ATL

AS-

CO

NF-

2015

-070

15D

ecem

ber

2015

ATLAS NOTEATLAS-CONF-2015-070

14th December 2015

Search for new phenomena in the dilepton final state usingproton-proton collisions at

√s = 13 TeV with the ATLAS detector

The ATLAS Collaboration

Abstract

A search is conducted for both resonant and non-resonant new phenomena in dielectron anddimuon final states. The LHC 2015 proton–proton collision dataset recorded by the ATLASdetector is used, corresponding to 3.2 fb−1 at

√s = 13 TeV. The dilepton invariant mass

spectrum is the discriminating variable in both searches. No significant deviations from theStandard Model expectation are observed. Lower limits are set on the signal parameters ofinterest at 95% credibility level, using a Bayesian interpretation. Limits on the Z′SSM are setin the combined dilepton channel for masses lower than 3.40 TeV, as well as for the Z′ E6models, such as Z′χ and Z′ψ below 3.08 TeV and 2.79 TeV, respectively. Limits on the ``qqcontact interaction scale Λ are set between 16.4 TeV and 23.1 TeV.

c© 2015 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

1 Introduction

The dilepton (ee or µµ) final state signature is a key search channel for a host of different new phenomenaexpected in theories that go beyond the Standard Model (SM). This search channel benefits from highsignal selection efficiencies and relatively small, well understood backgrounds.

Models with extended gauge groups often feature additional U (1) symmetries with corresponding heavyspin-1 Z′ bosons whose decay would manifest itself as a narrow resonance in the dilepton mass spectrum.Grand Unified Theories (GUT) have inspired models based on the E6 gauge group [1, 2], which, for aparticular choice of symmetry breaking pattern, includes two neutral gauge bosons that mix with anangle θE6 . This yields a physical state defined by Z′(θE6 ) = Z′ψ cos θE6 + Z′χ sin θE6 , where the gaugefields Z′ψ and Z′χ are associated with two separate U (1) groups resulting from the breaking of the E6symmetry. All Z′ signals in this model are defined by specific values of θE6 ranging from 0 to π, and thesix commonly motivated cases are investigated in this search, namely: Z′ψ , Z′η , Z′N, Z′I , Z′S, and Z′χ . Inaddition to the GUT-inspired E6 models, the Sequential Standard Model (SSM) [2] provides a commonbenchmark model that includes a Z′SSM boson with couplings to fermions identical to those in the SM. Aseries of models that are motivated by the large hierarchy between the electroweak and Planck scales alsopredict the presence of narrow dilepton resonances. These include the Randall–Sundrum model [3] witha warped extra dimension giving rise to spin-2 graviton excitations, the quantum black hole model [4],the Z∗ model [5], and the minimal walking technicolor model [6].

Some models of physics beyond the SM result in non-resonant deviations in the dilepton mass spectrum.Compositeness models motivated by the repeated pattern of quark and lepton generations predict newinteractions involving their constituents. These interactions may be represented as a contact interaction(CI) between initial-state quarks and final-state leptons. Other models producing non-resonant effects aremodels with large extra dimensions [7] motivated by the hierarchy problem. The following four-fermionCI Lagrangian [8, 9] is used to describe a new interaction or compositeness in the process qq → `+`−:

L =g2

Λ2 [ηLL (qLγµqL) (`Lγµ`L) + ηRR(qRγµqR) (`Rγ

µ`R) (1)

+ηLR(qLγµqL) (`Rγµ`R) + ηRL(qRγµqR) (`Lγ

µ`L)] ,

where g is a coupling constant set to be√

4π by convention, Λ is the CI scale, and qL,R and `L,R are left-handed and right-handed quark and lepton fields, respectively. The parameters ηi j , where i and j are L orR (left or right), define the chiral structure of the new interaction. Different chiral structures are invest-igated here, with the left-right (right-left) model obtained by setting ηLR = ±1 (ηRL = ±1) and all otherparameters to 0. Likewise, the left-left and right-right models are obtained by setting the correspondingparameters to ±1, and the others to zero. The sign of ηi j determines whether the interference betweenthe SM Drell–Yan (DY) qq → Z/γ∗ → `+`− process and the CI process is constructive (ηi j = −1) ordestructive (ηi j = +1).

The most sensitive previous Z′ searches were carried out by the ATLAS and CMS Collaborations [10,11]. Using 20 fb−1 of pp collision data at

√s = 8 TeV, ATLAS set a lower limit at 95% credibility level

(C.L.) on the Z′SSM pole mass of 2.90 TeV for the combined ee and µµ channels. Similar limits wereset by CMS. The most stringent constraints on CI searches are also provided by the CMS and ATLASCollaborations [11, 12]. The strongest lower limits on the ``qq CI scale are Λ > 21.6 TeV and Λ >

2

17.2 TeV at 95% C.L. for constructive and destructive interference, respectively, in the case of left-leftinteractions and given a uniform positive prior in 1/Λ2.

In this note, a search for both resonant and non-resonant new phenomena is presented using the observedee and µµ mass spectra extracted from pp collisions at the Large Hadron Collider (LHC) operating at√

s = 13 TeV, corresponding to an integrated luminosity of 3.2 fb−1. The analysis and interpretationof these spectra rely primarily on simulated samples of signal and background processes. The Z masspeak region is used to normalize the background contribution and perform cross checks of the simulatedsamples. The interpretation is then performed taking into account the expected shape of different signalsin the dilepton mass distribution.

