EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2013-231
Submitted to: PRD
Search for dark matter in events with a
Z
boson and missing
transverse momentum in
pp
collisions at
√
s = 8
TeV with the
ATLAS detector
The ATLAS Collaboration
Abstract
A search is presented for production of dark matter particles recoiling against a leptonically
decay-ing Z boson in 20.3 fb
−1of pp collisions at
√
s = 8
TeV with the ATLAS detector at the Large Hadron
Collider. Events with large missing transverse momentum and two oppositely-charged electrons or
muons consistent with the decay of a Z boson are analyzed. No excess above the Standard Model
prediction is observed. Limits are set on the mass scale of the contact interaction as a function of the
dark matter particle mass using an effective field theory description of the interaction of dark matter
with quarks or with Z bosons. Limits are also set on the coupling and mediator mass of a model in
which the interaction is mediated by a scalar particle.
c
2014 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.
Search for dark matter in events with a Z boson and missing transverse momentum in
pp collisions at
√
s = 8 TeV with the ATLAS detector
(Dated: July 8, 2014)
A search is presented for production of dark matter particles recoiling against a leptonically
decaying Z boson in 20.3 fb−1of pp collisions at√s = 8 TeV with the ATLAS detector at the Large
Hadron Collider. Events with large missing transverse momentum and two oppositely-charged
electrons or muons consistent with the decay of a Z boson are analyzed. No excess above the Standard Model prediction is observed. Limits are set on the mass scale of the contact interaction as a function of the dark matter particle mass using an effective field theory description of the interaction of dark matter with quarks or with Z bosons. Limits are also set on the coupling and mediator mass of a model in which the interaction is mediated by a scalar particle.
PACS numbers: 13.85.Rm,14.70.Hp,14.80.Nb
Astrophysical measurements indicate the existence of non-baryonic dark matter [1, 2]. However, collider based searches, nuclear scattering experiments, and searches for particles produced from dark-matter annihilation have not yet revealed its particle nature nor discovered its non-gravitational interactions, if they exist [3]. Collider-based searches for weakly interacting massive particles (WIMPs, denoted as χ), specifically pp→ χ ¯χ + X at the Large Hadron Collider (LHC) via some unknown inter-mediate state, are an important facet of the experimen-tal program and provide sensitivity over a broad range of values of the WIMP mass, mχ, including for low masses
where direct detection experiments are less sensitive. The presence of dark-matter particles, not directly observable in a collider detector, can be inferred from their recoil against Standard Model (SM) particles. The LHC col-laborations have reported limits on the cross section for the process that includes initial state radiation (ISR), pp→ χ ¯χ + X, where the ISR component X is a hadronic jet [4, 5], a photon [6, 7], or a W or Z boson decaying hadronically [8]. Limits on dark matter produced in the decay of the Higgs boson have also been reported [9]. In this analysis, limits are set using the final state of a Z boson decaying to two oppositely charged electrons or muons, plus missing transverse momentum, Emiss
T .
Since the nature of the intermediate state mediating the parton–WIMP interaction is not known, a useful ap-proach is to construct an effective field theory (EFT) [10– 12]. EFTs have often been used to describe interactions between dark-matter particles and quarks or gluons, but they have recently been extended to describe direct inter-actions with electroweak bosons [13–15]. In the context of the EFT framework, the WIMP is considered to be the only new particle accessible at LHC energies, in ad-dition to the SM fields. The mediator of the interaction is assumed to be heavy compared to the typical parton interaction energies involved, and the dark-matter parti-cles are also assumed to be produced in pairs.
The EFTs considered in this analysis, depicted in Fig. 1, are expressed in terms of two parameters: mχ and
a mass scale, M?, described in Ref. [10]. M?
parameter-izes the coupling between the WIMP and SM particles, where the coupling strength is normalized, or in inverse proportion, to the heavy-mediator mass scale. The
coef-Z χ ¯ χ q ¯ q (a) q ¯ q Z/γ∗ Z χ ¯ χ (b)
FIG. 1. The diagrams showing different types of pp → χ ¯χ+Z
production modes considered in this analysis [13]. Figure (a) shows a diagram that includes an ISR operator, and figure (b) shows a diagram that includes a ZZχχ operator.
ficients of the Lagrangian’s interaction terms appear as powers of M?, e.g. for the D1 operator as 1/M?3 and for
the D5 and D9 operators as 1/M2
?. The definition of the
D1, D5, and D9 operators and the region of validity of the EFT limits are discussed in Ref. [10, 16].
Following the approach of Ref. [13], the coupling of dark matter to electroweak bosons is considered for 5 and 7 operators. The dimension-7 operator couples dark matter to Zγ∗ as well as ZZ. Since a Z boson is in the final state for each operator, intermediate states with a Z or γ∗each contribute to the matrix element. The relative contribution of the Z and γ∗ diagrams is a parameter of the theory.
This analysis considers models of dark-matter produc-tion where a Z boson is radiated as ISR or interacts di-rectly with WIMPs. The latter case of an interaction between a Z-boson and a WIMP is a process not previ-ously investigated in the analysis of LHC experiments.
To complement the EFT analysis, this paper also ex-amines the results in terms of a model in which the in-termediate state is specified [17]. In this model a scalar-mediator η, with mass mη, and a scalar–WIMP coupling
strength f is responsible for the production of the dark-matter particles. The mediator η transforms as a color triplet and an electroweak doublet, and has a hyper-charge of 1/3. The production cross section is
propor-tional to f4. The same final state signature predicted by the EFT, Zχ ¯χ, is produced. This process is similar to SUSY processes in which the χ is a neutralino and the η is a squark doublet, but without a direct gluino ana-logue. This corresponds to a scenario where the gluino would be too heavy to be produced at the LHC and is therefore irrelevant.
