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Physics Letters B 763 (2016) 251–268
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Search for dark matter produced in association with a hadronically
decaying vector boson in pp collisions at
√
s =13 TeV with the ATLAS
detector
.The ATLAS Collaboration
a r t i c l e i n f o a b s t r a c t
Article history:
Received
9 August 2016
Received
in revised form 9 October 2016
Accepted
17 October 2016
Available
online 20 October 2016
Editor:
W.-D. Schlatter
A search is presented for dark matter produced in association with a hadronically decaying W or Z
boson
using 3.2 fb
−1
of pp collisions at
√
s = 13 TeV recorded by the ATLAS detector at the Large
Hadron Collider. Events with a hadronic jet compatible with a W or Z boson and with large missing
transverse momentum are analysed. The data are consistent with the Standard Model predictions and
are interpreted in terms of both an effective field theory and a simplified model containing dark matter.
© 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
Dark matter is the dominant component of matter in the uni-
verse,
but its particle nature remains a mystery. Searches for a
weakly interacting massive particle (WIMP), denoted by χ , and for
interactions between χ and Standard Model (SM) particles are a
central component of the current set of dark-matter experiments.
At
particle colliders, dark-matter particles may be produced
in pairs via some unknown intermediate state. While in many
models direct detection experiments have the greatest sensitivity
for dark-matter masses m
χ
between 10 and 100 GeV, searches
for dark matter at particle colliders are most powerful for lower
masses [1–3]. The final-state WIMPs are not directly detectable,
but their presence can be inferred from the recoil against a visible
particle [1]. Two example processes are shown in Fig. 1.
The
Tevatron and LHC collaborations have reported limits on
the cross section of p
¯
p → χ
¯
χ + X and pp → χ
¯
χ + X, respec-
tively,
where X is a hadronic jet [1–3], aphoton (γ ) [4,5], a W /Z
boson [6,7],
or a Higgs boson [8,9]. In many cases, results are re-
ported
in terms of limits on the parameters of an effective field
theory (EFT) formulated as a four-point contact interaction [10–18]
between
quarks and WIMPs. For such models, the strongest lim-
its
come from data in which the recoiling object is a jet. In other
models, however, the interaction is between dark matter and vec-
tor
bosons [19], such that the primary discovery mode would be in
final states such as those analysed here, where the recoiling object
is a W or Z boson.
E-mail address: atlas.publications@cern.ch.
In this Letter, asearch is reported for the production of a W
or
Z boson decaying hadronically (to q
¯
q
or q
¯
q, respectively) and
reconstructed as a single massive jet in association with large
missing transverse momentum from the undetected χ
¯
χ parti-
cles
in data collected by the ATLAS detector from pp collisions
with centre-of-mass energy
√
s = 13 TeV. This search is sensitive
to WIMP pair production, as well as to other dark-matter-related
models which predict invisible Higgs boson decays (WH or ZH
production
with H → χ
¯
χ ).
The ATLAS detector [20] at the LHC covers the pseudorapidity
1
range |η| < 4.9 and the full azimuthal angle φ. It consists of an
inner tracking detector surrounded by a superconducting solenoid,
electromagnetic and hadronic calorimeters, and an external muon
spectrometer incorporating large superconducting toroidal mag-
nets.
Atwo-level trigger system is used to select interesting events
to be recorded for subsequent offline analysis. Only data for which
beams were stable and all subsystems described above were oper-
ational
are used. Applying these requirements to pp collision data,
recorded during the 2015 LHC run, results in a data sample with a
time-integrated luminosity of 3.2fb
−1
. The systematic uncertainty
1
ATLAS uses a right-handed coordinate system with its origin at the nominal in-
teraction
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. Polar coordinates (r, φ) are used in the transverse (x, y) plane, φ being the
azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of
the polar angle θ as η =− lntan(θ/2).
http://dx.doi.org/10.1016/j.physletb.2016.10.042
0370-2693/
© 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
252 The ATLAS Collaboration / Physics Letters B 763 (2016) 251–268
Fig. 1. Pair production of WIMPs (χ
¯
χ ) in proton–proton collisions at the LHC in association with a vector boson (V , meaning W or Z ) via two hypothetical processes:
(a) production via an effective VVχχ interaction or (b) via a simplified model which includes an s-channel mediator.
of 2.1% in the luminosity is derived following the same methodol-
ogy
as that detailed in Ref. [21].