2 ATLAS detector

The ATLAS experiment [13, 14] at the LHC is a multi-purpose particle detector with a forward-backwardsymmetric cylindrical geometry and a near 4π coverage in solid angle.1 It consists of an inner trackingdetector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromag-netic and hadronic calorimeters, and a muon spectrometer. The inner tracking detector (ID) covers thepseudorapidity range |η | < 2.5. It consists of silicon pixel, silicon micro-strip, and transition radiationtracking (TRT) detectors. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM)energy measurements with high granularity. A hadronic (steel/scintillator-tile) calorimeter covers thecentral pseudorapidity range (|η | < 1.7). The end-cap and forward regions are instrumented with LArcalorimeters for both EM and hadronic energy measurements up to |η | = 4.9. The muon spectrometer(MS) surrounds the calorimeters and is based on three large superconducting air-core toroids with eightcoils each. Its bending power is in the range from 2.0 to 7.5 T m. It includes a system of precision track-ing chambers and fast detectors for triggering. A dedicated trigger system is used to select events. Thefirst-level trigger is implemented in hardware and uses the calorimeter and muon detectors to reduce theaccepted rate to 100 kHz. This is followed by a software-based trigger that reduces the accepted eventrate to 1 kHz on average.

3 Data and Monte Carlo samples

The data sample used in this analysis was collected during the 2015 LHC run with pp collisions at√

s = 13TeV. After selecting periods with stable beams and requiring that relevant detector systems be functional,the total integrated luminosity retained for analysis amounts to 3.2 fb−1.

Modelling of the various background sources primarily relies on Monte Carlo (MC) simulation. Thedominant background contribution arises from the Drell-Yan (DY) process. Other background sourcesoriginate from top-quark and diboson (WW , W Z , Z Z) production. In the case of the dielectron channel,multi-jet and W+jets processes also contribute due to the misidentification of jets as electrons. A data-driven method is used to estimate this background, see Section 5.

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detectorand 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 pointsupwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis.The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of∆R ≡

√(∆η)2 + (∆φ)2.

3

Drell-Yan events are generated with Powheg-box v2 [15] at next-to-leading order (NLO) in QCD usingthe CT10 parton distribution function (PDF) set [16] and Pythia 8.186 for parton showering and hadron-ization [17]. The AZNLO tune [18] is used with the CTEQ6L1 PDF set [19] to model non-perturbativeeffects and QED emissions are produced with Photos++ 3.52 [20]. A mass-dependent K-factor is appliedon an event-by-event basis to account for next-to-next-to-leading (NNLO) QCD corrections computedwith VRAP [21] and the CT14NNLO PDF set [22]. Mass-dependent Electroweak (EW) corrections arecomputed at next-to-leading (NLO) order with mcsanc [23] using CT14 PDF set. Those include photon-induced contributions (γγ → `` via t- and u-channel processes) computed with the MRST2004QED PDFset [24].

Diboson events are generated using Sherpa 2.1.1 [25] at NLO with the CT10 PDF set. Top-quark back-grounds include tt̄ production and single-top production with an associated W boson generated withPowheg-box v1 and v2, respectively, using the CT10 PDF set. The parton shower, fragmentation, and theunderlying event are simulated using Pythia 6.428 [26] with the CTEQ6L1 PDF set and the correspond-ing Perugia 2012 tune [27]. The top-quark mass is set to 172.5 GeV. Higher-order corrections to both tt̄and single-top cross sections are computed with Top++ 2.0 [28]. These incorporate NNLO corrections inQCD, including resummation of next-to-next-to-leading logarithmic soft gluon terms.

Resonant and non-resonant signal processes are produced at LO using Pythia 8.186 with the NNPDF23LOPDF set [29] for event generation, parton showering and hadronization. In the case of Z′ production, in-terference effects are not included. However, for the production of non-resonant signal events, bothDY and CI samples are generated to account for the significant interference effects between those twoprocesses. Higher-order QCD corrections are computed as for the DY background and applied to bothresonant and non-resonant MC samples. EW corrections are not applied to the resonant MC samples dueto the high model dependence. However, these corrections are applied to the non-resonant MC samplesas they involve interference between the DY and CI processes. Moreover, including the EW correctionsleads to a more conservative estimate of the search sensitivity.

For all MC samples, except the diboson samples produced with Sherpa, charm- and bottom-hadron decaysare handled by EvtGen 1.2.0 [30]. The detector response is simulated with Geant 4 [31, 32] and the eventsare processed with the same reconstruction software as used for the data. Furthermore, the simulationincludes the appropriate number of additional pp collisions (pileup) to reproduce running conditions.

4 Event selection

Electron reconstruction [33] in the central region of the ATLAS detector (|η | < 2.47) covered by thetracking detectors starts by electromagnetic seed cluster finding. A sliding window algorithm is appliedto the grid of calorimeter towers (EM calorimeter divisions spanning ∆η × ∆φ regions of EM calori-meter, corresponding to the granularity of the middle calorimeter layer). Electron track reconstructionis optimised to account for possible high bremsstrahlung energy losses. Seed clusters that have at leastone matching track are re-built using a larger window and their energies calibrated using a multi-variatetechnique followed by a final correction from a Z → ee sample. The electron energy is measured by itsassociated EM cluster whereas the direction is determined by the track associated with this cluster.

A likelihood discriminant is built to discriminate against electron candidates resulting from hadronic jets,photon conversions, Dalitz decays and semileptonic heavy flavor hadron decays. The likelihood dis-criminant utilizes lateral and longitudinal shower shape, tracking and cluster-track matching quantities.

