2.The MBTS are mounted at each end of the detector in front of the liquid-argon endcap-calorimeter cryostats at z = ±3.56m and are segmented into eight sectors in azimuth and two rings in pseudorapidity (2.09 < |η| < 2.82 and 2.82 < |η| < 3.84).Events were triggered by the MBTS system if at least one hit from either side of the detector was recorded above threshold.

The underlying event observables
The UE observables presented in this paper are constructed separately from charged-particle tracks with p T > 0.5 GeV and from three-dimensional clusters of calorimeter cells [11].
Tracks are required to be within |η| < 2.5 for all observables by the acceptance of the ATLAS tracker, while clusters are constructed separately for pseudorapidity acceptances of |η| < 4.8 and |η| < 2.5 to provide one measurement with full forward coverage and one compatible with the more restricted acceptance of the tracker.
These detector-level objects were corrected to hadronlevel quantities (i.e. in terms of particles with a mean proper lifetime τ > 0.3 × 10 −10 s either directly produced in the pp interactions or in the decay of particles with a shorter lifetime) using the definitions given in Refs.[3,6].The jet correction to hadron level is based on charged and neutral particles with this lifetime cut, excluding neutrinos.The selected tracks were corrected to primary charged particles with p T > 0.5 GeV and |η| < 2.5.No attempt was made to identify single calorimeter cell clusters (according to the ATLAS definition [11]) with primary particles, but momentum sums of cluster energies were corrected to momentum sums of primary charged particles with momentum p > 0.5 GeV and primary neutral particles (including neutrinos) with p > 0.2 GeV.Lower-momentum particles were not included because detector simulation indicated that they do not deposit significant energy in the ATLAS calorimeters, due to interactions with detector material at smaller radii and bending in the magnetic field.Since the properties of low-momentum particles are not well known or modelled, excluding them from the hadron-level phase space definition reduces the model dependence of the correction procedure.
The observables used in this study, defined in Tab. 1, employ the conventional UE azimuthal division of events into regions relative to the direction of the "leading" object in the event [1].The leading object in this case is defined by the anti-k t [12] jet with distance parameter R = 0.4 which has the largest p T (denoted by p lead T ) after application of the jet selection criteria described in Sect. 5.At hadron level the jets are constructed from primary particles as previously defined, excluding neutrinos.The azimuthal regions are defined with respect to the φ of the leading jet: a 120 • "towards" region surrounds the leading jet, an "away" region of the same size is azimuthally opposed to it and two "transverse" regions each of 60 • are defined orthogonal to the leading jet direction.This is illustrated in Fig. 1, which displays the azimuthal distance from the leading jet, |∆φ |, used to define the UE regions.
Since the towards region is dominated by the leading jet and the away region by the balancing jet (in the dominant dijet configuration), the transverse regions are the most sensitive to accompanying particle flow, i.e. the UE.In addition, the transverse regions may be distinguished event-by-event based on which one has more or less activity, named the "trans-max" and "trans-min" sides respectively.The transmax side is more likely to be affected by wide-angle emissions associated with the hard process and correspondingly the trans-min observables have the potential to be more sensitive to soft MPI and beam-remnant activity.In this analysis, the trans-min/max definition is specific to the observable being considered; for example the trans-max side for the charged-particle multiplicity (N ch ) observable (i.e. the side of the transverse region which contains more charged particles) can be different from the trans-max side for the scalar sum of the particle transverse momentum (∑ p T ) observable in the same event.The difference between trans-max and trans-min sides for a given observable is referred to as the "trans-diff" of that observable [13,14].The trans-diff observables are very sensitive to hard initial-and final-state radiation.
This azimuthal segmentation of events around the leadingjet direction is based on an assumption of dominant dijet topologies.Measurements of LHC jet rates [15] indicate that events with three or more jets contribute to inclusive jet UE observables; hence there are substantial contributions to the transverse regions from the hard partonic scattering.While this subverts the intent of the azimuthally segmented observable definitions, the resulting interplay of hard and soft event Fig. 1 Definition of regions in the azimuthal angle with respect to the leading jet.The towards, away and transverse regions are defined in the text.The balancing parts of the jet system are indicated with green arrows, compatible with the dominant dijet event topology.Multi-jet topologies, encountered in the inclusive jet event selection, are expected to contribute more substantially to the transverse regions than the geometry shown here.
features is itself interesting and relevant to modelling of hard pp interaction processes at the LHC.Hence, the transverseregion UE observables are studied both in inclusive jet events where multi-jet topologies contribute, and in the subset of exclusive dijet events where higher-order emissions beyond the leading dijet configuration are explicitly suppressed.
The particle and energy flow observables in the transverse regions are studied both as one-dimensional distributions, relatively inclusive in the properties of the hard process, and as "profile" histograms which present the dependence of the mean value of each observable (and its uncertainty) as a binned function of a hard process property, usually p lead T .

