JHEP07(2017)014
Published for SISSA by Springer
Received: March 5, 2017
Accepted: June 18, 2017
Published: July 5, 2017
Search for dark matter produced with an energetic jet
or a hadronically decaying W or Z boson at
√
s = 13 TeV
The CMS collaboration
E-mail: cms-publication-committee-chair@cern.ch
Abstract: A search for dark matter particles is performed using events with large miss-
ing transverse momentum, at least one energetic jet, and no leptons, in proton-proton
collisions at
√
s = 13 TeV collected with the CMS detector at the LHC. The data sample
corresponds to an integrated luminosity of 12.9 fb
−1
. The search includes events with jets
from the hadronic decays of a W or Z boson. The data are found to be in agreement with
the predicted background contributions from standard mo del processes. The results are
presented in terms of simplified models in which dark matter particles are produced through
interactions involving a vector, axial-vector, scalar, or pseudoscalar mediator. Vector and
axial-vector mediator particles with masses up to 1.95 TeV, and scalar and pseudoscalar
mediator particles with masses up to 100 and 430 GeV respectively, are excluded at 95%
confidence level. The results are also interpreted in terms of the invisible decays of the Higgs
boson, yielding an observed (expected) 95% confidence level upper limit of 0.44 (0.56) on
the corresponding branching fraction. The results of this search provide the strongest con-
straints on the dark matter pair production cross section through vector and axial-vector
mediators at a particle collider. When compared to the direct detection experiments, the
limits obtained from this search provide stronger constraints for dark matter masses less
than 5, 9, and 550 GeV, assuming vector, scalar, and axial-vector mediators, respectively.
The search yields stronger constraints for dark matter masses less than 200 GeV, assuming
a pseudoscalar mediator, when compared to the indirect detection results from Fermi-LAT.
Keywords: Jet substructure, Dark matter, Hadron-Hadron scattering (experiments),
Exotics, Higgs physics
ArXiv ePrint:
1703.01651
Open Access, Copyright CERN,
for the benefit of the CMS Collab oration .
Article funded by SCOAP
3
.
https://doi.org/10.1007/JHEP07(2017)014
JHEP07(2017)014
Contents
1 Introduction
1
2 The CMS detector 3
3 Event simulation 3
4 Event selection 4
5 Background estimation 6
6 Results and interpretation 13
6.1 Dark matter interpretation 13
6.2 Invisible decays of the Higgs boson 18
7 Summary 18
A Supplementary material 23
The CMS collaboration 31
1 Introduction
Astrophysical observations have provided compelling evidence for the existence of dark
matter (DM) in the universe [
1–3]. However, there is no compelling experimental evidence
for non-gravitational interactions between the DM and standard model (SM) particles.
Most current models of DM assume that it consists of weakly interacting massive particles
(WIMPs) [
2]. If such particles exist, direct pair production of WIMPs may occur in TeV-
scale collisions at the CERN LHC [
4]. If DM particles are produced at the LHC, they would
not generate directly observable signals in the detector. However, if they recoil against a jet
radiated from the initial state, they may produce an apparent, large transverse momentum
imbalance in the event. This is termed the ‘monojet’ final state [
5, 6]. The DM particles
may also be produced in association with an electroweak boson, resulting in the ‘mono-V’
signature, where V represents the W or Z boson [
7–9]. Observation of these final states
could be interpreted as evidence for DM particles. Additionally, the Higgs boson [
10–
12] could be a mediator between DM and SM particles [13–17]. The monojet and mono-V
signatures can be used to set a bound on the invisible branching fraction of the Higgs boson.