4

Probability density functions are combined in a product to give a global probability function for signalelectrons and for background. The discriminant value is then taken as a ratio of the signal probabil-ity density function to the sum of signal and background probability functions. Three operating pointsare defined for the likelihood discrimination: Loose, Medium and Tight each with progressively higherthreshold on the discriminant. The variables used in building the discriminant and the discriminant cutvalue are also varied based on the candidate electron transverse energy ET and η. The likelihoods aretuned for 13 TeV pileup conditions and detector performance in 2015 [34]. In this analysis, the Mediumworking point is used in the search and the Loose working point is used in the data-driven backgroundestimation (see Sec. 5). In addition to the likelihood discriminator, selection criteria based on track qual-ity are applied. The transition region between the central and forward regions of the calorimeters, inthe range 1.37 ≤ |η| ≤ 1.52, exhibits degraded energy resolution and is therefore excluded. To suppressbackground from misidentified jets as well as from light- and heavy-flavour hadron decays inside of jets,electrons are required to pass both calorimeter-based and track-based isolation criteria with a fixed ef-ficiency of 99% over the full range of electron momentum. The calorimeter-based isolation relies onthe ratio between the total transverse energy deposited in a cone of size ∆R =

√(∆η)2 + (∆φ)2 = 0.2

centered around the electron track and the electron ET. Likewise, the track-based isolation relies on theratio between the scalar sum of transverse momenta of tracks within a cone of radius ∆R = 10 GeV/pT(restricted to a maximum of ∆R = 0.3) and the electron track transverse momentum pT, where the tracksare required to have pT > 1 GeV and |η | < 2.5.

Candidate muon tracks are, at first, reconstructed independently in the ID and the MS [35]. The twotracks are then used as input to a combined fit which takes into account the energy loss in the calorimeterand multiple scattering effects. The ID track used for the combined fit is required to be within the IDacceptance, |η | < 2.5, and have a minimum number of hits in each ID sub-system. Muon candidatesin the overlap of MS barrel and endcap region (1.01 < |η | < 1.10) are rejected due to potential for pTmismeasurement resulting from relative barrel-endcap misalignment. On-going improvements in the re-construction aim to allow analyses to use this region in the future. In order to reduce the background fromlight and heavy hadron decays inside of jets, muons are required to fulfil relative track-based isolationrequirements with a fixed efficiency of 99%, as defined above for electron candidates. The selected muoncandidates must also pass within 10 mm of the primary interaction point in the z coordinate to suppresscosmic-ray background.

To improve momentum resolution and ensure a reliable measurement at very high momenta, muon tracksare required to have at least three hits in each of three precision chambers in the MS. Tracks which aretraversing precision chambers with poor alignment are rejected. Finally, the q/p measurements performedindependently in the ID and MS must agree within seven standard deviations of the sum in quadrature ofthe ID and MS momentum uncertainties.

In the dielectron channel, the presence of a two-electron trigger based on the Loose identification criteriawith ET threshold of 17 GeV is required. Events in the dimuon channel are required to pass at least oneof two single-muon triggers with pT thresholds of 26 GeV and 50 GeV, with the former also requiring themuon to be isolated. Electron (muon) candidates are required to have ET (pT) greater than 30 GeV andhave a transverse impact parameter consistent with the beam-line. Events are required to have at least onereconstructed primary vertex and at least one pair of same-flavour leptons.

Only the electron (muon) pair with the highest scalar sum ET (pT) is retained in each event and an oppositecharge requirement is applied in the dimuon case. The opposite charge requirement is not applied in thedielectron channel due to higher chance of charge mis-identification for high-ET electrons, as the electroncandidate charge is assigned based on ID information only.

5

5 Background estimation

The backgrounds from processes producing two real leptons are modelled using MC simulated samplesas described in Section 3. The processes for which MC simulation is used are: Drell-Yan, tt̄ and singletop as well as diboson production (WW , W Z , and Z Z). Energy (momentum) calibration and resolu-tion smearing is applied to electron (muon) candidates in the simulated samples to match performanceobserved in data. Event-level reweighting is applied in the simulated samples to match the trigger, recon-struction and isolation efficiencies. The simulated samples for the top-quark (single and pair) productionas well as diboson production are not simulated with sufficient statistics for modelling the dilepton massdistribution above several hundred GeV. Therefore, fits to smoothly decaying functions are used to extra-polate these background processes above dilepton masses (m``) of 400 GeV. Variations of the functionalform used as well as variations of the fit ranges contribute to the systematic uncertainty in the estimate ofthese background sources.

In the dimuon channel, contributions from W+jets and multi-jet production are negligible. However, theW+jets, multi-jet and other production processes where at most one real electron is produced contributeto the selected ee sample due to having one or more hadronic jets satisfying the electron selection criteria–so called “fakes”. The contribution from these processes is estimated simultaneously with a data-driventechnique, the matrix method, described in Ref. [10]. With this technique, exclusive samples are definedby loosening the selection criteria on one or both electron candidates. A matrix relationship is definedbetween counts of events in these sub-samples and sub-samples of events with zero, one or two trueelectrons and zero, one or two true jets. In this matrix, probabilities of electron identification from MCsimulated samples and jet misidentification as an electron from dedicated data samples are used. Thematrix is then inverted to obtain the contribution of events where one or both electron candidates resultfrom jet fakes. The estimate is extrapolated using a smooth function fit to the mee distribution between150 and 600 GeV to mitigate effects of limited statistics in the high mass region. The uncertainties inthis background estimate are evaluated by considering differences in the estimates for same-charge andopposite-charge reconstructed electron pairs as well as by varying the measured rates for real electronsand changing the parameters of the extrapolation.

As a final step, the sums of backgrounds estimated using MC samples are rescaled independently inboth channels so that the estimated count of events matches the data in the normalisation region80 GeV < m`` < 120 GeV.