Monte Carlo models of the underlying event
In scattering processes modelled by perturbative QCD twoto-two partonic scatters, at sufficiently low p T the partonic jet cross-section exceeds that of the total hadronic crosssection.This apparent problem is resolved by extending the single-hard-scatter model to include the possibility of multiple partonic scatters in a given hadron-hadron interaction.In this picture, the ratio of the partonic jet cross-section to the total cross-section is interpreted as the mean number of par- Tracks are selected if they satisfy the criteria described in Sect. 5.In the profile plots shown later, these per-event observables are averaged over the events in each bin of the profile (i.e. in p lead T or N ch ).The event-ensemble averages shown in the profiles are indicated with • notation, hence the form "mean p T " is used to distinguish the per-event mean p T which is profiled as the double mean, mean p T .The trans-max and trans-min sub-regions are defined per-event and are also specific to the observable being considered.[16][17][18][19][20].This analysis uses simulated inclusive jet events created by the PYTHIA 6 [16], PYTHIA 8 [17], HERWIG+JIMMY [21], HERWIG++ [18,22], ALPGEN+HERWIG+JIMMY [23], and POWHEG+PYTHIA 6 [24] event generators.All but the last of these are leading-order parton shower generators, but use different hadronisation models and different parton shower formalisms; the PYTHIA family uses a hadronisation model based on the Lund string and a p T -or virtualityordered parton shower, while HERWIG+JIMMY and HERWIG++ implement a cluster hadronisation scheme and their parton showers are ordered in emission angle. 2 The FORTRAN HER-WIG [21] generator by itself does not simulate multiple partonic interactions; these are added by the JIMMY [25] package.The ALPGEN generator provides leading-order multileg matrix element events, i.e. it includes more complex hard process topologies than those used by the other generators but omits loop-diagram contributions.The ALPGEN partonic events are showered and hadronised by the HER-WIG+JIMMY generator combination, making use of MLM matching [23] between the matrix element and parton shower to avoid double-counting of jet production mechanisms.A related matching process is used to interface PYTHIA 6 to 2 The PYTHIA showers include an angular veto on the first ISR emission to approximate the colour coherence effect implicit in the HERWIG angular ordering.The HERWIG++ shower additionally uses massive splitting functions for heavy-quark emissions.

Event
the next-to-leading-order (NLO) POWHEG generator, where the matching scheme avoids both double-counting and NLO subtraction singularities.The POWHEG matrix element simulates the partonic dijet process at NLO, i.e. including the loop correction, while the third (real emission) partonic jet is calculated at leading order.Revision r2169 of POWHEG is used; this version contains an important modification to the original POWHEG dijet matching which reduces the incidence of spikes in physical distributions [26,27].
Such models typically introduce several parameters, which are to be tuned to data at different centre-of-mass energies and for a variety of hadronic processes.MC tuning in recent years has made extensive use of ATLAS and Tevatron underlying event and minimum bias data for a variety of event generators, most notably the PYTHIA and HERWIG families.In this study we have used tuned MC generators both for data correction and systematic uncertainties, and for comparison to the detector-corrected data observables.The combinations of generators, PDFs and tunes are listed in Tab. 2. No currently available tunes make use of UE data from a pp initial state and high-p T jet events as measured here, so the comparisons of corrected data to MC models give a good indication of the level of predictivity of models tuned to Tevatron or low-p T LHC data.
The AMBT1 tune (ATLAS Minimum Bias Tune 1) [37] of PYTHIA 6 was the first LHC-data tune constructed by ATLAS, and primarily used diffraction-suppressed observables from the early ATLAS minimum bias (MB) measurements [40] as input to the tuning.
Table 2 Details of the MC models used in this paper.It should be noted that all tunes use data from different experiments for constraining different processes, but for brevity only the data which had most weight in each tune is listed.A "main data" value of "LHC" indicates data taken at √ s = 7 TeV, although √ s = 900 GeV data were also included with much smaller weight in the ATLAS tunes.Some tunes are focused on describing the minimum bias (MB) distributions better, while the rest are tuned to describe the underlying event (UE) distributions, as indicated in "focus".The detector-simulated MC configurations used for data correction are separated from those used in the results comparison plots, for clarity.For the POWHEG+PYTHIA 6 entry, separate parton distribution functions (PDFs) were used for the matrix element and parton shower / multiple scattering aspects of the modelling, indicated with "ME" and "PS/MPI" respectively.Perugia 2011 [30] is the latest in the "Perugia" set of PYTHIA 6 tunes, which use early LHC minimum bias and underlying event data and the PYTHIA p T -ordered parton shower.A consistent definition of the strong coupling α S is used throughout the parton showers for smooth interfacing to multi-leg matrix element generators, particularly ALPGEN.This tune uses the CTEQ5L1 PDF [31].