In this analysis, a search for the production of a Z boson with subsequent decay to e+e− or µ+µ− in
asso-ciation with large ETmiss from the escaping χ ¯χ particles is reported, based on 20.3 fb−1 of pp collision data col-lected by the ATLAS detector at a center-of-mass energy of √s = 8 TeV. Only data collected with stable beams and all detector subsystems fully operational are used. Several signal regions with different requirements on the ETmiss are defined to best probe the variety of models tested.
The ATLAS detector [18] consists of an inner detec-tor (ID) surrounded by a solenoid that produces a 2 T magnetic field, electromagnetic and hadronic calorime-ters, and a muon spectrometer (MS) employing toroidal magnets. The ID measures charged-particle tracks over the full azimuthal angle and in a pseudorapidity [19] range of|η| < 2.5 using silicon pixel, silicon microstrip, and transition-radiation straw-tube detectors, the last of which also distinguishes electrons from heavier charged particles in the range |η| < 2.0. Liquid-argon (LAr) electromagnetic sampling calorimeters cover the range |η| < 3.2 with a typical granularity in ∆η × ∆φ of 0.025× 0.025. A scintillator-tile calorimeter provides hadronic calorimetry for |η| < 1.7. In the endcaps (|η| > 1.5), LAr is also used for the hadronic calorimeters matching the outer |η| limit of the endcap electromag-netic calorimeters. The LAr forward calorimeters extend the coverage to |η| < 4.9 and provide both the electro-magnetic and hadronic energy measurements. The MS covers |η| < 2.7 and provides triggering and precision tracking for muons. A three-level trigger system is used to select interesting events to be recorded for subsequent offline analysis.
Electrons are required to have transverse energy, ET,
larger than 20 GeV and |η| < 2.47. The ET is
mea-sured from the energy deposited in the electromagnetic calorimeter, and the electron’s direction from the ID track. Electrons must satisfy the medium object quality requirements from Ref. [20] updated for 2012 run con-ditions, which are based on calorimeter shower shape, ID track quality, and the spatial match between the shower and the track. Electrons must be isolated, sat-isfying P∆R<0.2
ptrackT /ET< 0.1, where the sum is over
the transverse momenta, ptrack
T , of all other ID tracks
with ptrack
T > 1 GeV within a cone of radius ∆R =
q
(∆η)2+ (∆φ)2= 0.2 around the electron direction. Muons are required to have pT> 20 GeV and|η| < 2.5.
A combined fit of the ID and MS tracks is used to re-construct the muon pT. High-quality tracks are ensured
by requirements on the number of hits in the ID.
Lon-gitudinal and transverse impact parameters, z0 and d0
respectively, must satisfy |z0| < 10 mm and |d0| < 1
mm, with respect to the primary vertex, defined as the vertex with the highestP ptrack
T
2
. The muon must be isolated, satisfyingP∆R<0.2ptrack
T /pT< 0.1; here again,
the muon track itself is excluded from the sum.
The anti-kt jet algorithm [21] with radius parameter
of 0.4 is used to reconstruct jets from topological clus-ters [22], which are three-dimensional clusclus-ters of neigh-boring energy deposits in the calorimeter cells. A cali-bration procedure is used in which the raw energy mea-surement from the calorimeter cluster is corrected to the jet energy scale. Jets are required to have pT> 25 GeV
and|η| < 2.5. Jets from secondary proton–proton colli-sions are removed by requiring that most of the tracks associated with the jet, weighted by pT, originate at the
primary vertex.
Since muons may generate delta-ray electrons or radi-ate photons that produce electron–positron pairs, elec-trons closer than ∆R = 0.2 to a muon that passes the analysis selection are rejected. In addition, electrons and muons closer than ∆R = 0.4 to a jet are also rejected.
The measurement of the missing transverse momen-tum, a vector in the transverse plane, ~Emiss
T , with
mag-nitude Emiss
T , is based on the measurement of the
en-ergy collected by the calorimeters and the momenta of muons. Muons and electrons with pT > 10 GeV, jets
with pT > 20 GeV, low-pT tracks which don’t seed a
topological cluster, and topological clusters not associ-ated with a jet are included in the ~Emiss
T calculation [23].
The candidate signal events were accepted by at least one of the several triggers that require either two leptons with low pTor a single lepton with higher pT. An event
must have at least one reconstructed vertex with at least three associated tracks with pT > 400 MeV to remove
non-collision background. In addition, events must have two oppositely charged electrons or muons with invariant mass m``∈ [76, 106] GeV to form a Z boson candidate.
In order to suppress events where the Emiss
T originates
from mismeasured jets, the azimuthal angle between the dilepton system and the ~Emiss
T , ∆φ( ~ETmiss, p``T), must be
greater than 2.5, the absolute value of the pseudorapidity of the dilepton system,|η``
|, must be less than 2.5, and the ratio |p``T− ETmiss|/p``T must be less than 0.5, where p``T is the transverse momentum of the dilepton system. Events are removed if they contain one or more jets with pT > 25 GeV to suppress top-quark pair background.
Similarly, events containing a third lepton with pT >
7 GeV, satisfying looser identification requirements than invoked for the leptons produced in the decay of the Z boson, are removed to suppress diboson background.
The various dark-matter models considered here have different ETmiss spectra, leading to a variety of optimal lower thresholds of Emiss
T . Four inclusive signal regions
are defined with lower thresholds in Emiss
T of 150, 250,
350, and 450 GeV.