Three
non-exclusive categories of jet candidates are built, each
using the anti-k
⊥
clustering algorithm [22]. Two categories use
clusters of energy deposits in calorimeter cells seeded by those
with energies significantly above the measured noise and cali-
brated
at the hadronic energy scale [25]. They are distinguished by
their radius parameters; jets with radius parameter of 1.0 (0.4) are
referred to as large-R jets (narrow jets). Large and narrow jets can
share a fraction of their energy deposits. Athird type of jet candi-
date
is reconstructed from inner-detector tracks using the anti-k
⊥
algorithm with R = 0.2, referred to as track jets. Large-R jets are
trimmed [26] to remove energy deposited by pile-up jets, the un-
derlying
event, and soft radiation. In this process, the constituents
of large-R jets are reclustered using the k
⊥
algorithm [23,24] with
a distance parameter of 0.2, and subjets with transverse momen-
tum
p
T
less than 5% of the large-R jet p
T
are removed. Large-R
jets
are required to satisfy p
T
> 200 GeV and |η| < 2.0. These
large-R jets are intended to capture the hadronic products of both
quarks from the decay of a W or Z boson, while the narrow jets
and track jets are helpful in background suppression. The internal
structure of the large-R jet is characterized in terms of two quanti-
ties:
D
2
[27,28], which identifies jets with two distinct concentra-
tions
of energy [29,30], and m
jet
, which is the calculated invariant
mass of the jet. Narrow jets are required to satisfy p
T
> 20 GeV for
|η| < 2.5or p
T
> 30 GeV for 2.5 < |η| < 4.5. Track jets are required
to satisfy p
T
> 10 GeV and |η| < 2.5. For both the large-R and nar-
row
jets, jet momenta are calculated by performing a four-vector
sum over these component clusters, treating each topological clus-
ter [25] as
an (E,
p ) four-vector with zero mass, and are calibrated
to the hadronic scale. For narrow jets, the direction of
p is given by
the line joining the reconstructed vertex with the barycentre of the
energy cluster. The missing transverse momentum E
miss
T
is calcu-
lated
as the negative of the vector sum of the transverse momenta
of reconstructed jets, leptons, and those tracks which are associ-
ated
with the reconstructed vertex but not with any jet or lepton.
Aclosely related quantity, E
miss
T
,noμ
, is calculated in the same way but
excluding reconstructed muons. Athird variant, p
miss
T
, is the miss-
ing
transverse momentum measured using inner detector tracks.
The magnitudes of the three missing-transverse-momentum vari-
ants
are denoted by E
miss
T
, E
miss
T
,noμ
, and p
miss
T
, respectively. Electrons,
muons, jets, and E
miss
T
are reconstructed as described in Refs. [25,
31–33],
respectively.
Candidate
signal events are selected by an inclusive E
miss
T
trigger that is more than 99% efficient for events with E
miss
T
>
200 GeV. Events triggered by detector noise and non-collision
backgrounds are rejected as described in Ref. [34]. In addition,
events are required to satisfy the requirements of E
miss
T
> 250 GeV,
no reconstructed electrons or muons, and at least one large-R
jet
with p
T
> 200 GeV, |η| < 2.0, m
jet
and D
2
consistent with a
W or Z boson decay as in Ref. [35]. To further suppress back-
grounds
from multijet and t
¯
t production, events are required to
satisfy p
miss
T
> 30 GeV, a minimum azimuthal angular distance,
φ, of 0.6 between the E
miss
T
and the nearest narrow jet, and
φ(E
miss
T
, p
miss
T
) < π/2. Within a fiducial volume defined at par-
ton
level by similar selection requirements (except those on D
2
and p
miss
T
), the reconstruction efficiency for the signal models de-
scribed
above varies from 38% to 49%.