6 Systematic uncertainties

As a result of the background yield normalisation described above, the analysis is protected against theluminosity uncertainty as well as any other mass-independent effect. A uniform uncertainty of 4% due tothe uncertainty in the Z/γ∗ cross-section in the normalisation region is applied to signal due to this pro-cedure. This uncertainty was obtained using a calculation based on VRAP at NNLO evaluating variationsin PDF, scale and αS . Mass-dependent systematic uncertainties, on the other hand, are considered asnuisance parameters in the statistical interpretation and include both theoretical and experimental effectson the background and experimental effects on the signal. Theoretical uncertainties in the backgroundprediction arise from the choice of the PDF set, the variations among different PDF eigenvector sets, thePDF αS scale and higher-order EW corrections. The uncertainties in the DY background associated tothe PDF scale and αS are derived using VRAP with the former obtained by varying the renormalisation

6

and factorisation scales of the nominal CT14NNLO PDF up and down simultaneously by a factor of two.The PDF variation systematic uncertainty is obtained using the CT14NNLO error set and by followingthe procedure described in Ref. [10]. It is treated as a single nuisance paramenter in the statistical ana-lysis of the results. An additional uncertainty is derived due to the choice of the nominal PDF set, bycomparing the central values of CT14NNLO with those from other PDF sets, namely MMHT14 [36],NNPDF3.0 [37], ABM12 [38], and JR14 [39]. The maximum absolute deviation from the envelope ofthese comparisons is used symmetrically as the PDF choice uncertainty.

The following sources of experimental uncertainties are accounted for: lepton trigger efficiency, recon-struction and isolation efficiency, lepton energy scale and resolution, and MC statistics. Efficiencies areevaluated using events from the Z → `` peak and then extrapolated to high energies. To estimate thesystematic uncertainty due to this extrapolation in the electron channel, differences in the electron showershapes between data and Monte Carlo simulation in the Z → ee peak are propagated to the high-ETelectron sample. The effect on the electron ID efficiency was found to be 2.0% and is independent of ETfor electrons with ET above 150 GeV. The uncertainty in the muon reconstruction efficiency includes theuncertainty obtained from Z → µµ data studies as well as a high-pT extrapolation uncertainty corres-ponding to the magnitude of the drop in the muon reconstruction and selection efficiency with increasingpT that is predicted by the MC simulation. Mismodelling of the muon momentum resolution due to re-sidual misalignments in the MS can alter the steeply falling background shape at high dilepton mass andcan significantly modify the width of the signal line shape. This uncertainty is obtained by studying ded-icated data-taking periods with no magnetic field in the MS. For the dielectron channel, the systematicuncertainty includes a contribution from the multi-jet and W+jets data-driven estimation that is obtainedby varying both the overall normalisation and the extrapolation methodology as explained in Section 5.Systematic uncertainties used in the statistical analysis of the results are summarised in Table 1 at dileptonmass values of 2 TeV and 3 TeV.

7 Event yields

Expected and observed event yields are shown in Table 2 in bins of invariant mass, for both the dielectron(top) and the dimuon channel (bottom). Expected events are split into the different background sourcesand the numbers for two signal scenarios are also given. Distributions of m`` in the dielectron and dimuonchannels are shown in Fig. 1. No significant excess is observed as discussed in Section 8.

8 Statistical analysis

A search for a resonant signal is performed using the m`` distribution in the dielectron and dimuonchannels utilizing the log likelihood ratio test (LLR). For a given signal hypothesis a likelihood functionL(n |Θ,θ) is constructed where n is a vector of event counts in the bins of the m`` histogram, Θ is theparameter of interest, here set to the signal strength µ, and θ is a vector of nuisance parameters modellingsystematic uncertainties. The likelihood is a product over all bins of the m`` histogram of individualbin likelihoods. The product is taken over the bins of m`` histograms in the ee and µµ channels for theindividual channel tests and over all bins of both m`` histograms for the combined test. The likelihood forbin i is the Poisson probability to observe a number of events ni , given the expected number of events inthat bin ni,exp. The quantity ni,exp is a function of the parameter of interest Θ and the nuisance parameters

7

Table 1: Summary of the systematic uncertainties in the expected number of events at a dilepton mass of2 TeV (3 TeV). For the background the values quoted represent relative shift in the m`` histogram bin spanningthe given reconstructed m`` mass of 2 TeV (3 TeV). For the signal uncertainties the values were computed using aZ′χ signal model with a pole mass of 2 TeV (3 TeV) by comparing yields in the core of the mass peak (within thefull width at half maximum) between the distribution varied under a given uncertainty and the nominal distribution.Uncertainties due to high-pT extrapolation are included in the efficiency uncertainty. N/A represents cases wherethe uncertainty is not applicable.

Source Dielectron DimuonSignal Background Signal Background

Normalisation 4.0% (4.0%) N/A 4.0% (4.0%) N/APDF Choice N/A 9.1% (17%) N/A 5.3% (7.4%)PDF Variation N/A 5.3% (11%) N/A 4.4% (6.5%)PDF Scale N/A 1.8% (2.3%) N/A 1.7% (1.9%)Photon-induced corrections N/A 3.4% (5.4%) N/A 3.2% (3.8%)Efficiency 5.1% (5.0%) 5.1% (5.0%) 13% (19%) 13% (19%)Scale & Resolution <1.0% (<1.0%) 7.8% (9.1%) 20% (26%) 20% (46%)Multi-jet & W+jets N/A <1.0% (<1.0%) N/A N/AMC Statistics <1.0% (<1.0%) <1.0% (<1.0%) <1.0% (<1.0%) <1.0% (<1.0%)

Total 6.5% (6.4%) 15% (24%) 25% (32%) 26% (51%)

Table 2: Expected and observed event yields in the dielectron (top) and dimuon (bottom) channels in differentdilepton mass intervals. The quoted errors correspond to the combined statistical and systematic uncertainties.

