Results of a search for new phenomena in final states with an energetic
jet and large missing transverse momentum are reported. The search uses
proton-proton collision data corresponding to an integrated luminosity of
fb
at a centre-of-mass energy of TeV
collected in 2015 and 2016 with the ATLAS detector at the Large Hadron Collider.
Events are required to have at least one jet with a transverse momentum above
GeV and no
leptons ( or
). Several signal
regions are considered with increasing requirements on the missing transverse momentum
above GeV.
Good agreement is observed between the number of events in data and Standard
Model predictions. The results are translated into exclusion limits in models with
pair-produced weakly interacting dark-matter candidates, large extra spatial
dimensions, and supersymmetric particles in several compressed scenarios.
Hadron-Hadron scattering (experiments)
Article funded by SCOAP3
Introduction
250~\GeV$, and no leptons ($e$ or $\mu$)
constitutes a distinctive signature for new physics beyond the Standard Model
(SM) at colliders.
The monojet signature has been extensively studied at the LHC in the context of
searches for large extra spatial dimensions (LED), supersymmetry (SUSY), and
weakly interacting massive particles (WIMPs) as candidates for dark matter (DM)~\cite{Aaboud-ml-2016tnv,Sirunyan-ml-2017hci,Aaboud-ml-2017buf}.
The results of the analysis are therefore interpreted in terms of each of these
models, which are described in the following~paragraphs.
A range of astrophysical measurements, such as the rotational speed of stars in galaxies
and gravitational lensing, point to the existence of a non-baryonic form of
matter~\cite{Trimble-ml-1987ee,Bertone-ml-2004pz,Feng-ml-2010gw}. The existence of a new,
weakly interacting massive particle is often hypothesized~\cite{Steigman-ml-1984ac},
as it leads to the correct relic density for non-relativistic matter in the early
universe~\cite{Kolb-ml-1990vq} as measured
from data from the
Planck~\cite{Adam-ml-2015rua} and
WMAP~\cite{bib2013ApJS..208...19H} Collaborations, if the mass is between a few \GeV{}
and one \TeV{} and if it has electroweak-scale interaction cross sections.
WIMPs may be pair-produced at the LHC
and when
accompanied by
a jet of particles, for example from initial-state radiation (ISR), these
events produce the signature of a jet and missing transverse momentum.
As with the initial results obtained in this search channel at
$\sqrt{s}=13~\TeV$~\cite{Aaboud-ml-2016tnv}, simplified models are used to
interpret the results, providing a framework to characterize the new
particles acting as mediators of the interaction between the SM and the
dark sector~\cite{Abdallah-ml-2015ter,Abercrombie-ml-2015wmb,Buchmueller-ml-2014yoa}.
The results from simplified models
involving $s$-channel
Feynman diagrams such
as the one shown in figure~\ref{fig:feynman}\protect\subref{fig1a}
are comparable to those previously
obtained~\cite{Aad-ml-2015zva}
by using an effective-field-theory
approach~\cite{Goodman-ml-2010ku} when the mediator mass considered is
above $10~\TeV$~\cite{Busoni-ml-2013lha}.
Results are presented for DM models where Dirac fermion WIMPs ($\chi$) are pair-produced
from quarks via $s$-channel exchange of a spin-1 mediator particle ($Z_A$) with
axial-vector couplings, a spin-1 mediator particle ($Z_V$) with vector couplings, or a spin-0 pseudoscalar ($Z_P$).
These models are defined by four
free parameters: the WIMP mass ($m_\chi$); the mediator mass ($m_{Z_A}$, $m_{Z_V}$ or $m_{Z_P}$, depending on the model); the
flavour-universal coupling to quarks ($g_q$), where all three quark generations are included; and the coupling of the mediator to
WIMPs ($g_\chi$). Couplings to other SM particles are not considered.
In each case, a minimal mediator width is defined, as detailed in refs.~\cite{Buchmueller-ml-2014yoa,Abercrombie-ml-2015wmb}, which
in the case of the axial-vector mediator takes the form:
\begin{equation*}
\Gamma(m_{Z_A})_{\textrm{min}}=
\frac{g_\chi^2 m_{Z_A}}{12\pi} \beta_\chi^3 \theta(m_{Z_A}-2m_\chi)
+ \sum_q \frac{3 g_q^2 m_{Z_A}}{12\pi}\beta_q^3 \theta(m_{Z_A}-2m_q)\;,
\end{equation*}
\noindent
where $\theta(x)$ denotes the Heaviside step function and
$\beta_f=\sqrt{1 - {4m_f^2}/{m_{Z_A}^2}}$ is the velocity in the mediator rest frame of
fermion $f$
(either $\chi$ or $q$) with mass $m_f$. The quark sum runs over all
flavours. The monojet signature in this model emerges from initial-state
radiation of a gluon as shown in figure~\ref{fig:feynman}\protect\subref{fig1a}.