The PYTHIA 6 DW [32] tune uses a virtuality-ordered parton shower and an MPI model not interleaved with the ISR.This tune was constructed to describe CDF Run II underlying event and Drell-Yan data and also uses the leadingorder CTEQ5L1 PDF; it is included here for comparison to previous results.PYTHIA 6 is also used in conjunction with a matched POWHEG NLO matrix element using the CT10 PDF set, as this is the highest perturbative order of QCD jet event modelling currently available in fully showered/hadronised form.The Perugia 2011 tune of PYTHIA 6 is used to shower these POWHEG events.While commonly used together, the Perugia 2011 tune was constructed based on leading-order matrix elements only, and without the POWHEG matching modification to the parton shower; the interest in comparing this model to data is hence to observe whether the POWHEG+ PYTHIA 6 matching procedure has any adverse effect on UE distributions relative to standalone PYTHIA 6. PYTHIA 8 adds to the established PYTHIA-family MPI model by interleaving not only the ISR emission sequence with the MPI scatterings, but also the FSR; all three processes compete against each other for emission phase space in the resulting evolution.The AU2 CT10 tune [28] used here is the variant of the latest ATLAS PYTHIA 8 UE tune set intended for use with the NLO CT10 PDF [41].This configuration is the standard setup for jet event simulation in current ATLAS production use, with the model tuned to give a very good description of leading-track UE data at √ s = 7 TeV.
Two tunes of HERWIG+JIMMY are used in this study: the ATLAS AUET2 LO * * tune for standalone HERWIG+ JIMMY, and the older AUET1 CTEQ6L1 used in the ALP-GEN sample [35].For HERWIG++ the standard 7 TeV underlying event tune UE7-2 [33] for the MRST LO * * PDF is used.This model includes a colour reconnection model -the first for a cluster hadronisation generator -and provides a good description of both leading-track UE and minimum bias data at 7 TeV.The LO * * PDF, like the LO * PDF used in the PYTHIA 6 AMBT1 sample, is one of a series of "modified leading order" PDFs which attempt to mimic full NLO simulated event characteristics by relaxation of PDF momentum sum rules and use of a p 2 T -based factorisation scale for better compatibility with the approximate resummation inherent in parton shower algorithms.
The PYTHIA 6 AMBT1 and HERWIG++ 2.5.0 samples were processed through the ATLAS detector simulation framework [42], which is based on GEANT4 [43], then reconstructed and analysed similarly to the data.These reconstructed events were used to calculate detector acceptances and efficiencies, to correct the data for detector effects.The fully simulated and reconstructed samples include overlay of MC pile-up events, simulated using PYTHIA 8 with the AM2 tune [44], with the mean number of interactions distributed according to data conditions.The HERWIG++ sample used for unfolding (i.e.correction of residual detector effects) was generated using HERWIG++ 2.5.0 with the default LO * _ JETS [39] tune -an older configuration than that shown in the physics comparison plots in this paper.All other MC models described are used at the generated stable particle level only.

Analysis object selection
This analysis uses the full ATLAS 2010 dataset of jet events in proton-proton collisions at √ s = 7 TeV, in which the average number of multiple pp interactions per bunch crossing ("pile-up") was much smaller than in the 2011 data-taking period.Basic requirements on data quality and the operating conditions of the beam, the relevant sub-detectors and the triggers resulted in a dataset corresponding to an integrated luminosity of 37 ± 1.3 pb −1 , uncorrected for trigger prescales [45].
To select jet events, two different trigger systems were used: the MBTS trigger and the central jet-triggers, the latter of which has several p T thresholds.The MBTS trigger selects events containing charged particles within the fiducial acceptance of the minimum bias trigger scintillator, and was used to select events with jets having transverse momenta in the range 20-60 GeV.Jets with p T greater than 60 GeV are above the threshold of full efficiency of the calorimeter-based jet-trigger, hence this was used to select jet events above this scale.A single jet-trigger was used for each p lead T bin in the observables, specifically the fully efficient (> 99%) trigger with the smallest possible prescale factor for that bin [46].
To reject events due to cosmic-ray muons and other noncollision backgrounds, events were required to have at least one reconstructed "primary" pp interaction vertex, each having at least five tracks satisfying the following criteria [40]: p T > 0.5 GeV; -|η| < 2.5; a minimum of one pixel and six SCT hits; a hit in the innermost pixel layer, if the corresponding pixel module was active; transverse and longitudinal impact parameters with respect to primary vertex |d 0 | < 1.5 mm and |z 0 | sin θ < 1.5 mm; for tracks with p T > 10 GeV, a χ 2 probability of track fit greater than 0.01 was required in order to remove mismeasured tracks.
Events with p lead T < 100 GeV were taken in conditions with negligible pile-up, while the bulk of events with higher p lead T were taken in the second 2010 data-taking period, with a mean of 2-3 pp interactions per bunch crossing.To reduce the contributions from pile-up, events containing more than one reconstructed primary vertex with at least two associated tracks were removed.