mee [GeV] 500-700 700-900 900-1200 1200-1800 1800-3000 3000-6000

Drell–Yan 145 ± 30 38 ± 6 16 ± 4 5.6 ± 1.6 0.87 ± 0.26 0.026 ± 0.012Top Quarks 43.8 ± 2.9 5.4 ± 1.2 0.9 ± 0.5 0.09 ± 0.11 0.002 ± 0.006 <0.001Diboson 7.7 ± 1.1 1.4 ± 0.5 0.39 ± 0.26 0.08 ± 0.12 0.005 ± 0.030 <0.001Multi-Jet & W+Jets 4 ± 4 1.1 ± 0.8 0.40 ± 0.16 0.089 ± 0.019 0.0042 ± 0.0014 <0.001

Total SM 201 ± 31 46 ± 7 17 ± 4 5.8 ± 1.6 0.88 ± 0.26 0.026 ± 0.012

Data 202 44 17 9 0 0

SM+Z ′ (mZ ′ = 3 TeV) 201 ± 31 46 ± 7 17 ± 4 5.9 ± 1.6 2.6 ± 1.1 1.44 ± 0.34SM+CI (Λ−LL = 25 TeV) 207 ± 31 49 ± 7 20 ± 4 8.0 ± 1.6 2.11 ± 0.27 0.251 ± 0.019

mµµ [GeV] 500-700 700-900 900-1200 1200-1800 1800-3000 3000-6000

Drell–Yan 110 ± 7 27.5 ± 2.2 11.8 ± 1.1 4.5 ± 0.7 0.70 ± 0.08 0.079 ± 0.023Top Quarks 39.5 ± 0.8 6.7 ± 0.4 0.89 ± 0.15 0.046 ± 0.032 <0.001 <0.001Diboson 3.98 ± 0.32 0.65 ± 0.11 0.229 ± 0.028 0.022 ± 0.006 0.00104 ± 0.00034 <0.001

Total SM 151 ± 7 35.5 ± 2.3 14.2 ± 1.1 4.6 ± 0.7 0.71 ± 0.08 0.079 ± 0.024

Data 169 28 13 4 0 0

SM+Z ′ (mZ ′ = 3 TeV) 151 ± 7 35.5 ± 2.3 14.2 ± 1.1 4.6 ± 0.7 2.13 ± 0.26 0.8 ± 0.4SM+CI (Λ−LL = 25 TeV) 162 ± 8 38.1 ± 2.4 15.3 ± 1.2 5.5 ± 0.8 0.87 ± 0.09 0.099 ± 0.035

θ. Signal acceptance varying as a function of signal pole mass and decay channel is taken into accountin the computation of ni,exp. The nuisance parameters are assumed to be Gaussian-distributed. The test

8

Eve

nts

2−10

1−10

1

10

210

310

410

510

610 Data

*γZ/

Top Quarks

Diboson

Multi­Jet & W+Jets

(3 TeV)χZ’

= 20 TeV­

LLΛ

PreliminaryATLAS­1 = 13 TeV, 3.2 fbs

Dilepton Search Selection

Dielectron Invariant Mass [GeV]

90100 200 300 400 1000 2000 3000

Da

ta /

Bkg

0.6

0.8

1

1.2

1.4

100

(a)

Eve

nts

2−10

1−10

1

10

210

310

410

510

610 Data

*γZ/

Top Quarks

Diboson

(3 TeV)χZ’

= 20 TeV­

LLΛ

PreliminaryATLAS­1 = 13 TeV, 3.2 fbs

Dilepton Search Selection

Dimuon Invariant Mass [GeV]

90100 200 300 400 1000 2000 3000

Da

ta /

Bkg

0.6

0.8

1

1.2

1.4

100

(b)

Figure 1: Dielectron (a) and dimuon (b) reconstructed mass distributions after selection, for data and the SM back-ground estimates as well as their ratio. Two selected signals are overlaid, resonant Z′χ with pole mass of 3 TeVand non-resonant CI with LL constructive interference and Λ−LL = 20 TeV. The bin width of the distributions isconstant in log(m``) and the green band in the lower panel illustrates the total systematic uncertainty, as explainedin Section 6.

statistic q0 is defined as:

q0 = 0,± ln[L(n | 0, θ̂0)

L(n | Θ̂, θ̂)

], (2)

where Θ̂ and θ̂ denote the values of the strength parameter and the nuisance parameters for which Lis maximized and θ̂0 denotes the values of the nuisance parameters that maximize L when the strengthparameter is held at 0. The negative sign is selected for µ̂ > 0. For µ̂ < 0, the positive sign is chosenfor test signal masses below 900 GeV (where substantial SM background is expected) to quantify thesignificance of potential deficits in the data, otherwise q0 is set to 0. In the presence of background only,q0 is distributed as a χ2 for one degree of freedom and therefore the p-value for finding a more signal-likeexcess than observed is computed analytically [40, 41]. Multiple mass hypotheses are tested using Z′χ asa signal in pole mass steps corresponding to the histogram bin width to compute the local p-values - that isp-values corresponding to specific signal mass hypotheses. The bin width of the m`` histogram is chosento correspond to the resolution in the specific dilepton channel varying from 5 GeV (25 GeV) at mee

(mµµ) of 500 GeV to 15 GeV (180 GeV) at mee (mµµ) of 2 TeV. Pseudo-experiments are used to estimatethe distribution of the lowest local p-value in the absence of any signal. The p-value to find anywhere inthe m`` distribution an excess more significant than the one in the data (global p-value) is then computed.The test does not reveal any signal-like excess in the data. In addition, a test for any excess anywhere inthe m`` histogram following the BumpHunter methodology [42] confirms compatibility of the data withthe SM prediction.