\begin{figure}
\centering
\subfigure[]{
\includegraphics[width=0.30\linewidth]{fig_01a.pdf}\label{fig1a}
}\\
\subfigure[]{
\includegraphics[width=0.25\linewidth]{fig_01b.pdf}\label{fig1b}
}
\subfigure[]{
\includegraphics[width=0.30\linewidth]{fig_01c.pdf}\label{fig1c}
}
\subfigure[]{
\includegraphics[width=0.25\linewidth]{fig_01d.pdf}\label{fig1d}
}\\
\subfigure[]{
\includegraphics[width=0.30\linewidth]{fig_01e.pdf}\label{fig1e}
}
]]>
ATLAS detector
$~1.5), copper/LAr and tungsten/LAr hadronic
calorimeters match the outer $|\eta|$ limits of the endcap electromagnetic calorimeters. The LAr
forward calorimeters provide both the electromagnetic and hadronic energy measurements, and extend
the coverage to $|\eta| < 4.9$.
The muon spectrometer measures the deflection of muons
in the magnetic field provided by
large superconducting air-core toroidal magnets
in the pseudorapidity range $|\eta|<2.7$, instrumented with separate trigger and high-precision tracking chambers.
Over most of the $\eta$ range, a measurement of the track coordinates in the bending direction of the magnetic
field is provided
by monitored drift tubes. Cathode strip chambers with higher granularity are used in the innermost plane over $2.0 < |\eta| < 2.7$.
The muon
fast trigger detectors cover the pseudorapidity range $|\eta| < 2.4$ and provide a measurement of the coordinate in the non-bending plane.
The data were collected using an online two-level trigger system~\cite{Aaboud-ml-2016leb} that selects events of interest and reduces
the event rate from an average of 33 MHz to about 1\,kHz for recording and offline processing.
]]>
Monte Carlo simulationSignal simulationBackground simulationEvent reconstruction
20~\GeV$ and $|\eta|
<2.8$ are considered in the analysis. Track-based variables to suppress
pile-up jets have been developed, and a combination of two such variables, called the
jet-vertex tagger~\cite{ATLAS-CONF-2014-018}, is constructed. In order to remove jets originating from
pile-up collisions, for central jets ($|\eta| < 2.4$) with $p_{\mathrm T} < 50~\GeV$
a significant fraction of the tracks associated with each jet must have an origin
compatible with the primary vertex, as defined by the jet-vertex~tagger.
Jets with $\pt > 30~\GeV$ and $|\eta|<2.5$ are identified as $b$-jets if tagged by a multivariate algorithm which uses
information about the impact parameters of inner-detector tracks matched to the
jet, the presence of displaced secondary vertices, and the reconstructed flight
paths of $b$- and $c$-hadrons inside the jet~\cite{Aad-ml-2015ydr,ATL-PHYS-PUB-2016-012}. A 60$\%$ efficient
$b$-tagging working point, as determined in a simulated sample of $\ttbar$ events,
is chosen. This corresponds to a rejection factor of approximately 1500, 35
and 180 for light-quark and gluon jets, $c$-jets, and $\tau$-leptons decaying
hadronically, respectively.
The presence of
electrons or muons in the final state is used
in the analysis to define control samples and to reject background contributions in
the signal regions (see sections~\ref{sec:evt}~and~\ref{sec:backg}).
Electrons are found by combining energy deposits in the calorimeter
with tracks found in the inner detector, and are initially required to
have $p_{\mathrm T} > 20~\GeV$ and $|\eta|
<2.47$,
to satisfy the
`Loose' electron shower shape and track selection criteria described in refs.~\cite{ATLAS-CONF-2014-032}, and must also be isolated.
The latter uses track-based isolation requirements with an efficiency of about 99$\%$, as determined using $\zee$ data.
Overlaps between identified electrons
and jets with $\pt > 30~\GeV$ in the final state are resolved. Jets are discarded if they are not
$b$-tagged and their separation $\Delta R = \sqrt{(\Delta \eta)^2 + (\Delta \phi)^2}$
from an identified electron is less than~0.2. Otherwise, the electron is removed as it most likely originates from a
semileptonic $b$-hadron decay. The electrons separated by $\Delta R$ between 0.2
and 0.4 from any remaining jet are removed.