Finally, to obtain an inclusive jet event selection, each event was required to contain at least one jet with p T > 20 GeV and rapidity |y| < 2.8.The resulting sample is entirely dominated by pure QCD jet events.For the exclusive dijet event selection an additional requirement of one and only one subleading jet was made, where the subleading jet had to pass the same cuts as the leading jet and also have p T > 0.5 p lead T and |∆φ | > 2.5 to the leading jet.In both selections the jets were corrected to account for the calorimeters' response to the deposited energy.
Around 429,000 and 99,000 events were selected for the inclusive jet and exclusive dijet selections respectively.

Correction to particle level
To allow comparison of these results with theoretical predictions and other experimental studies, the underlying event distributions need to be corrected for selection efficiencies and detector resolution effects.A two-step correction procedure was used, where first the track efficiency corrections were applied for the track-based observables, then the remaining detector effects were unfolded to produce observables at particle level which may be directly compared to MC model predictions.

Track reconstruction efficiency and cluster calibration
The efficiency of the ATLAS detector to reconstruct a charged particle as a track was measured in a previous analysis [40], with the same track selection as used here.Each track was reweighted by the inverse of this efficiency, which also accounts for the contributions of tracks reconstructed from secondary particles, and particles whose true kinematics were outside the kinematic range (OKR) of the selection but which were reconstructed within the acceptance cuts due to detector resolution.For tracks with p T > 500 MeV, the effects of fake tracks (those constructed from tracker noise and/or hits which were not produced by a single particle) and OKR migrations were found to be negligible.
For cluster-based observables, both the hadronic and electromagnetic calorimeter cell clusters were used, with calibrations as described in Refs.[47] and [11].The cluster energy was corrected to the momentum of the charged or neutral hadron, and the simulation was validated using the diphoton invariant mass distribution, M γγ , for π 0 → γγ candidates [6].

Unfolding
Bayesian iterative unfolding [48] was used to correct for residual detector resolution effects, using the Imagiro 0.9 software package [49].
The Bayesian iterative unfolding method requires two inputs: a prior probability distribution for the observable (the MC generator-level distribution is used for this), and a smearing matrix which relates the measured distribution of an observable to its hadron-level distribution.The smearing matrix element S i j is the probability of a particular event from bin i of the hadron-level distribution being found in bin j of the corresponding reconstructed distribution, as calculated using MC samples.For the profile histogram observables in this paper, a two-dimensional (2D) histogram was created with dense binning in the observable whose evolution is being profiled, such that each unfolding bin corresponds to a 2D range in e.g.p lead T vs. ∑ p T space: the 2D nature of the bin has no effect on the mathematics of the unfolding procedure.Migrations involving the p lead T < 20 GeV region, excluded from the analysis phase space, were handled in detail for the unfolding of observables binned in p lead T , but for other observables such in/out migrations were treated as fake or missing events respectively; this was required because a more detailed approach would add an extra dimension to the smearing matrix, which would then be too statistically limited to be usable.
The unfolding process is iterated to avoid dependence on the prior probability distribution; the corrected data distribution produced in each iteration is used as the prior for the next.In this analysis, two iterations were performed since this gave the smallest residual bias when tested on MC samples while keeping the statistical uncertainties small.The central values of the data distributions corrected to hadron level were calculated using prior distributions and smearing matrices from the PYTHIA 6 AMBT1 MC sample.

Systematic uncertainties
Systematic uncertainties on the measured distributions were assessed using the same unfolding procedure as for the central values of the observables, but with the input p lead T , track & cluster p T and track & cluster weights shifted by ±1σ variations in each source of uncertainty.The following sources of uncertainty are included: Jet reconstruction: These uncertainties -dependent on the jet energy scale calibration procedure, the impact of pileup on the jet energy, the jet reconstruction efficiency and the jet energy resolution -have been calculated as in Ref. [50].For the UE observables profiled against leading-jet p T , they add up to approximately 1%.Track reconstruction-efficiency uncertainty: Tracking efficiency uncertainties were studied in Ref. [40], the two largest being found to be due to the amount of material in the inner detector and the consequence of the χ 2 probability cut to remove misreconstructed tracks.The effect of uncertainties in the amount of material in the inner detector is a 2% relative uncertainty in the efficiency in the barrel region, rising to over 7% for 2.3 < |η| < 2.5, for tracks with p T > 500 MeV.The maximum difference between the fraction of events in data and MC simulation which passed the χ 2 probability cut was found to be 10%.This value was taken as a conservative estimate of the systematic uncertainty, and was applied to tracks with p T > 10 GeV only.
Cluster reconstruction efficiency: The accuracy with which the MC samples simulate the energy response of the calorimeters to low-energy particles was determined separately for electromagnetic and hadronic particles.An average is then obtained, using the PYTHIA 6 AMBT1 prediction of the relative contribution to ∑ E T by different particle types [6].For electromagnetic particles the systematic uncertainty arises from the extraction of the energy scale from fits to the M γγ distributions in π 0 → γγ candidates.The total uncertainty depends on the |η| region and is typically 2-4%, but is as large as 15% in the regions where different calorimeter subsystems overlap.