(` = e, µ), an irreducible background. The other irre-ducible background is W W → `+ν`−ν, which may only¯ be reduced through the mass window requirement. Re-ducible backgrounds may have jets produced in associa-tion with two leptons, where the jets are misidentified or unreconstructed, such as t¯t→ `+νb`−ν¯¯b, ZZ→ `+`−qq,¯ W Z → ¯qq0`+`−, or Z+jets (including decays to τ lep-tons). Additional reducible sources may produce events with more than two leptons where the additional leptons are misidentified or not reconstructed, or less than two leptons where jets are misidentified as leptons, such as W Z → `ν`+`− and W +jets, respectively.
The W Z and ZZ backgrounds are estimated from Monte Carlo (MC) simulation. The next-to-leading-order MC generator POWHEG BOX 1.0 [24] is used, which models the production from a q ¯q initial state. The ZZ background sample is normalized to include the gg → ZZ contribution using MCFM 6.2 [25]. Par-ton distribution functions (PDFs) for these samples are modeled using CT10 [26]. The underlying event, as well as parton showers and hadronization, are simu-lated with PYTHIA 8.165 [27], using the AU2 tune [28]. QED radiative corrections are calculated using PHO-TOS++ 3.0 [29]. The detector response is simulated with GEANT 4 [30, 31]. The simulated samples are generated with pileup conditions similar to those observed in data. Pileup refers to the multiple interactions occurring in the same, or adjacent, beam bunch crossings as the hard pro-cess. Simulated events are reweighted so that the number of pileup interactions has the same distribution as in data events.
The W W , t¯t, W t, and Z → ττ backgrounds are es-timated from data using the absence of signal in the eµ channel and the relative production rate of 1:1:2 for the ee, µµ, and eµ channels. An eµ control region similar to the signal region is defined, and the background esti-mate for the ee and µµ signal regions is obtained from the number of eµ events in the control region after correcting for the slightly different electron and muon acceptances and efficiencies.
The Z+jets background is estimated using two data-driven techniques. The first method, commonly referred to as the ABCD method [32], considers the distribution of signal and background events in a phase space defined by two uncorrelated variables, here Emiss
T and η``, for
which the signal and background have different shapes. The phase space is partitioned into four regions labeled A, B, C, and D. Region A is the signal region where se-lection requirements on both variables are invoked, while regions B, C, and D are control regions in which one or both selections are reversed. Contamination by signal events in the control regions is found to be negligible. The number of events in one control region scaled by the ratio of background events in two other control regions estimates the background contribution in the signal re-gion. In the second method, the contribution is measured by fitting the distributions of ∆φ( ~ETmiss, p``T) and ETmissat small values (Emiss
T < 80 GeV and ∆φ( ~ETmiss, p``T) < 2.5)
and extrapolating them to the signal regions. The two methods invoke all the standard selection requirements and give consistent results. The ABCD method is used to provide the background estimate, and the difference between the two is taken as a systematic uncertainty on the estimate.
The W +jets background is estimated by reversing the electron isolation condition and loosening identification requirements for one electron in order to obtain a data sample enriched in jets reconstructed as electrons. The resultant ETmiss distribution is fitted with a function of the form N = A· ETmissb below 300 GeV and extrap-olated to the highest 450 GeV signal region. The fitted function is integrated over Emiss
T to obtain an estimated
background above a given Emiss
T threshold. A
normaliza-tion factor is derived from data in the low-Emiss T region
with all the analysis selections applied. This factor is ap-plied to the extrapolated result to obtain an estimate of this background.
Background estimates are validated in signal-depleted control regions that are determined by similar selection criteria used to define the signal region, but where a re-quirement may be inverted or modified. For the dom-inant ZZ → `+`−νν background, estimated with MC¯
simulation, the control region probes four-lepton events and is defined by the presence of two pairs of same-flavor, oppositely-charged leptons for which the invariant mass of the pairs is within the Z boson mass window. For the subdominant W Z → `ν`+`− background, the
con-trol region is characterized by three leptons: a pair of same-flavor, oppositely-charged leptons for which the in-variant mass is within the Z boson mass window, an ad-ditional electron or muon, and a reconstructed ETmiss> 80 GeV. For the minor W W and top-quark background, de-rived from a data-driven technique, events containing an electron and a muon (eµ) with opposite charge are used. The expected signal region event yield is obtained from correction factors that account for the relative dilepton reconstruction efficiencies and the ratio of same-flavor lepton production to mixed flavor. The predicted yields from MC simulation are consistent with the data-driven estimates and in all cases are consistent with the control region yields observed in data.
Samples of pp→ Zχ ¯χ signals are generated using Mad-Graph 5 1.5.2 [33] with parton showering and hadroniza-tion modeled by PYTHIA 8.170 using the MSTW2008 leading-order PDFs [34] and the AU2 tune. EFT op-erators D1 (scalar, spin independent), D5 (vector, spin independent), and D9 (tensor, spin-dependent), follow-ing the definitions of Ref. [10], are representative of the full set of operators in which the Z boson is emitted as ISR. Similar Emiss
T distributions result from all the
oper-ators within each of the three types: scalar, vector, and tensor.
Two examples of the dimension-7 ZZχχ operator mix-tures are considered: one in which the Zγ∗contribution is
negligible and one in which it is maximal. Therefore the dimension-7 operators are referred to as
ZZχχ-maximal-γ∗ and ZZχχ-no-γ∗ while the dimension-5 operator is referred to simply as ZZχχ. Cross sections for a few representative operators and for the scalar-mediator the-ory with representative coupling constant, f = 6, and mη = 1 TeV are given in Table I.