Muon candidates are
formed by combining information from the muon spectrometer and
inner tracking detectors. They are
required to pass `Medium' identification requirements, as described in ref.~\cite{Aad-ml-2016jkr}, and
to have $p_{\mathrm T} > 10~\GeV$ and $|\eta| < 2.5$.
Jets with $p_{\mathrm T} >
30~\GeV$ and fewer than three tracks with $\pt > 0.5~\GeV$ associated with them are
discarded if their separation $\Delta R$ from an identified muon is less than~0.4.
The muon is discarded if it is matched to a jet with
$p_{\mathrm T} > 30~\GeV$ that has at least three tracks
associated with it.
The $\met$ value is reconstructed using all energy deposits in the calorimeter up to
pseudorapidity $|\eta| = 4.9$. Clusters associated with either electrons,
photons or jets with $\pt >20~\GeV$
make use of the corresponding calibrations.
Softer jets and clusters not associated with electrons, photons or jets
are calibrated using tracking
information~\cite{ATL-PHYS-PUB-2015-023}. As discussed below, in this analysis the
missing transverse momentum
is not corrected for the presence of muons in the final state.
]]>
Event selection
250~\GeV$, as determined using a data sample with
muons in the final state.
Events are required to have at least one reconstructed primary vertex
consistent with the beamspot envelope and that contains at least two
associated tracks of $\pt>0.4~\GeV$. When more than one such vertex is
found, the vertex with the largest summed $\pt^2$ of the associated
tracks is chosen. Events having identified muons with $\pt > 10~\GeV$ or
electrons with $\pt > 20~\GeV$ in the final state are vetoed.
Events are selected with $\met > 250~\GeV$,
a leading jet with $p_{\mathrm{T}, j1} > 250~\GeV$ and $|\eta| < 2.4$, and
a maximum of four jets with $\pt > 30~\GeV$ and $|\eta| < 2.8$.
Separation in the azimuthal angle of $\Delta\phi(\mathrm{jet},{\ptmi})
> 0.4$ between the missing transverse momentum direction and each
selected jet is required to reduce the multijet background
contribution, where a large $\met$ can originate from jet energy
mismeasurement.
Jet quality criteria~\cite{clean} are imposed, which involve selections based
on quantities such as the pulse shape of the energy depositions in the
cells of the calorimeters, electromagnetic fraction in the calorimeter,
calorimeter sampling fraction, and the charged-particle fraction.\footnote{The charged-particle fraction is defined as
$f_{{\mathrm{ch}}}=\sum p_{\mathrm T}^{{\textrm{track,jet}}}
/p_{\mathrm T}^{{\textrm{jet}}}$, where $\sum p_{\mathrm
T}^{{\textrm{track,jet}}}$ is the scalar sum of the transverse momenta
of tracks associated with the primary vertex within a cone of radius
$\Delta R=0.4$ around the jet axis, and $p_{\mathrm T}^{{ \textrm{jet}}}$
is the transverse momentum of the jet as determined from calorimetric measurements.}
Loose selection criteria are applied to all jets with $\ptjet > 30~\GeV$
and $|\eta| < 2.8$, which remove anomalous energy depositions due to
coherent noise and electronic noise bursts in the calorimeter~\cite{Aad-ml-2013zwa}.
Events with any jet not satisfying the loose criteria, as described in ref.~\cite{clean},
are discarded.
Non-collision backgrounds, for example energy depositions in the calorimeters
due to muons of beam-induced or cosmic-ray origin, are
suppressed by imposing tight selection criteria on the leading jet and the ratio
of the jet charged-particle fraction to the calorimeter sampling
fraction,\footnote{The variable $f_{{\textrm{max}}}$ denotes the maximum fraction of
the jet energy collected by a single calorimeter layer.}
$f_{{\textrm{ch}}}/f_{{\textrm{max}}}$, is required to be larger than 0.1.
These requirements have a negligible effect on the signal efficiency.
The analysis uses two sets of signal regions, with inclusive and exclusive
$\met$ selections, where the regions are defined with increasing
$\met$ thresholds from $250~\GeV$ to $1000~\GeV$ (table~\ref{tab:sr}).