Several previous searches at the LHC have exploited the mono-V and monojet signa-
tures. Results from earlier searches [18–20] have typically been interpreted using effective
field theories that model contact interactions between the DM and SM particles. Recent
– 1 –
JHEP07(2017)014
q
¯χ
q
¯q
Z
0
χ
q
¯q
¯χ
W/Z
q
q
¯q
Z
0
χ
Figure 1. Leading order Feynman diagrams of monojet (left) and mono-V (right) production and
decay of a spin-1 mediator.
g
g
¯χ
t
t
t
S
t
g
χ
q
¯q
¯χ
¯q
W/Z
W/Z
S
q
χ
Figure 2. Leading order Feynman diagrams of monojet (left) and mono-V (right) production and
decay of a spin-0 mediator.
search results [21–23] have been interpreted in terms of simplified DM models [24–30]. The
invisible branching fraction of the Higgs boson, B(H → inv), has been constrained by sev-
eral searches at the LHC [20, 31–34], with the ATLAS and CMS Collaborations setting
upper limits of 0.25 and 0.24, at 95% confidence level (CL), respectively, through direct
searches [
35, 36]. Precise measurements of the Higgs boson couplings from a combination
of 7 and 8 TeV data sets, collected by the ATLAS and CMS experiments, provide indirect
constraints on additional contributions to the Higgs boson width from non-SM decay pro-
cesses. The resulting indirect upper limit on the Higgs boson branching fraction to non-SM
decays is 0.34, at 95% CL [
37].
This paper presents the results of a search for DM in the mono-V and monojet channels
using a data set of proton-proton collisions at
√
s = 13 TeV, collected with the CMS detector
in the first half of 2016, and corresponding to an integrated luminosity of 12.9 fb
−1
. In the
case of the mono-V signature, a hadronic decay of a W or Z boson reconstructed as a single
large-radius jet is considered. The results of the search are interpreted using simplified DM
models in which the interaction between the DM and SM particles is mediated by a spin-1
particle such as a Z
′
boson, as shown in figure
1, or a spin-0 particle (S), as shown in
figure
2. The results are also interpreted in terms of B(H → inv). The Feynman diagrams
for the production of the SM Higgs boson and its decay to invisible particles resulting in
the monojet and mono-V final states are similar to those shown for a spin-0 mediator in
figure
2.
– 2 –
JHEP07(2017)014
2 The CMS detector
The CMS detector is a multi-purpose apparatus designed to study a wide range of physics
processes in proton-proton and heavy ion collisions. Its central feature is a superconducting
solenoid of 6 m internal diameter that produces a magnetic field of 3.8 T parallel to the beam
direction. A silicon pixel and strip tracker is contained inside the solenoid and measures
the momentum of charged particles up to a pseudorapidity of |η| = 2.5. The tracker is
surrounded by a lead tungstate crystal electromagnetic calorimeter (ECAL) and a sampling
hadron calorimeter (HCAL) made of brass and scintillator, which provide coverage up to
|η| = 3. The steel and quartz-fiber
ˇ
Cerenkov hadron forward calorimeter extends the
coverage to |η| = 5. The muon system consists of gas-ionization detectors embedded in the
steel flux-return yoke of the solenoid, and covers |η| < 2.4. A more detailed description
of the CMS detector, together with a definition of the coordinate system used and the
relevant kinematic variables, can be found in ref. [
38].
The particle-flow (PF) event algorithm [
39, 40] reconstructs and identifies each individ-
ual particle with an optimized combination of information from the various elements of the
CMS detector. The energy of photons is directly obtained from the ECAL measurement.
The energy of elec trons is determined from a combination of the electron momentum at the
primary interaction vertex as determined by the tracker, the energy of the corresponding
ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with
originating from the electron track. The energy of muons is obtained from the curvature
of the corresponding track. The energy of charged hadrons is determined from a combi-
nation of their momentum measured in the tracker and the matching ECAL and HCAL
energy deposits, corrected for zero-suppression effects and for the response function of the
calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from
the corresponding ECAL and HCAL energies.
The missing transverse momentum vector (~p
miss
T
) is computed as the negative vector
sum of the transverse momenta (p
T
) of all the PF candidates in an event, and its magnitude
is denoted as E
miss
T
. Jets are reconstructed by clustering PF candidates using the anti-k
T
algorithm [
41]. Jets clustered with distance parameters of 0.4 and 0.8 are referred to as
AK4 and AK8 jets, respectively. The primary vertex with the largest sum of p
2
T
of the
associated tracks is chosen as the vertex corresponding to the hard interaction in an event.