TABLE I. The power dependence of 1/M?for the EFT and
the cross sections of WIMP production in association with an on-shell Z boson for various EFT operators and the scalar-mediator theory are shown. For the calculation of the
pro-duction cross section, M? is taken to be 1 TeV for the EFT
operators. The coupling constant of the scalar-mediator
the-ory, f , is taken to be 6 and the mass of the mediator, mη, is
1 TeV.
D5 D9 ZZχχ
max. γ∗
Scalar mediator
mχ [GeV] Cross sections [fb]
1 7.2 130 3.1 830 10 7.1 120 3.1 810 200 5.6 89 2.0 300 400 3.1 47 0.83 70 1000 0.25 3.4 0.023 -M?−1power 2 2 3
-Samples of pp→ Zχ ¯χ events are propagated through the ATLAS detector using the full simulation of the ID and muon trackers and the parameterized simulation of the calorimeter [30], tuned to full simulation and data. The shapes of the simulated Emiss
T distributions for the
signal operators are shown in Fig. 2 compared to the dominant SM background process ZZ→ `+`−νν.¯
Contributions to the systematic uncertainty of the ex-pected SM backgrounds are due largely to experimental sources affecting the Emiss
T measurement and to the
effi-ciencies for the reconstruction and identification of elec-trons and muons. For example, when ETmiss>120 GeV, the experimental systematic uncertainty for the ZZ back-ground is dominated by the jet–energy scale (1.7% and 2.3% for electron and muon final states, respectively) and the electron and muon momentum scale (2.3% and 0.8%, respectively). Smaller systematic uncertainties are asso-ciated with the Emiss
T measurement and with the
efficien-cies for the reconstruction and identification of electrons and muons.
For the dominant background, ZZ → `+`−νν, de-¯
termined from simulated samples, systematic theoretical uncertainties are derived from the generator differences, QCD factorization and renormalization scales, and PDF modeling. The largest theoretical uncertainty, the gener-ator difference, is evaluated as the difference in yields cal-culated from samples simulated with SHERPA 1.4.1 [35] and POWHEG BOX. The systematic uncertainties asso-ciated with the ZZ background are summarized in Ta-ble II for each signal region. The luminosity uncertainty is 2.8% and is derived from beam-separation scans per-formed following the procedure described in Ref. [36].
The expected background and observed yields are re-ported in Table III. Figure 3 shows the Emiss
T distribution [GeV] T miss E 0 200 400 600 800 1000 1200 [1/50 GeV] T miss 1/N dN/E -3 10 -2 10 -1 10 1 D1 D5 χ χ ZZ γ max. χ χ ZZ Mediator η ν ν ll → ZZ Simulation ATLAS =200 GeV χ m s=8 TeV
FIG. 2. Shape of the Emiss
T distribution in simulated samples
of ZZ background, effective field theories of dark-matter in-teraction with a q ¯q initial state (D1, D5, and D9 [10]) and
in-teraction with a Z/γ∗intermediate state [13], and the
scalar-mediator theory. The shapes of ZZχχ-no-γ∗ and
ZZχχ-maximal-γ∗ are similar, as are the shapes of D9 and the
dimension-5 ZZχχ EFT, so only one of each is plotted. Each distribution is normalized to unit area. The mass of the scalar
mediator, mη is 1 TeV, and the dark-matter particle mass is
mχ= 200 GeV.
TABLE II. Summary of the systematic uncertainties for the
largest background process: (ZZ → `+`−¯νν). Statistical
un-certainties are from MC simulation sample size.
Uncertainty Source E miss T threshold [GeV] 150 250 350 450 Statistical [%] 2 6 13 24 Experimental [%] 3 6 9 8 Theoretical [%] 36 37 37 38 Luminosity [%] 3 3 3 3 Total [%] 36 38 40 46
after applying all selection requirements other than the Emiss
T thresholds for the observed data, the expected SM
backgrounds, and the hypothetical pp→ Zχ ¯χ signals for various values of the mass scale.
No excess over the background is observed. Upper limits on the number of events from a new source are calculated employing a frequentist method with a pro-file likelihood ratio [37] using the unbinned yields and uncertainties from each ETmiss region. The likelihood is a product of a Poisson distribution and Gaussian con-straints for the total signal and background systematic uncertainties. The mean of the Poisson distribution, for either signal and background or background alone, in-cludes the effect of varying the nuisance parameters.
The Emiss
T region with the best expected limit is used to
calculate the observed limit for each operator and mass point. Limits on the cross section for pp → Zχ ¯χ pro-duction are translated into limits on the mass scale of
TABLE III. Observed yields and expected SM backgrounds in each signal region. Statistical, systematic, and luminosity uncertainties are added in quadrature to give the total back-ground estimate and uncertainties.
Process E miss T threshold [GeV] 150 250 350 450 ZZ 41 ± 15 6.4 ± 2.4 1.3 ± 0.5 0.3 ± 0.1 W Z 8.0 ± 3.1 0.8 ± 0.4 0.2 ± 0.1 0.1 ± 0.1 W W , t¯t, Z → τ+τ− 1.9 ± 1.4 0+0.7−0.0 0 +0.7 −0.0 0 +0.7 −0.0 Z+jets 0.1 ± 0.1 – – – W +jets 0.5 ± 0.3 – – – Total 52 ± 18 7.2 ± 2.8 1.4 ± 0.9 0.4+0.7−0.4 Data 45 3 0 0 [GeV] miss T E Entries / 50 GeV -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 ATLAS =200 GeV χ m -1 L=20.3 fb
∫
s=8 TeV =0.050 TeV * D1, M =0.7 TeV * , M γ max. χ χ ZZ =1 TeV, f=6 η Mediator, m η Data W/Z+jets WW/Top quark WZ ν ν ll → ZZ Systematic Unc. [GeV] miss T E 0 50 100 150 200 250 300 350 400 450 500 Data/MC 0.6 0.81 1.2 1.4FIG. 3. ETmiss distributions after all event selections other
than the Emiss
T thresholds for the observed data; the
ex-pected SM backgrounds taken from simulation; the
hypothet-ical pp → Zχ ¯χ signals for various values of the mass scale,
M?. The dark-matter particle mass is mχ = 200 GeV. The
last bin contains the events with EmissT > 450 GeV. The ratio of data to simulated backgrounds is also shown. The band shows the experimental systematic uncertainties on the ratio.