The inclusive selections are used for a model-independent search for new physics, and
the exclusive selections are used for the interpretation of the results
within different models of new physics.
\begin{table}
\centering\renewcommand\arraystretch{1.2}
\scalebox{.7}{\begin{tabular}{|lcccccccccc|}
\hline
Inclusive (IM)& IM1 & IM2 & IM3 & IM4 & IM5 & IM6 & IM7 & IM8 & IM9 & IM10 \\
$\met$ [\GeV] & $>\!250$ & $>\!300$ & $>\!350$ & $>\!400$ & $>\!500$ & $>\!600$ & $>\!700$ & $>\!800$ & $>\!900$ & $>\!1000$ \\ \hline
Exclusive (EM)& EM1 & EM2 & EM3 & EM4 & EM5 & EM6 & EM7 & EM8 & EM9 & EM10 \\
$\met$ [\GeV] &\!250--300\!&\!300--350\!&\!350--400\!&\!400--500\!&\!500--600\!&\!600--700\!&\!700--800\!&\!800--900\!&\!900--1000\!& $>\!1000$ \\ \hline
\end{tabular}}
]]>
1~\TeV$, whereas
the EM10 background prediction is obtained from fitting the full $\met$ shape in data and simulation,
as described in section~\ref{sec:backg}.]]>
Background estimationControl samples
10~\GeV$, and
transverse mass
in the range $30 < m_{\mathrm T} < 100~\GeV$.
The transverse mass $m_{\mathrm T} = \sqrt{2\pt^{\ell}\pt^{\nu}[1-\cos(\phi^{\ell}-\phi^{\nu})]}$ is defined by the lepton and neutrino transverse momenta,
where the $(x,y)$ components of the neutrino momentum are taken to be
the same as the corresponding $\ptmi$ components. Events with identified electrons in the final state are vetoed.
In addition, events with an identified $b$-jet in the final state are vetoed in order to reduce the contamination from top-quark-related processes.
Similarly, a $\zmm$+jets control
sample is selected by requiring the presence of two muons with $\pt >10~\GeV$ and
invariant mass in the range $66 < m_{\mu \mu} < 116~\GeV$. In the $\wmn$+jets and
$\zmm$+jets control regions, the $\met$ value is not corrected for the presence of
the muons in the final state,
motivated by the fact that these control regions
are used to estimate the $\znn$+jets, $\wmn$+jets and $\zmm$+jets backgrounds
in the signal regions with no identified muons.
The $\met$-based online trigger used in the analysis
does not include muon information in the $\met$ calculation. This allows the
collection of $\wmn$+jets and $\zmm$+jets control samples with the same trigger as for the signal regions.
A $\wen$+jets-dominated control sample was collected using online triggers that
select events with an electron in the final state. The control sample
is defined
with an isolated electron candidate with $\pt >30~\GeV$, $30 < m_{\mathrm T} < 100~\GeV$, and
no additional identified leptons in the final state.
Electron candidates in the
transition region between the barrel
and endcaps of the electromagnetic calorimeter, $1.37 < |\eta| < 1.52$, are excluded.
The $\met$ value is corrected by subtracting the contribution from the electron cluster in the calorimeter.
In this way, the measured $\met$ in the event better reflects the magnitude of the $W$-boson $\pt$ in the final state, which
is necessary for a proper implementation of the $W$-boson $\pT$ reweighting procedure, as explained in section~\ref{sec:mc},
that accounts for higher-order QCD and electroweak corrections.
In order to
suppress backgrounds from multijet processes with jets faking high-$\pt$ electrons, the events are required to have $\met/\sqrt{H_{\rm T}} > 5~\GeV{}^{1/2}$, where
in this case $\met$ still includes the contribution from the electron energy deposits in the calorimeter and $H_{\rm T}$ denotes the scalar
sum of the $\pt$ of the identified jets in the final~state.
Finally, a control sample enriched in $\ttbar$ events is constructed using the same selection criteria as in the case of the $\wmn$+jets but
requiring that at least one of the jets is $b$-tagged.
]]>
Multijet backgroundNon-collision background
5$~ns.
The results indicate an almost negligible contribution from non-collision backgrounds in the signal regions.
]]>
250~\GeV$ inclusive selection.
The background predictions include both the statistical and systematic uncertainties.
The individual uncertainties are correlated, and do not necessarily add
in quadrature to the total background uncertainty. The dash ``\textendash'' denotes negligible background contributions.]]>
250~\GeV$ inclusive selection, compared to
the background predictions.
The latter include the global normalization factors extracted from the fit.
The error bands in the ratios include the statistical and systematic uncertainties in the background predictions as
determined by the binned-likelihood fit to the data in the control regions.