The uncertainty in the energy response for hadronic particles in the central region (|η| < 2.4), where there is good coverage from the inner tracking detector, was obtained from studies of the ratio of the energy measured by the calorimeter to the track momentum measured by the inner detector for isolated charged particles and is within a few percent [50].Pile-up and merged vertices: The effect of pile-up on the underlying event observables after the tight vertex selection was assessed using an MC sample with realistic modelling of the pile-up conditions in 2010 data; the largest deviation from the sample without pile-up was observed to be 1%.A ±1% shift was hence applied to the values of all observable bins used as input to the unfolding, and the resultant shifts on unfolded observables have been used as the systematic uncertainty due to merged vertices.This uncertainty is less than 2% for most bins, but increases to approximately 5% at high p lead T .Unfolding: The uncertainty due to model-dependence of the unfolding procedure was taken as the difference between the results of unfolding with each of the two MC samples, PYTHIA 6 AMBT1 and HERWIG++.The dominant effect arises from modelling of low p T QCD radiation, which produces a typical uncertainty of 1% but can reach 20% at the edges of the fiducial phase space studied here.An additional uncertainty was estimated using two different priors: the unmodified generator-level distribution, and the generator-level distribution after reweighting so that the reconstructed distribution matches the data.This uncertainty is less than 1% throughout the fiducial phase space of the measurement.
Systematic uncertainty contributions from electronic noise and beam-induced background, simulation of the primary vertex position, and simulation of the trigger selection were also considered and were found to be negligible.Table 3 summarises the sizes of contributions to systematic uncertainties for the UE profile observables with both the inclusive jet and exclusive dijet selections.The mean p T vs. N ch profile observables have flat symmetric uncertainties of 1% each for unfolding and reconstruction efficiency, increasing to ∼ 10% in the first and last bins of N ch .This section presents and discusses the key distributions from this analysis, primarily profile observables of mean UE characteristics as functions of p lead T (i.e.hard process scale), but also distributions of charged-particle ∑ p T and multiplicity density within bins of p lead T , and the correlation of transverseregion mean p T with the charged-particle multiplicity.
In these plots, all observables are studied for both the inclusive jet and exclusive dijet event selections.The data, corrected to particle level, are compared to predictions of PYTHIA 6 with the Perugia 2011 and DW tunes, HERWIG+ JIMMY with the AUET2 tune, PYTHIA 8 with the AU2 CT10 tune, HERWIG++ with the UE7-2 tune, ALPGEN+HERWIG+ JIMMY with the AUET1 tune, and POWHEG+PYTHIA 6 with the Perugia 2011 tune.
To allow direct comparison between full transverse and trans-min/max/diff region quantities, between central and full-η cluster quantities, and to other experiments with different angular acceptances, the observables are presented as densities in η-φ space.Specifically, the raw quantities are divided by the total angular area of the region in which they were measured to produce the number, transverse momentum, and transverse energy densities: N ch /δη δφ , ∑ p T /δη δφ , and ∑ E T /δη δφ respectively.The central transverse-region observables are scaled by δη δφ = (2 × 2.5) × (2 × π/3) = 10π/3.The total transverse energy of charged and neutral particles, ∑ E T , is defined using the full pseudorapidity range in the transverse region, so its area normalisation is δη δφ = (2 × 4.8) × (2 × π/3) = 19.2π/3.The trans-max, trans-min and trans-diff regions have only half of the corresponding transverse-region area since by definition they only consider one side in ∆φ .

Distributions of N ch and ∑ p T densities
In Fig. 2 the distributions of N ch and ∑ p T densities in the transverse, trans-max and trans-min regions, for the inclusive jet selection, are shown for p lead T bins of 20-60 GeV, 60-210 GeV, and > 210 GeV.This presentation displays the evolution of each distribution in bins of increasing p lead T , where each p lead T bin is independently normalised to unity.For both the ∑ p T and N ch density observables, particularly in the transverse and trans-max regions shown in the top two rows, the development of hard tails in the distributions is clearly seen as the p lead T cut is increased.The trans-min region in the bottom row also shows evolution in the tails, but the total contribution to the normalisation from the tails is much less, as may be seen from the lack of p lead T dependence in the peak height for the trans-min region plots as compared to the transverse and trans-max ones.The peak regions for both variables are narrower and biased toward low values for trans-min, and wider for trans-max.These characteristics of p lead T and region dependence, and the importance of tails at high values, indicate that extra jet activity is responsible for the changes in the transverse and trans-max region distributions, while the relative stability of the trans-min peak region against jet activity reflects the particular suitability of the trans-min region observables for measurement of the multi-parton scattering contribution to the UE.8.2 Charged-particle ∑ p T and multiplicity densities vs. p lead T In Fig. 3 the transverse region charged-particle multiplicity and ∑ p T density profiles are shown as functions of p lead T .For the inclusive jet events in the left column, the total trans- verse region activity increases with p lead T according to both the mean ∑ p T and N ch density measures.The exclusive dijet topology shown in the right column, where multi-jet events are explicitly excluded, provides an alternative view of the same observables.The exclusive dijet p lead T profiles are seen to decrease as p lead T increases, although the dependence is much weaker than the opposite behaviour seen in the inclusive jet events.This behaviour is somewhat surprising and is not understood in detail, however we note that in addition to excluding events with extra jets from the hard process, the exclusive dijet requirement also excludes events with extra jets produced by MPI.This unavoidable consequence of the dijet cut may be responsible for the downward trend which is also seen in some MC predictions, particularly those from PYTHIA 6.The data are hence broadly consistent with modelling of the UE as independent of the hard process scale at the leading-jet p T scales considered here.However the details of the data behaviour, in particular the decreasing transverse region activities with p lead T in the exclusive dijet event selection are not fully understood.