the effective operators mediating the interaction of the dark-matter particles with the initial state quarks or the Z/γ∗ intermediate state. This is done using the relation, Mlimit ? = M generator ? × σgenerator/σlimit 1/2p , where the superscript indicates whether the parameter is a mea-sured limit or calculated using MC simulation, and p indicates the power of (1/M?) appearing in the EFT
Lagrangian. These limits are shown in Fig. 4. They are also translated into limits on the χ–nucleon scatter-ing cross section usscatter-ing the method in Ref. [10] for sev-eral effective operators mediating the interaction of the dark-matter particles with the q ¯q initial state, and are compared with other experimental results described in Refs. [38–46]. These limits, shown at 90% C.L. in Figs. 5 and 6, are less stringent than the lower limits for dark-matter candidates recoiling against a W or Z boson de-caying to hadrons reported in Ref [8]. The limits degrade
[GeV] χ m 0 200 400 600 800 1000 [GeV] * M 2 10 3 10 4 10 D1 D5 D9 χ χ ZZ γ max. χ χ ZZ γ no χ χ ZZ ATLAS
∫
-1 L=20.3 fb =8 TeV 90% C.L. sFIG. 4. Observed 90% C.L. lower limits on the mass scale,
M?, of considered effective field theories as a function of mχ. For each operator, the values below the corresponding line are excluded.
by 13-23% at 95% C.L., depending on the ETmiss signal region under consideration.
A lower limit on the coupling, f , of the scalar-mediator model is also calculated based on the WIMP relic abun-dance in Ref. [47] and the expression for the freeze-out temperature from Ref. [48]. If the relic abundance lower limit calculated at some mass point (mχ, mη) is greater
than the upper limit measured in this analysis, that mass point is excluded. Limits on the cross section times branching ratio in the scalar-mediator model are shown in Fig. 7, and limits on f as a function of mediator mass mηand mχ, as well as the exclusion region, are shown in
Fig. 8.
Fiducial cross-section limits are calculated in each sig-nal region to complement the limits on specific mod-els. The reconstruction efficiency is defined as the ratio of reconstructed events satisfying all the selection crite-ria to the number of generated events within a fiducial region characterized by selection requirements at par-ticle level identical to all the requirements on the re-constructed dilepton+Emiss
T system, where the ETmiss is
calculated summing over all neutrinos and dark-matter particles. The acceptance is the ratio of the number of generated events within the fiducial region to the to-tal number of generated events. In addition, the gen-erated leptons are required to be separated by at least ∆R = 0.2 to match the isolation requirement. The recon-struction efficiency ranges from (56.9±0.9)% for ZZχχ-max.-γ∗ at mχ = 1000 GeV to (77.9±3.1)% for D5 at
mχ = 400 GeV. The lowest value of the reconstruction
efficiency is used to calculate the fiducial cross-section limits in order to be conservative. The corresponding acceptances for the previous operators are (30.3±0.5)% and (2.6±0.2)%, respectively, where the uncertainties are purely statistical and the variation in the acceptance arises primarily from the different Emiss
[GeV] χ m 1 10 102 103 ] 2 section [cm -nucleon cross χ -43 10 -42 10 -41 10 -40 10 -39 10 -38 10 -37 10 -36 10 -35 10 -34 10 -33 10 -32 10 -31 10 spin dependent D9 ) χ χ
D9 ATLAS 8 TeV W/Z had.( )
χ χ
D9 ATLAS 7 TeV jet( COUPP 2012 SIMPLE 2011 Picasso 2012 -W + IceCube W b IceCube b ATLAS
∫
-1 L=20.3 fb =8 TeV 90% C.L. sFIG. 5. Observed 90% C.L. upper limits on the χ–nucleon
scattering cross section as a function of mχ for the
spin-dependent D9 effective operators mediating the interaction of the dark-matter particles with the q ¯q initial state. The limits are compared with results from the published ATLAS hadron-ically decaying W/Z [8] and j + χχ [4] searches, COUPP [38], SIMPLE [39], PICASSO [40], and IceCube [41]. These limits are shown as they are given in the corresponding publications and are only shown for comparison with the results from this analysis, since they are obtained assuming the interactions are mediated by operators different from those used for the ATLAS limits. [GeV] χ m 1 10 102 103 ] 2 section [cm -nucleon cross χ -46 10 -45 10 -44 10 -43 10 -42 10 -41 10 -40 10 -39 10 -38 10 -37 10 -36 10 -35 10 -34 10 -33 10 -32 10 -31 10 -30 10 spin independent D1 D5 ) χ χ