The last bin of the $\met$ and leading-jet $\pt$ distributions contains overflows.
The contributions from multijet and non-collision backgrounds are negligible and are not shown in the figures.
]]>
250~\GeV$ inclusive selection, compared to
the background predictions.
The latter include the global normalization factors extracted from the fit.
The error bands in the ratios include the statistical and systematic uncertainties in the background predictions as
determined by the binned-likelihood fit to the data in the control regions.
The last bin of the $\met$ and leading-jet $\pt$ distributions contains overflows.
The contributions from multijet and non-collision backgrounds are negligible and are not shown in the figures.
]]>
Systematic uncertaintiesBackground systematic uncertaintiesSignal systematic uncertaintiesResults and interpretation
250~\GeV$, for which
the normalization factors applied to the MC predictions, and the related uncertainties,
are determined from the global fit carried out in exclusive $\met$ bins.
For illustration purposes, the distributions include the impact of
example
ADD, SUSY, and WIMP scenarios.
In general, the SM predictions provide a good description of the measured distributions.
The differences observed in the jet multiplicity distribution do not have an impact in the results.
Statistical tests using the binned profile likelihood fit described above, and considering different scenarios for new physics, give
$p$-values for a background-only hypothesis in the range 0.01--0.04, corresponding to
agreement with the SM predictions
within approximately 2.1$\sigma$ to 1.7$\sigma$.
\begin{figure}
\centering
\subfigure[]{
\includegraphics[width=0.47\textwidth]{fig_04a.pdf}\label{fig4a}
}
\subfigure[]{
\includegraphics[width=0.47\textwidth]{fig_04b.pdf}\label{fig4b}
}\\
\subfigure[]{
\includegraphics[width=0.47\textwidth]{fig_04c.pdf}\label{fig4c}
}
\subfigure[]{
\includegraphics[width=0.47\textwidth]{fig_04d.pdf}\label{fig4d}
}
]]>
250~\GeV$ selection compared to the SM predictions. The latter are normalized with normalization
factors as determined by the global fit that considers exclusive $\met$ regions.
For illustration purposes, the distributions of
example
ADD, SUSY, and WIMP scenarios are included.
The error bands in the ratios shown in the lower panels include both the statistical and systematic uncertainties
in the background predictions.
The last bin of the $\met$ and leading-jet $\pt$ distributions contains overflows.
The contributions from multijet and non-collision backgrounds are negligible and are only shown in the case of the $\met$ distribution.
]]>
Model-independent exclusion limits
Weakly interacting massive particles
2m_\chi$, typical
$A \times \epsilon$ values for the signal models with a $1~\TeV$ mediator range
from 25\% to 0.4\% for IM1 and IM10 selections, respectively. Very similar
values are obtained in the case of the vector mediator, whereas $A \times \epsilon$ values
in the range between $32 \%$ and $1 \%$ are computed for the pseudoscalar mediator model
with $m_{Z_P} = 1~\TeV$ and $m_\chi = 10~\GeV$.
Finally, in the case of the coloured scalar
mediator, $A \times \epsilon$ values in the range from $35 \%$ to $0.7 \%$ are obtained
for IM1 and IM10 selections, respectively, for a mediator mass of
$1~\TeV$ and
$m_\eta \gg m_\chi$.
The experimental uncertainties related to the jet and $\met$ scales and
resolutions introduce similar uncertainties in the signal yields for axial-vector, vector and pseudoscalar models.
They vary between $2\%$ and $7\%$ for the IM1 selection and between $3\%$ and $9\%$ for the IM10 selection, depending on the parameters of the model.
In the case of the coloured scalar mediator model, these uncertainties vary between
2$\%$ and 6$\%$ for IM1 and between 4$\%$ and about 10$\%$ for IM10.
The uncertainty related to the modelling of the initial- and final-state radiation
translates into a $20\%$ uncertainty in the signal acceptance, common to all the $s$-channel models.
In the case of the coloured scalar mediator model, this uncertainty varies between 10$\%$ and 30$\%$, depending on the
kinematic selection.
The choice of different PDF sets results in up to a $20\%$
uncertainty in the acceptance and up to a $10\%$ uncertainty in the cross section, depending on the model considered.
Varying the renormalization and factorization scales introduces up to $25\%$
variations of the cross section and up to $10\%$ change in the acceptance, depending on the model considered. In
addition, the uncertainty in the integrated luminosity is included.