The division of the transverse regions into per-event transmax and trans-min sides, and the corresponding per-event differences between them, the "trans-diff" observables, are shown in Fig. 4. In the inclusive jet events, the trans-max activity (for both ∑ p T and N ch ) grows with p lead T , similarly to the full transverse-region trend, but its trans-min complement is almost constant over the whole range of p lead T .This observation is compatible with the interpretation of the trans-min region as being less affected by the hard part of the underlying event.
In the max/min characterisation of exclusive dijet events, the distinction between the behaviours of the min and max Fig. 4 Profiles of charged-particle ∑ p T (top row) and charged multiplicity (bottom row) densities against the leading-jet p T , for the inclusive jet (left column) and exclusive dijet (right column) event selection.The jets are required to have p T of at least 20 GeV, and be within |y| < 2.8, whereas the charged particles have at least a p T of 0.5 GeV and |η| < 2.5.The plots compare the trans-max/min/diff observables to each other and the PYTHIA 6 Perugia 2011 MC model.The error bands in the top plot show the combined statistical and systematic uncertainty, while the grey error band in the bottom plot is the envelope of the maximum combined statistical and systematic uncertainty of the trans-max and trans-min regions.
sides is reduced relative to the inclusive jet selection, with either both slightly falling (N ch ) or the trans-max observable remaining roughly constant while the trans-min one falls (∑ p T ).As in the general transverse-region observables of Fig. 3, this fall-off behaviour is not fully understood, but is consistent with the exclusive dijet cuts excluding events with hard MPI activity, an effect which is expected to be more pronounced in the trans-min region where contamination from hard process radiation is minimised.
The insensitivity of the inclusive jet trans-min region to changes in p lead T indicates that UE activity can indeed be modelled as approaching a constant as a function of hard process scale once the scale is hard enough that the proton impact parameters are effectively zero and all collisions are central.However, the observed dependence of the exclusive dijet trans-min observables to changes in hard process scale is clearly worthy of further investigation.
All MC models considered reproduce the qualitative features of the inclusive jet data.However, the PYTHIA models, which have received the most UE tuning attention in recent years, are unexpectedly further from the data than the less flexible and less tuned HERWIG++ and HERWIG+JIMMY models on these observables.
The spread of MC models around the exclusive dijet data is in fact slightly less than for the inclusive jet ones, although the MC models tend not to predict quite as steep a decrease in UE activity with p lead T as in the data.The PYTHIA 6 Perugia 2011 model provides a good combined description of transverse-region ∑ p T and N ch densities, but PYTHIA 8 produces too much transverse-region activity and PYTHIA 6 DW and HERWIG++ undershoot the data.A substantial differ-  ence is seen between HERWIG+JIMMY and the combination of HERWIG and JIMMY with ALPGEN matrix elements; the ALPGEN+HERWIG+JIMMY combination is more active in all observables, for both inclusive jet and exclusive dijet selections.It is surprising that this is the case for the exclusive dijet selection, since that is dominated by the 2 → 2 QCD hard process contained in both HERWIG and ALPGEN.
The POWHEG+PYTHIA 6 model is seen to produce slightly lower mean UE activity than standalone PYTHIA 6 Perugia 2011 in both the N ch and ∑ p T density profile observables and for both inclusive jet and exclusive dijet event selections, although the two models produce similar shapes; neither is consistently closer to data than the other, however, and a specialised shower generator tune for use with POWHEG could achieve a better data description.