Upper limits are set on the Z′ production cross section times branching ratio to the dilepton final state(σB) and lower limits are set on the CI scale Λ in a variety of interference and chiral coupling scenarios.In both cases, the likelihood functions L(n |Θ,θ) for individual channels and for the full dataset areconstructed as above. For constraining the Z′ (CI) models, the parameter of interest is σB (Λ). Thelogarithmic m`` histogram binning shown in Fig. 1 is chosen for setting limits on resonant signals using

9

Z′χ signal templates as in the search phase. For setting the limits on the CI interaction scale Λ, them`` mass distribution above 400 GeV is used with bin widths varying from 100 to 500 GeV. The BayesTheorem is applied and nuisance parameters are marginalised to obtain the posterior probability densityfunction P (Θ|n). The prior probability P(Θ) is chosen to be uniform and positive in either the crosssection for the Z′ search and 1/Λ2 or 1/Λ4 for the CI search. For the CI search, these choices of the priorare selected to study the cases where dilepton production cross section is dominated by the interferenceterms and when it is dominated by the pure contact interaction term. The upper (lower) 95% percentile ofP (Θ|n) is then quoted as the upper (lower) 95% credibility level limit on σB (Λ). The above calculationshave been performed with the Bayesian Analysis Toolkit (BAT) [43], which uses a Markov Chain MonteCarlo technique to integrate over the nuisance parameters. Limit values obtained using the experimentaldata are quoted as observed limits, while median values of the limits from a large number of pseudo-experiments, where only SM background is present, are quoted as the expected limits. The upper limitson the Z′ σB are interpreted as lower limits on the Z′ pole mass using the relationship between the polemass and the theoretical Z′ cross section.

9 Results

The statistical tests described in the previous section do not reveal presence of a signal. The BumpHuntertests find SM p-values of 70% and 75% in the dielectron and dimuon channels, respectively. The resultsof the LLR tests are shown in Fig. 2, which show the local p-value distributions and the global p-valuefor the most significant excess in the dielectron, dimuon and combined channels. The largest deviationscorrespond to global SM p-values of 73%, 24% and 92% in the dielectron and dimuon channels, as wellas for both channels combined, respectively. Upper limits on σB for Z′ production and decay in thedielectron, dimuon and combined channels are shown in Fig. 3. The observed and expected lower polemass limits for various Z′ scenarios are summarised in Table 3. The lower limits on the CI interactionscale Λ where a prior uniform and positive in 1/Λ2 is used are summarised in Fig. 4. Table 4 gives anoverview of Λ lower limits for all considered chiral coupling and interference scenarios as well as bothchoices of the prior Λ probability.

Table 3: Observed and expected 95% C.L. lower mass limits for various Z′ gauge boson models.

Model Width [%]ee [TeV] µµ [TeV] `` [TeV]

Exp Obs Exp Obs Exp ObsZ′SSM 3.0 3.17 3.18 2.91 2.98 3.37 3.40Z′χ 1.2 2.87 2.88 2.64 2.71 3.05 3.08Z′S 1.2 2.83 2.84 2.59 2.67 3.00 3.03Z′I 1.1 2.78 2.78 2.53 2.62 2.95 2.98Z′N 0.6 2.64 2.64 2.38 2.48 2.81 2.85Z′η 0.6 2.64 2.65 2.38 2.48 2.81 2.85Z′ψ 0.5 2.58 2.58 2.32 2.42 2.74 2.79

10

[TeV]Z’

m

0.2 0.3 0.4 1 2

0Local p

4−10

3−10

2−10

1−10

1

10

210

σ0Local significance

σ1

σ2

σ3

σ0

σ1

σ2

Global significance for largest excess

↑

ATLAS Preliminary­1

Ldt = 3.2 fb∫ = 13 TeV, s

ee→χ, Z’0

Observed p

(a)

[TeV]Z’

m

0.2 0.3 0.4 1 2

0Local p

4−10

3−10

2−10

1−10

1

10

210

σ0Local significance

σ1

σ2

σ3

σ0

σ1

σ2

Global significance for largest excess

↑

ATLAS Preliminary­1

Ldt = 3.2 fb∫ = 13 TeV, s

µµ→χ, Z’0

Observed p

(b)

[TeV]Z’

m

0.2 0.3 0.4 1 2

0Local p

4−10

3−10

2−10

1−10

1

10

210

σ0Local significance

σ1

σ2

σ3

σ0

σ1

σ2

Global significance for largest excess

↑

ATLAS Preliminary­1

Ldt = 3.2 fb∫ = 13 TeV, s

ll→χ, Z’0

Observed p

(c)

Figure 2: Distributions of local p-value for (a) dielectron, (b) dimuon and (c) combined channels derived for idealZ′χ signals with pole mass between 0.15 and 2.5 TeV. Also indicated are local and global significance levels shownas dashed lines. Global significance level is computed for the most significant excess.

11

[TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B [p

b]

σ

­410

­310

­210

­110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

ee→Z’

­1 = 13 TeV, 3.2 fbs

(a)

[TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B [p

b]

σ

­410

­310

­210

­110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

µµ →Z’

­1 = 13 TeV, 3.2 fbs

(b)

[TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B [

pb

]σ

­410

­310

­210

­110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

ll→Z’

­1 = 13 TeV, 3.2 fbs

(c)

Figure 3: Upper 95% C.L. limits on the Z′production cross section times branching ratio to two leptons. Shown areresults for the (a) dielectron channel, (b) dimuon channel and (c) combined channels

12

Chiral Structure

LL Const LL Dest LR Const LR Dest RL Const RL Dest RR Const RR Dest

[T

eV

]Λ

15

20

25

30

35

40

Observed

Expected

σ 1 ±Expected

σ 2 ±Expected

­1 = 8 TeV, 20 fbs

PreliminaryATLAS­1 = 13 TeV, 3.2 fbs

2ΛPrior: 1/

Figure 4: Lower 95% C.L. limits on the CI scale Λ for different chiral coupling and interference scenarios usinga uniform positive prior in 1/Λ2. For the LL and RR cases, the ATLAS

√s = 8 TeV results [12] are shown for

comparison. In that publication the LR case was obtained by setting ηLR = ηRL = ±1 and therefore is not directlycomparable to the results presented here.