D5 ATLAS 8 TeV W/Z had.( )
χ χ
D1 ATLAS 7 TeV jet( )
χ χ
D5 ATLAS 7 TeV jet( CoGeNT 2010 CDMS 2014 XENON100 2012 LUX 2014 ATLAS
∫
-1 L=20.3 fb =8 TeV 90% C.L. sFIG. 6. Observed 90% C.L. upper limits on the χ–
nucleon scattering cross section as a function of mχfor
spin-independent effective operators mediating the interaction of the dark-matter particles with the q ¯q initial state. The limits are compared with results from the published ATLAS hadron-ically decaying W/Z [8] and j + χχ [4] searches, CoGeNT [42], XENON100 [43], CDMS [44, 45], and LUX [46]. These limits are shown as they are given in the corresponding publications and are only shown for comparison with the results from this analysis, since they are obtained assuming the interactions are mediated by operators different from those used for the ATLAS limits. [GeV] χ m 0 50 100 150 200 250 300 350 400 450 500 ) [fb] χχ ll → χχ Z → (pp σ -3 10 -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 =1000 GeV η Observed limit m =1000 GeV η Expected limit m =1000 GeV f=1 η m =1000 GeV f=4 η m =1000 GeV f=6 η m 68% C.L. 95% C.L. ATLAS =8 TeV s -1 L=20.3 fb
∫
FIG. 7. Observed 95% C.L. upper limits on the cross section
multiplied by the branching ratio of Z → `+`−
of the
scalar-mediator theory as a function of mχ. The observed
cross-section limit for a scalar-mediator mass, mη, of 1000 GeV is
shown. Production cross sections predicted from theory are
shown for mη= 1 TeV and for different values of the coupling
strength, f . [GeV] χ m 100 200 300 400 500 600 700 800 900 1000 [GeV]η m 200 300 400 500 600 700 800 900 1000 1100 1200 95% C.L. on coupling f 0 2 4 6 8 10 12 ATLAS =8 TeV s -1 L=20.3 fb
∫
FIG. 8. Observed 95% C.L. upper limits on the coupling
constant, f , of the scalar-mediator theory as a function of
mχ and the mediator mass, mη. The cross-hatching shows
the theoretically accessible region outside the range covered by this analysis. The white region is phase space beyond the model’s validity. In the excluded region in the upper left-hand corner, demarcated by the black line, the lower limit on f from the relic abundance calculations based on [47, 48] is greater than the upper limit measured in this analysis.
operators. The observed and expected upper limits on the fiducial cross section are given in Table IV.
In conclusion, a search for the production of dark-matter particles in association with a Z boson that decays leptonically in 20.3 fb−1 of pp collisions at √s =8 TeV is presented for three EFT operators where the dark matter interacts directly with quarks: D1, D5, and D9. The new limits complement the limits reported
TABLE IV. The observed and expected upper limits on the fiducial cross section at 95% C.L. for each signal region.
ETmissthreshold [GeV]
150 250 350 450
Fiducial cross section [fb]
Expected Limits [fb] 3.0 0.73 0.36 0.27
Observed Limits [fb] 2.7 0.57 0.27 0.26
in other LHC analyses. The results are also interpreted using EFT models where the dark matter interacts di-rectly with pairs of electroweak bosons. Initial limits are set on the mass scale of the ZZχχ EFT operators de-scribing the interaction between dark matter and a Z or γ∗ intermediate state. Upper limits are also set on the scattering cross section of dark-matter particles with nu-cleons for effective operators mediating the interaction of dark-matter particles with a q ¯q initial state, and on a model in which the interaction between the dark matter and Z/γ∗is mediated by a scalar particle.
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada;
CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; BRF and RCN, Norway; MNiSW and NCN, Poland; GRICES and FCT, Portugal; MNE/IFA, Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MIZˇS, Slove-nia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Tai-wan; TAEK, Turkey; STFC, the Royal Society and Lev-erhulme Trust, United Kingdom; DOE and NSF, United States of America.
The crucial computing support from all WLCG part-ners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Tai-wan), RAL (UK) and BNL (USA) and in the Tier-2 fa-cilities worldwide.
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F. Deliot137, M. Deliyergiyev74, A. Dell’Acqua30, L. Dell’Asta22, M. Della Pietra103a,h, D. della Volpe49,