Finally, it is interesting to compare the trans-diff observables between the inclusive and exclusive jet selections; transdiff is intended to be most sensitive to additional hard scattering from either MPI or ISR from hard-process, and indeed it may be seen in Fig. 4 to be much flatter for the exclusive dijet topology, as compared to its large increase with p lead T for the inclusive distributions.Again, this behaviour is wellmodelled by the PYTHIA 6 MC generator, with particularly good numerical agreement for the simulation of trans-diff in the exclusive dijet selection.8.3 Charged and neutral particle ∑ E T vs. p lead T In Fig. 5 the corrected charged and neutral particle ∑ E T density is shown for both the central region (in the top row) and the full η acceptance range (the middle row), for the inclusive jet and exclusive dijet topologies.The trends are broadly similar to those for the track-based observables, and for the central |η| range the comparison between the data and MC models is comparable to that seen for the equivalent charged-particle ∑ p T density plots.However, the full acceptance plots show increased disagreement between the MC models and the data; the MC models undershoot the observed level of activity at low p lead T values in both the inclusive and exclusive event selections.This discrepancy is notable since all MPI models have to date been tuned to observables measured solely for central rapidities.In the fullacceptance inclusive jet observable, all models except pure HERWIG+JIMMY predict a faster rise of ∑ E T as a function of p lead T than seen in the data, although notably most start significantly below the data at low p lead T .Finally, the profiles of the ratio ∑ p T (charged)/ ∑ E T (all) in |η| < 2.5 against p lead T are shown in the bottom row of Fig. 5.These observables are mostly flat, and are described well by models other than those using HERWIG+JIMMY parton showering and hadronisation, including the ALPGEN sample.These models lie 10-20% below the data, indicating a too-low charged fraction resulting from the HERWIG+ JIMMY modelling.The ratio nature of this observable means that a large statistical error is seen in the bin around 50 GeV, corresponding to the low-statistics tail of events from the minimum bias trigger before the transition to the jet trigger at p lead T = 60 GeV.
8.4 Charged-particle mean p T vs. p lead T and N ch In Fig. 6, the distributions of transverse-region chargedparticle mean p T against p lead T and the transverse region charged-particle multiplicity are shown.No max/min region subdivision is made for the mean p T observables since while there is a clear case for identifying the more and less active sides of an event based on particle multiplicity or momentum flow, the physics interpretation of the transverse side with the higher/lower average particle p T is not as clear as for the pure ∑ p T and N ch observables.
The mean p T vs. p lead T profile displays a very different behaviour between the inclusive jet and exclusive dijet event selections; in the inclusive jet case mean p T rises strongly with increasing p lead T , but when the event selection is restricted to dijet events only, the correlation disappears to give a distribution flat within uncertainties.The roots of this behaviour may be seen in Fig. 3: in the inclusive jet case the N ch profile (the denominator in construction of mean p T ) is less sharply rising than ∑ p T (the numerator) as a function of p lead T , while for the exclusive dijet selection there is less distinction between ∑ p T and N ch , leading to the flat ratio.Based on previous conclusions about the nature of the contributions to the trans-max and trans-min components of the ∑ p T and N ch density vs. p lead T profiles, this distinction between inclusive and exclusive mean p T behaviours implies that it is the high-p T tails of UE particle production (which are effectively removed by the dijet selection) that are responsible for the slight increase in mean p T in the inclusive jet selection.
For both the inclusive jet and exclusive dijet selections, the transverse-region mean p T as a function of p lead T is welldescribed by the MC models -within 10% of the data.This is as expected, since the descriptions of the related transverseregion charged-particle ∑ p T and multiplicity densities were described to similar levels of precision.
The mean p T vs. N ch plots follow the pattern established by previous experiments, with mean particle p T increasing as a function of the number of charged particles.This observable is particularly well described by HERWIG++, which is the only generator to give a good description of the observable for inclusive jet events with fewer than 17 particles in the transverse region.The bulk of the MC models considered give predictions consistent with the data for the exclusive dijet event selection.The main outliers are PYTHIA 6 Tune DW, which overshoots the data in both selections for events with more than about 10 charged particles, and HERWIG+JIMMY both standalone and in combination with ALPGEN, which significantly undershoot.The ALP-GEN+HERWIG+JIMMY configuration, which uses the older AUET1 tune of JIMMY, undershoots the data by the greatest amount.
An underestimation of mean p T vs. N ch data are not unexpected from the JIMMY model, as it contains no colour reconnection mechanism to redistribute momentum in highmultiplicity events [51].The newer AUET2 tune of HERWIG+ JIMMY manages to do slightly better than AUET1 as used with ALPGEN, but remains significantly outside the experimental error.By comparison HERWIG++, which has a similar MPI implementation but does use a colour reconnection model, agrees well with the data.
Finally, the ATLAS tunes of both PYTHIA 6 and PYTHIA 8 are seen to undershoot the data for low N ch , particularly in the inclusive jet sample, but describe the mean p T of highermultiplicity events well for both event selections.As both these tunes incorporated the equivalent of this observable in the ATLAS leading charged-particle UE analysis [3], the flaws in their data description seen here are unexpected, and use of these data in future tunes may substantially change the MPI model parameters.9 Summary and conclusions ATLAS measurements sensitive to the underlying event in 37 pb −1 of 7 TeV proton-proton collisions at the LHC have been presented, using observables constructed with respect to QCD jets with p T up to 800 GeV.Inclusive jet and exclusive dijet event topologies have been considered separately, and measures of UE activity azimuthally transverse to the leading jet computed using both charged-particle tracks and all-particle clusters of energy deposited in the calorimeters.The observables have been further subdivided into trans-max and trans-min regions on an event-by-event basis depending on which side of the event had more activity: this subdivision provides additional discriminating power between the component processes of the UE.