All charged PF candidates originating from any other vertex are ignored during the jet
reconstruction. Jet momentum is determined as the vectorial sum of all particle momenta
in the jet, and is found from simulation to b e within 5 to 10% of the true momentum,
over the whole p
T
spectrum and detector acceptance. An offset correction is applied to jet
energies to take into account the contribution from additional proton-proton interactions
within the same or adjacent bunch crossings (pileup). Jet energy corrections are derived
from simulation and are confirmed with in situ measurements of the energy balance in dijet
and γ+jet events [
42]. These are also propagated to the E
miss
T
calculation [
43].
3 Event simulation
The Monte Carlo generators used to simulate various signal and background processes
are listed in table
1. Simulated samples of background events are produced for the
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JHEP07(2017)014
Z+jets and γ+jets processes at leading order (LO) with up to four partons in the final
state, using MadGraph5
amc@nlo 2.2.3 [44]. This generator is also used to simulate
the W(ℓν)+jets process at next-to-leading order (NLO), with up to two partons in the
final state, and the quantum chromodynamics (QCD) multijet background at LO. The t
t
and single top quark background samples are produced using Powheg 2.0 [
45–47], and a
set of diboson samples is produced with Pythia 8.205 [
48]. The monojet DM signal is
simulated at NLO for spin-1 mediators, and at LO for spin-0 mediators with the resolved
top quark loop calculations carried out using Powheg [29, 49]. The mono-V DM signal
samples are produced at LO with the JHUGen 5.2.5 generator [
50–52] for the scalar me-
diator, and with MadGraph5
amc@nlo for the spin-1 mediators. Standard model Higgs
boson signal events produced through gluon fusion and vector boson fusion are generated
using Powheg, while SM Higgs boson production in association with W or Z bosons is
simulated using the JHUGen generator.
Events produced by the MadGraph5
amc@nlo, Powheg, and JHUGen generators
are further processed with Pythia using the CUETP8M1 tune [
53] for the simulation of
fragmentation, parton shower, hadronization, and the underlying event. In the case of the
MadGraph5
amc@nlo samples, jets from the matrix element calculations are matched
to the parton shower description, following the FxFx matching prescription [
54] for the
NLO samples and the MLM scheme [
55] for the LO ones. The NNPDF 3.0 [56] parton
distribution functions (PDFs) are used for all generated samples. Interactions of final-
state particles with the CMS detector are simulated with Geant4 [
57]. Simulated events
include the effects of pileup, and are weighted to reproduce the distribution of rec onstructed
primary vertices observed in data.
4 Event selection
Candidate events are selected using triggers that have thresholds of 90, 100, or 110 GeV
applied equally to both E
miss
T,trig
and H
miss
T,trig
, where E
miss
T,trig
is computed as the magnitude
of the vector sum of the p
T
of all the particles reconstructed at the trigger level, and
H
miss
T,trig
is the magnitude of the vector p
T
sum of jets reconstructed at the trigger level.
Jets used in the H
miss
T,trig
computation are required to have p
T
> 20 GeV and |η| < 5.0. The
energy fraction attributed to neutral hadrons in these jets is required to be less than 0.9.
This requirement removes jets reconstructed from detector noise. The values of E
miss
T,trig
and
H
miss
T,trig
are calculated without including muon candidates, allowing the same triggers to
be used for selecting events in the muon control samples used for background estimation.
The trigger efficiency is measured to be about 95% for events passing the analysis selection
with E
miss
T
≈ 200 GeV. The triggers become fully efficient for events with E
miss
T
> 350 GeV.
Events considered in this search are required to have E
miss
T
> 200 GeV, which ensures that
the trigger efficiency is higher than 95%. The leading AK4 jet in the event is required to
have p
T
> 100 GeV and |η| < 2.5. Unlike earlier searches performed by the CMS Collabo-
ration in this final state [
19, 21], there is no requirement on the number of reconstructed
jets in the event. The leading AK4 jet must have at least 10% of its energy associated with
charged hadrons, and less than 80% of its energy coming from neutral hadrons. These re-
– 4 –