The
dominant source of background events is Z → ν
¯
ν produc-
tion
in association with jets. A secondary contribution comes from
the production of jets in association with a leptonically decaying
W or Z boson in which the charged leptons are not identified
or the τ leptons decay hadronically. The third major background
contribution comes from top-quark pair production. The kinematic
distributions of these three largest backgrounds are estimated us-
ing
simulated event samples but the normalization is determined
using control regions where the dark-matter signal is expected to
be negligible. Each control region requires E
miss
T
> 200 GeV and
p
miss
T
> 30 GeV as well as one large-R jet satisfying the substruc-
ture
requirement on D
2
as applied in the signal region. The Z
boson
control region requires exactly two muons with dimuon
invariant mass 66 < m
μμ
< 116 GeV. The W boson (top quark)
control region requires exactly one muon, and zero (at least one)
b-tagged track jet not associated with the large-R jet. Validation
of the reconstruction of hadronic W boson decays with large-R
jets
is performed in the top-quark control region, as shown in
Fig. 2, which also presents the distribution of the D
2
substructure
variable. Other sources of background are diboson production and
single-top-quark production. The contribution to the signal region
from multijet production is negligible.
Samples
of simulated W + jets and Z + jets events are gen-
erated
using Sherpa 2.1.1 [36]. Matrix elements are calculated
for up to two partons at next-to-leading order (NLO) and four
partons at leading order (LO) using the Comix [37] and Open-
Loops [38] matrix
element generators and merged with the Sherpa
parton
shower [39] using the ME+PS@NLO prescription [40]. The
CT10 [41] PDF set is used in conjunction with dedicated par-
ton
shower tuning developed by the Sherpa authors. The W /Z
production
rates are normalized to a next-to-next-to-leading or-
der
(NNLO) calculation [42]. The production of t
¯
t and single-top
processes, including s-channel, t-channel and Wt production is
modelled with the Powheg-Box v2 generator [43–45] interfaced to
Pythia6.428 [46].
In these generators the CT10 and CTEQ6L1 [47]
PDF
sets are used, respectively. Top-quark pair production is nor-
malized
to NNLO with next-to-next-to-leading-logarithm correc-
tions [48] in
QCD while single-top processes are normalized at
NLO [49,50] in QCD. The diboson (WW, WZ, ZZ) processes are
simulated using Sherpa 2.1.1 with the CT10 PDF and normalized at
NLO [51,52] in QCD. The multijet process is described using sam-
ples
simulated with Pythia8.186 [53] and the NNPDF2.3LO [54]
PDF
at leading order in QCD; these multijet samples were used
to develop the background estimation strategy but not for the fi-
nal
background prediction.
The ATLAS Collaboration / Physics Letters B 763 (2016) 251–268 253
Fig. 2. Pane (a) Distribution of m
jet
in the data and for the predicted background in the top-quark control region. Pane (b) Distribution of jet substructure variable D
2
in the
data and for the predicted background in events satisfying all signal region requirements other than those on D
2
. Also shown is the distribution for the simplified model
with a vector-boson mediator, scaled by a factor of 10
4
for given values of m
χ
and m
med
, the mediator mass. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
Fig. 3. The E
miss
T
,noμ
distribution of the events in the control regions after the profile-likelihood fit to the data under the background-only hypothesis. Pane (a) shows the t
¯
t
control
region, pane (b) shows the Z + jets control region, and pane (c) shows the W + jets control region. The total background prediction before the fit is shown as
a dashed line. The inset at the bottom of each plot shows the ratio of the data to the total post-fit background. The hatched bands represent the total uncertainty in the
background. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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