Table 4: Expected and observed 95% C.L. lower exclusion limits on Λ for the LL, LR, RL, and RR chiral couplingscenarios, for both the constructive and destructive interference cases using a uniform positive prior in 1/Λ2 or 1/Λ4.The dielectron, dimuon, and combined dilepton channel limits are shown.

Channel PriorLeft-Left [TeV] Left-Right [TeV] Right-Left [TeV] Right-Right [TeV]

Const. Destr. Const. Destr. Const. Destr. Const. Destr.

Exp: ee1/Λ2 18.5 15.2 18.1 15.8 17.7 16.1 17.9 15.9

Obs: ee 18.3 15.3 17.6 15.8 17.5 15.9 17.5 15.8

Exp: ee1/Λ4 16.9 14.3 16.6 14.8 16.4 14.8 16.5 14.7

Obs: ee 16.7 14.1 16.2 14.5 16.1 14.6 16 14.6

Exp: µµ1/Λ2 18.2 14.5 17.5 15.1 17.4 15.4 18.1 14.5

Obs: µµ 20.2 15.8 19.7 17.0 19.4 17.1 20.4 15.8

Exp: µµ1/Λ4 16.6 13.8 16.3 14.4 16.1 14.5 16.6 13.9

Obs: µµ 18.1 15.0 17.7 15.8 17.4 15.9 18.1 15.0

Exp: ``1/Λ2 21.4 16.4 21.0 17.4 20.4 17.7 20.9 16.9

Obs: `` 23.1 17.5 22.1 18.8 21.7 19.0 22.6 17.7

Exp: ``1/Λ4 19.9 15.6 19.0 16.6 18.7 16.6 19.4 16.0

Obs: `` 20.7 16.4 20.0 17.5 19.8 17.6 20.3 16.6

13

10 Conclusions

In conclusion, the ATLAS detector at the Large Hadron Collider has been used to search for resonant andnon-resonant new phenomena in the dilepton invariant mass spectrum above the Z-boson pole. The searchis conducted with 3.2 fb−1 of pp collision data at

√s = 13 TeV, recorded during 2015. The observed

dilepton invariant mass spectrum is consistent with the Standard Model expectation, within systematicand statistical uncertainties. Upper 95% C.L. exclusion limits are therefore set on the cross-section timesbranching ratio σB for a spin-1 Z′ gauge boson. The resulting lower mass limits are 3.40 TeV for theZ′SSM, 3.08 TeV for the Z′χ , and 2.79 TeV for the Z′ψ . Other E6 Z′ models are also constrained. Thelower 95% C.L. exclusion limits on the energy scale Λ for various ``qq contact interaction models rangebetween 16.4 TeV and 23.1 TeV.

14

11 Event displays

Figure 5: Highest dielectron invariant mass event displayed in Atlantis (upper), and VP1 (lower). The highestmomentum electron has an ET of 373 GeV and an η of -1.03. The subleading electron has an ET of 246 GeV andan η of 2.45. The invariant mass of the pair is 1775 GeV.

15

Figure 6: Highest dimuon invariant mass event displayed in Atlantis (upper), and VP1 (lower). The highest mo-mentum muon has a pT of 712 GeV and an η of 0.87. The subleading muon has a pT of 676 GeV and an η of 0.95.The invariant mass of the pair is 1390 GeV.

16

References

[1] D. London and J. L. Rosner, Extra Gauge Bosons in E(6), Phys. Rev. D34 (1986) 1530.

[2] P. Langacker, The Physics of Heavy Z′ Gauge Bosons, Rev. Mod. Phys. 81 (2009) 1199,arXiv: 0801.1345 [hep-ph].

[3] L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension,Phys. Rev. Lett. 83 (1999) 3370, arXiv: hep-ph/9905221 [hep-ph].

[4] P. Meade and L. Randall, Black Holes and Quantum Gravity at the LHC, JHEP 05 (2008) 003,arXiv: 0708.3017 [hep-ph].

[5] M. V. Chizhov, V. A. Bednyakov and J. A. Budagov,Proposal for chiral bosons search at LHC via their unique new signature,Phys. Atom. Nucl. 71 (2008) 2096, arXiv: 0801.4235 [hep-ph].

[6] F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking,Phys. Rev. D71 (2005) 051901, arXiv: hep-ph/0405209 [hep-ph].

[7] N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phenomenology, astrophysics and cosmologyof theories with submillimeter dimensions and TeV scale quantum gravity,Phys. Rev. D59 (1999) 086004, arXiv: hep-ph/9807344 [hep-ph].

[8] E. Eichten, K. D. Lane and M. E. Peskin, New Tests for Quark and Lepton Substructure,Phys. Rev. Lett. 50 (1983) 811.

[9] E. Eichten et al., Super Collider Physics, Rev. Mod. Phys. 56 (1984) 579.

[10] ATLAS Collaboration, Search for high-mass dilepton resonances in pp collisions at√

s = 8 TeVwith the ATLAS Detector, Phys. Rev. D90 (2014) 052005, arXiv: 1405.4123 [hep-ex].

[11] CMS Collaboration, Search for physics beyond the standard model in dilepton mass spectra inproton-proton collisions at

√s = 8 TeV, JHEP 04 (2015) 025, arXiv: 1412.6302 [hep-ex].

[12] ATLAS Collaboration, Search for contact interactions and large extra dimensions in the dileptonchannel using proton-proton collisions at

√s = 8 TeV with the ATLAS detector,

Eur. Phys. J. C74.12 (2014) 3134, arXiv: 1407.2410 [hep-ex].

[13] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider,JINST 3 (2008) S08003.