M. Delmastro5, P.A. Delsart55, C. Deluca106, S. Demers177, M. Demichev64, A. Demilly79, S.P. Denisov129,
D. Derendarz39, J.E. Derkaoui136d, F. Derue79, P. Dervan73, K. Desch21, C. Deterre42, P.O. Deviveiros106, A. Dewhurst130, S. Dhaliwal106, A. Di Ciaccio134a,134b, L. Di Ciaccio5, A. Di Domenico133a,133b,
C. Di Donato103a,103b, A. Di Girolamo30, B. Di Girolamo30, A. Di Mattia153, B. Di Micco135a,135b, R. Di Nardo47,
A. Di Simone48, R. Di Sipio20a,20b, D. Di Valentino29, M.A. Diaz32a, E.B. Diehl88, J. Dietrich42, T.A. Dietzsch58a,
S. Diglio87, A. Dimitrievska13a, J. Dingfelder21, C. Dionisi133a,133b, P. Dita26a, S. Dita26a, F. Dittus30, F. Djama84,
T. Djobava51b, M.A.B. do Vale24c, A. Do Valle Wemans125a,125g, T.K.O. Doan5, D. Dobos30, E. Dobson77, C. Doglioni49, T. Doherty53, T. Dohmae156, J. Dolejsi128, Z. Dolezal128, B.A. Dolgoshein97,∗, M. Donadelli24d, S. Donati123a,123b, P. Dondero120a,120b, J. Donini34, J. Dopke30, A. Doria103a, A. Dos Anjos174, A. Dotti123a,123b,
M.T. Dova70, A.T. Doyle53, M. Dris10, J. Dubbert88, S. Dube15, E. Dubreuil34, E. Duchovni173, G. Duckeck99,
O.A. Ducu26a, D. Duda176, A. Dudarev30, F. Dudziak63, L. Duflot116, L. Duguid76, M. D¨uhrssen30, M. Dunford58a,
H. Duran Yildiz4a, M. D¨uren52, M. Dwuznik38a, M. Dyndal38a, J. Ebke99, W. Edson2, N.C. Edwards46,
W. Ehrenfeld21, T. Eifert144, G. Eigen14, K. Einsweiler15, T. Ekelof167, M. El Kacimi136c, M. Ellert167, S. Elles5, F. Ellinghaus82, K. Ellis75, N. Ellis30, J. Elmsheuser99, M. Elsing30, D. Emeliyanov130, Y. Enari156, O.C. Endner82,
M. Endo117, R. Engelmann149, J. Erdmann177, A. Ereditato17, D. Eriksson147a, G. Ernis176, J. Ernst2, M. Ernst25,
J. Ernwein137, D. Errede166, S. Errede166, E. Ertel82, M. Escalier116, H. Esch43, C. Escobar124, B. Esposito47,
A.I. Etienvre137, E. Etzion154, H. Evans60, L. Fabbri20a,20b, G. Facini30, R.M. Fakhrutdinov129, S. Falciano133a,
Y. Fang33a, M. Fanti90a,90b, A. Farbin8, A. Farilla135a, T. Farooque12, S. Farrell164, S.M. Farrington171, P. Farthouat30, F. Fassi168, P. Fassnacht30, D. Fassouliotis9, A. Favareto50a,50b, L. Fayard116, P. Federic145a, O.L. Fedin122, W. Fedorko169, M. Fehling-Kaschek48, S. Feigl30, L. Feligioni84, C. Feng33d, E.J. Feng6, H. Feng88,
P. Ferrari106, R. Ferrari120a, D.E. Ferreira de Lima53, A. Ferrer168, D. Ferrere49, C. Ferretti88, A. Ferretto Parodi50a,50b, M. Fiascaris31, F. Fiedler82, A. Filipˇciˇc74, M. Filipuzzi42, F. Filthaut105, M. Fincke-Keeler170, K.D. Finelli151, M.C.N. Fiolhais125a,125c, L. Fiorini168, A. Firan40, J. Fischer176,
M.J. Fisher110, W.C. Fisher89, E.A. Fitzgerald23, M. Flechl48, I. Fleck142, P. Fleischmann175, S. Fleischmann176,
G.T. Fletcher140, G. Fletcher75, T. Flick176, A. Floderus80, L.R. Flores Castillo174, A.C. Florez Bustos160b,
M.J. Flowerdew100, A. Formica137, A. Forti83, D. Fortin160a, D. Fournier116, H. Fox71, S. Fracchia12,
P. Francavilla12, M. Franchini20a,20b, S. Franchino30, D. Francis30, M. Franklin57, S. Franz61, M. Fraternali120a,120b, S.T. French28, C. Friedrich42, F. Friedrich44, D. Froidevaux30, J.A. Frost28, C. Fukunaga157,
E. Fullana Torregrosa82, B.G. Fulsom144, J. Fuster168, C. Gabaldon55, O. Gabizon173, A. Gabrielli20a,20b,
A. Gabrielli133a,133b, S. Gadatsch106, S. Gadomski49, G. Gagliardi50a,50b, P. Gagnon60, C. Galea105,
B. Galhardo125a,125c, E.J. Gallas119, V. Gallo17, B.J. Gallop130, P. Gallus127, G. Galster36, K.K. Gan110,
R.P. Gandrajula62, J. Gao33b,g, Y.S. Gao144,e, F.M. Garay Walls46, F. Garberson177, C. Garc´ıa168, J.E. Garc´ıa Navarro168, M. Garcia-Sciveres15, R.W. Gardner31, N. Garelli144, V. Garonne30, C. Gatti47, G. Gaudio120a, B. Gaur142, L. Gauthier94, P. Gauzzi133a,133b, I.L. Gavrilenko95, C. Gay169, G. Gaycken21,
E.N. Gazis10, P. Ge33d,j, Z. Gecse169, C.N.P. Gee130, D.A.A. Geerts106, Ch. Geich-Gimbel21, K. Gellerstedt147a,147b,
C. Gemme50a, A. Gemmell53, M.H. Genest55, S. Gentile133a,133b, M. George54, S. George76, D. Gerbaudo164,
A. Gershon154, H. Ghazlane136b, N. Ghodbane34, B. Giacobbe20a, S. Giagu133a,133b, V. Giangiobbe12,
P. Giannetti123a,123b, F. Gianotti30, B. Gibbard25, S.M. Gibson76, M. Gilchriese15, T.P.S. Gillam28, D. Gillberg30, A.R. Gillman130, D.M. Gingrich3,d, N. Giokaris9, M.P. Giordani165a,165c, R. Giordano103a,103b, F.M. Giorgi16,