The most notable features of the observables presented in this paper are as follows: -Rising levels of transverse-region activity as a function of leading-jet p T , as previously observed in UE studies, are seen in the inclusive jets event selection, with the exception of the inclusive trans-min region.-Application of an exclusive dijet event selection requirement removes this feature, producing instead transverseregion activity measures which are constant or which slightly decrease with increasing leading-jet p T .This decrease in activity is not obviously expected from a simple picture of the underlying event and is deserving of further investigation.-The behaviour of underlying event particle flow observables in exclusive dijet topologies indicates that pure MPI activity can largely be modelled as independent of hard process scale, provided that scale is hard enough that all proton-proton interactions are central.
These observables have been compared to a number of MC models, using several tunes of commonly used underlying event models.The data are broadly consistent with the predictions of the multiple partonic scattering paradigm, although indicative of several areas where MPI parameter tuning may improve MC data description in further LHC studies.Again, several key features are of note: -MC models in general provide a good qualitative description of the data behaviour, but there are some significant discrepancies.The HERWIG+JIMMY and HERWIG++ generators currently describe inclusive jet UE observables slightly better than the PYTHIA family, but the PYTHIA 6 tunes perform better on UE in exclusive dijet topologies.
-HERWIG++ shows significant improvements over the HER-WIG+JIMMY configuration.However, PYTHIA 8 is seen to produce too much UE activity, and will require retuning of underlying event parameters to perform comparably to its FORTRAN predecessor.-For the exclusive dijet event selection, the decrease of transverse region activity in data is stronger than seen in the available MC models, indicating that there are aspects of the UE yet to be understood and incorporated into MC models.-Full |η|-range cluster observables show larger deviations from MC predictions than in the central region, indicating a region of phase space in which all MC models can be improved.
These data provide a detailed measurement of the pp underlying event in QCD jet events, with momentum sums and charged-particle multiplicities measured both as distributions and as profiles of their means as functions of the hard process scale.The separate evaluations of the observables for inclusive jet vs. exclusive dijet event selections, charged-particle vs. all-particle energy flows, central vs. full η acceptance, and transverse/trans-max/trans-min categories enable more specific MC model comparisons than possible with preceding public data.These measurements are hence expected to play a significant role in the future development and tuning of MC models of the underlying event.

Fig. 2 Fig. 3
Fig. 2 Comparison of ∑ p T (left column) and N ch (right column) density distributions for different p lead T requirements, data only.The jets are required to have p T of at least 20 GeV, and be within |y| < 2.8, whereas the charged particles have at least a p T of 0.5 GeV and |η| < 2.5.The top, middle and bottom rows, respectively, show the transverse, trans-max and trans-min regions.Each p lead T slice is independently normalised to unity via division by the number of events in the slice, N. The error bars show the combined statistical and systematic uncertainty.

Fig. 5
Fig.5Transverse region profiles of ∑ E T of the neutral and charged particles for the inclusive (left) and exclusive dijet (right) selection against the leading-jet p T for the central region (top row) and the full acceptance region (middle row).The bottom row shows transverse region profiles of ∑ p T (charged)/ ∑ E T (all) for the inclusive (left) and exclusive dijet (right) selection constructed from charged and neutral particles against the leading-jet p T .The jets are required to have p T of at least 20 GeV, and be within |y| < 2.8.The error bars show the statistical uncertainty while the shaded area shows the combined statistical and systematic uncertainty.

Fig. 6
Fig.6Transverse region profiles of the mean p T of charged particles for the inclusive (left) and exclusive dijet (right) selection against the leading-jet p T (top row) and charged-particle multiplicity (bottom row).The jets are required to have p T of at least 20 GeV and to be within |y| < 2.8, whereas the charged particles have at least a p T of 0.5 GeV and |η| < 2.5.The error bars show the statistical uncertainty while the shaded area shows the combined statistical and systematic uncertainty.

Table 1
Definition of the observables measured in each event at hadron and detector level.The hadron-level observables based on momentum use only particles with p T > 0.5 GeV, and those based on energy use p > 0.5 GeV for charged particles and p > 0.2 GeV for neutral particles.All hadron-level definitions are based on particles with mean proper lifetime τ > 0.3 × 10 −10 s.

Table 3
[50]ary of systematic uncertainties for inclusive jet and exclusive dijet profiles vs. p lead T .The "efficiency" uncertainties include material uncertainties in the tracker and calorimeter geometry modelling.The "JES" uncertainty source for jets refers to the jet energy scale calibration procedure[50].