[14] ATLAS Collaboration, ‘ATLAS Insertable B-Layer Technical Design Report’,tech. rep. CERN-LHCC-2010-013. ATLAS-TDR-19, CERN, 2010,url: http://cds.cern.ch/record/1291633.

[15] S. Alioli et al., A general framework for implementing NLO calculations in shower Monte Carloprograms: the POWHEG BOX, J. High Energy Phys. 1006 (2010) 043,arXiv: 1002.2581 [hep-ph].

[16] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D 82 (2010) 074024,arXiv: 1007.2241 [hep-ph].

[17] T. Sjostrand, S. Mrenna and P. Z. Skands, A Brief Introduction to PYTHIA 8.1,Comput. Phys. Commun. 178 (2008) 852, arXiv: 0710.3820 [hep-ph].

[18] ATLAS Collaboration, Measurement of the Z/γ∗; boson transverse momentum distribution in ppcollisions at

√s = 7 TeV with the ATLAS detector, JHEP 2014 (2014) 55,

arXiv: 1406.3660 [hep-ex].

17

[19] J. Pumplin et al.,New generation of parton distributions with uncertainties from global QCD analysis,JHEP 07 (2002) 012, arXiv: hep-ph/0201195 [hep-ph].

[20] N. Davidson, T. Przedzinski and Z. Was,PHOTOS Interface in C++: Technical and Physics Documentation (2010),arXiv: 1011.0937 [hep-ph].

[21] C. Anastasiou et al., High precision QCD at hadron colliders: Electroweak gauge boson rapiditydistributions at NNLO, Phys. Rev. D69 (2004) 094008, arXiv: hep-ph/0312266 [hep-ph].

[22] S. Dulat et al., The CT14 Global Analysis of Quantum Chromodynamics (2015),arXiv: 1506.07443 [hep-ph].

[23] S. G. Bondarenko and A. A. Sapronov,NLO EW and QCD proton-proton cross section calculations with mcsanc-v1.01,Comput. Phys. Commun. 184 (2013) 2343, arXiv: 1301.3687 [hep-ph].

[24] A. D. Martin et al., Parton distributions incorporating QED contributions,Eur. Phys. J. C39 (2005) 155, arXiv: hep-ph/0411040 [hep-ph].

[25] T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 0902 (2009) 007,arXiv: 0811.4622 [hep-ph].

[26] T. Sjostrand, S. Mrenna and P. Z. Skands, PYTHIA 6.4 Physics and Manual,J. High Energy Phys. 0605 (2006) 026, arXiv: hep-ph/0603175 [hep-ph].

[27] P. Z. Skands, Tuning Monte Carlo Generators: The Perugia Tunes,Phys. Rev. D82 (2010) 074018, arXiv: 1005.3457 [hep-ph].

[28] M. Czakon and A. Mitov,Top++: A Program for the Calculation of the Top-Pair Cross-Section at Hadron Colliders,Comput. Phys. Commun. 185 (2014) 2930, arXiv: 1112.5675 [hep-ph].

[29] R. D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B867 (2013) 244,arXiv: 1207.1303 [hep-ph].

[30] D. J. Lange, The EvtGen particle decay simulation package,Nucl. Instrum. Meth. A462 (2001) 152.

[31] S. Agostinelli et al., GEANT4: A Simulation toolkit, Nucl. Instrum. Meth. A 506 (2003) 250.

[32] G. Aad et al., The ATLAS Simulation Infrastructure, Eur. Phys. J. C70 (2010) 823,arXiv: 1005.4568 [physics.ins-det].

[33] ATLAS Collaboration, Electron efficiency measurements with the ATLAS detector using the 2012LHC proton–proton collision data, ATLAS-CONF-2014-032, 2014,url: http://cdsweb.cern.ch/record/1706245.

[34] ATLAS Collaboration, ‘Electron identification measurements in ATLAS using√

s = 13 TeV datawith 50 ns bunch spacing’, tech. rep. ATL-PHYS-PUB-2015-041, CERN, 2015,url: http://cds.cern.ch/record/2048202.

[35] ATLAS Collaboration, ‘Muon reconstruction performance in early√

s = 13 TeV data’,tech. rep. ATL-PHYS-PUB-2015-037, CERN, 2015,url: http://cds.cern.ch/record/2047831.

18

[36] P. Motylinski et al., ‘Updates of PDFs for the 2nd LHC run’, International Conference on HighEnergy Physics 2014 (ICHEP 2014) Valencia, Spain, July 2-9, 2014, 2014,arXiv: 1411.2560 [hep-ph],url: http://inspirehep.net/record/1326954/files/arXiv:1411.2560.pdf.

[37] R. D. Ball et al., Parton distributions for the LHC Run II, JHEP 04 (2015) 040,arXiv: 1410.8849 [hep-ph].

[38] S. Alekhin, J. Blumlein and S. Moch, The ABM parton distributions tuned to LHC data,Phys. Rev. D89 (2014) 054028, arXiv: 1310.3059 [hep-ph].

[39] P. Jimenez-Delgado and E. Reya, Delineating parton distributions and the strong coupling,Phys. Rev. D89 (2014) 074049, arXiv: 1403.1852 [hep-ph].

[40] G. Cowan et al., Asymptotic formulae for likelihood-based tests of new physics,Eur. Phys. J. C71 (2011) 1554, arXiv: 1007.1727 [physics.data-an].

[41] S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses,Ann. Math. Statist. 9 (1938) 60.

[42] G. Choudalakis, On hypothesis testing, trials factor, hypertests and the BumpHunter (2011),eprint: http://arxiv.org/abs/1101.0390.

[43] A. Caldwell, D. Kollar and K. Kroninger, BAT: The Bayesian Analysis Toolkit,Comput. Phys. Commun. 180 (2009) 2197, arXiv: 0808.2552 [physics.data-an].

19