P.F. Giraud137, D. Giugni90a, C. Giuliani48, M. Giunta94, B.K. Gjelsten118, I. Gkialas155,k, L.K. Gladilin98,
C. Glasman81, J. Glatzer30, A. Glazov42, G.L. Glonti64, M. Goblirsch-Kolb100, J.R. Goddard75, J. Godfrey143,
J. Godlewski30, C. Goeringer82, S. Goldfarb88, T. Golling177, D. Golubkov129, A. Gomes125a,125b,125d,
L.S. Gomez Fajardo42, R. Gon¸calo76, J. Goncalves Pinto Firmino Da Costa42, L. Gonella21,
S. Gonz´alez de la Hoz168, G. Gonzalez Parra12, M.L. Gonzalez Silva27, S. Gonzalez-Sevilla49, L. Goossens30,
P.A. Gorbounov96, H.A. Gordon25, I. Gorelov104, G. Gorfine176, B. Gorini30, E. Gorini72a,72b, A. Goriˇsek74,
E. Gornicki39, A.T. Goshaw6, C. G¨ossling43, M.I. Gostkin64, M. Gouighri136a, D. Goujdami136c, M.P. Goulette49,
A.G. Goussiou139, C. Goy5, S. Gozpinar23, H.M.X. Grabas137, L. Graber54, I. Grabowska-Bold38a,
P. Grafstr¨om20a,20b, K-J. Grahn42, J. Gramling49, E. Gramstad118, F. Grancagnolo72a, S. Grancagnolo16, V. Grassi149, V. Gratchev122, H.M. Gray30, E. Graziani135a, O.G. Grebenyuk122, Z.D. Greenwood78,l, K. Gregersen36, I.M. Gregor42, P. Grenier144, J. Griffiths8, N. Grigalashvili64, A.A. Grillo138, K. Grimm71,
S. Grinstein12,m, Ph. Gris34, Y.V. Grishkevich98, J.-F. Grivaz116, J.P. Grohs44, A. Grohsjean42, E. Gross173,
J. Grosse-Knetter54, G.C. Grossi134a,134b, J. Groth-Jensen173, Z.J. Grout150, K. Grybel142, L. Guan33b,
F. Guescini49, D. Guest177, O. Gueta154, C. Guicheney34, E. Guido50a,50b, T. Guillemin116, S. Guindon2, U. Gul53, C. Gumpert44, J. Gunther127, J. Guo35, S. Gupta119, P. Gutierrez112, N.G. Gutierrez Ortiz53, C. Gutschow77, N. Guttman154, C. Guyot137, C. Gwenlan119, C.B. Gwilliam73, A. Haas109, C. Haber15, H.K. Hadavand8,
N. Haddad136e, P. Haefner21, S. Hageboeck21, Z. Hajduk39, H. Hakobyan178, M. Haleem42, D. Hall119,
G. Halladjian89, K. Hamacher176, P. Hamal114, K. Hamano87, M. Hamer54, A. Hamilton146a, S. Hamilton162,
P.G. Hamnett42, L. Han33b, K. Hanagaki117, K. Hanawa156, M. Hance15, P. Hanke58a, J.R. Hansen36,
J.B. Hansen36, J.D. Hansen36, P.H. Hansen36, K. Hara161, A.S. Hard174, T. Harenberg176, S. Harkusha91, D. Harper88, R.D. Harrington46, O.M. Harris139, P.F. Harrison171, F. Hartjes106, A. Harvey56, S. Hasegawa102, Y. Hasegawa141, S. Hassani137, S. Haug17, M. Hauschild30, R. Hauser89, M. Havranek126, C.M. Hawkes18,
R.J. Hawkings30, A.D. Hawkins80, T. Hayashi161, D. Hayden89, C.P. Hays119, H.S. Hayward73, S.J. Haywood130,
S.J. Head18, T. Heck82, V. Hedberg80, L. Heelan8, S. Heim121, T. Heim176, B. Heinemann15, L. Heinrich109,
S. Heisterkamp36, J. Hejbal126, L. Helary22, C. Heller99, M. Heller30, S. Hellman147a,147b, D. Hellmich21, C. Helsens30, J. Henderson119, R.C.W. Henderson71, C. Hengler42, A. Henrichs177, A.M. Henriques Correia30, S. Henrot-Versille116, C. Hensel54, G.H. Herbert16, Y. Hern´andez Jim´enez168, R. Herrberg-Schubert16, G. Herten48,
R. Hertenberger99, L. Hervas30, G.G. Hesketh77, N.P. Hessey106, R. Hickling75, E. Hig´on-Rodriguez168, J.C. Hill28,
K.H. Hiller42, S. Hillert21, S.J. Hillier18, I. Hinchliffe15, E. Hines121, M. Hirose117, D. Hirschbuehl176, J. Hobbs149,
N. Hod106, M.C. Hodgkinson140, P. Hodgson140, A. Hoecker30, M.R. Hoeferkamp104, J. Hoffman40, D. Hoffmann84,
J.I. Hofmann58a, M. Hohlfeld82, T.R. Holmes15, T.M. Hong121, L. Hooft van Huysduynen109, J-Y. Hostachy55, S. Hou152, A. Hoummada136a, J. Howard119, J. Howarth42, M. Hrabovsky114, I. Hristova16, J. Hrivnac116,
T. Hryn’ova5, P.J. Hsu82, S.-C. Hsu139, D. Hu35, X. Hu25, Y. Huang146c, Z. Hubacek30, F. Hubaut84, F. Huegging21,
T.B. Huffman119, E.W. Hughes35, G. Hughes71, M. Huhtinen30, T.A. H¨ulsing82, M. Hurwitz15, N. Huseynov64,b,
J. Huston89, J. Huth57, G. Iacobucci49, G. Iakovidis10, I. Ibragimov142, L. Iconomidou-Fayard116, J. Idarraga116,
E. Ideal177, P. Iengo103a, O. Igonkina106, T. Iizawa172, Y. Ikegami65, K. Ikematsu142, M. Ikeno65, D. Iliadis155, N. Ilic159, Y. Inamaru66, T. Ince100, P. Ioannou9, M. Iodice135a, K. Iordanidou9, V. Ippolito57, A. Irles Quiles168, C. Isaksson167, M. Ishino67, M. Ishitsuka158, R. Ishmukhametov110, C. Issever119, S. Istin19a, J.M. Iturbe Ponce83,
![FIG. 1. The diagrams showing different types of pp → χ¯ χ+Z production modes considered in this analysis [13]](https://thumb-eu.123doks.com/thumbv2/123dok_br/16051539.1105574/2.918.482.829.321.492/diagrams-showing-different-types-production-modes-considered-analysis.webp)