A simultaneous fit to the signal and control regions in the exclusive $\met$ bins
is performed, and used to set observed and expected 95\% CL exclusion limits on the
parameters of the model.
Uncertainties in the signal acceptance times
efficiency, the background predictions, and the luminosity are considered, and
correlations between systematic uncertainties in signal and background
predictions are taken into account. The fit accounts for the contamination of
the control regions by signal events which a priori is estimated to be very small.
Figure~\ref{fig:dm2}\protect\subref{fig5a} shows the observed and expected 95\% CL exclusion
contours in the $m_{Z_A}$--$m_\chi$
parameter plane for a simplified model with an
axial-vector mediator, Dirac WIMPs, and couplings $g_q = 1/4$ and $g_\chi = 1$.
In addition, observed limits are shown using
$\pm1\sigma$ theoretical uncertainties in the signal cross sections. In the
on-shell regime, the models with mediator masses up to $1.55~\TeV$ are excluded for
$m_\chi=1~\GeV$. For $m_\chi < 1~\GeV$, the monojet analysis maintains its sensitivity for excluding DM models.
This analysis loses sensitivity to the models in the off-shell regime, where
cross sections are suppressed due to the virtual production of the mediator.
Perturbative unitarity is
violated in the parameter region defined by $m_\chi > \sqrt{\pi/2}\ m_{Z_A}$~\cite{Kahlhoefer-ml-2015bea}. The masses corresponding to the relic density~\cite{Boveia-ml-2016mrp}
as determined by the Planck and WMAP
satellites~\cite{Adam-ml-2015rua,bib2013ApJS..208...19H}, within the WIMP dark-matter model and in the absence of any
interaction other than the one considered, are indicated in the figure as a line
that crosses the excluded region at $m_{Z_A} \sim 1200~\GeV$ and $m_\chi \sim 440~\GeV$.
The region towards lower WIMP masses or higher mediator masses corresponds to
dark-matter overproduction.
\begin{figure}
\setlength\subfigcapskip{-2mm}
\centerline{
\subfigure[]{
\includegraphics[width=0.475\textwidth]{fig_05a.pdf}\label{fig5a}
}
\subfigure[]{
\includegraphics[width=0.475\textwidth]{fig_05b.pdf}\label{fig5b}
}\quad}
]]>
\sqrt{\pi/2}\ m_{Z_A}$, is indicated by the
hatched area. The dotted line indicates the kinematic limit for on-shell production $m_{Z_A} = 2 \times m_\chi$.
The cyan line indicates previous results at $13~\TeV$~\cite{Aaboud-ml-2016tnv} using 3.2~$\ifb$.
\protect\subref{fig5b} A comparison of the inferred limits (black line) to the constraints from
direct detection experiments (purple line) on the spin-dependent WIMP-proton scattering cross
section in the context of the simplified model with axial-vector
couplings. Unlike in the
$m_{Z_A}$--$m_\chi$
parameter plane, the limits are shown at
90\% CL. The results from this analysis, excluding the region to the left of the
contour, are compared with limits from
the
PICO~\cite{Amole-ml-2017dex} experiment.
The comparison is model-dependent and solely valid in the context of this model,
assuming minimal mediator width and the coupling values $g_q=1/4$ and $g_\chi=1$.
]]>
Squark-pair production
Large extra spatial dimensions
400~\GeV$,
where the SM background is moderate and the shape difference between signal and the SM background becomes apparent,
have
sufficient sensitivity to ADD signal.
The typical value of $A \times \epsilon$ of the selection criteria varies, as the number of extra dimensions $n$ increases from $n=2$ to $n=6$,
between 13$\%$ and 17$\%$ for IM4 and between $0.8\%$ and 1.4$\%$ for IM10.
The effect of experimental uncertainties related to jet and $\met$
scales and resolutions is found to be similar to the effect in the WIMP models.
The uncertainties related to the modelling of the initial- and final-state
gluon radiation
translate into
uncertainties in the ADD signal acceptance which
vary between $11\%$ and $13\%$ with increasing $\met$ and approximately independent of $n$.
The uncertainties due to the
PDFs, affecting the predicted signal yields, increase from $11\%$ at $n=2$ to $43\%$ at $n=6$.
Similarly, the variations of the renormalization and factorization scales
introduce a $23\%$ to $36\%$ uncertainty
in the signal yields, with increasing $n$.
Observed and expected 95$\%$ CL exclusion limits are set as in the case of the WIMP and SUSY models.
The $- 1\sigma$ variations of the ADD
theoretical cross sections result in about a 7$\%$ to 10$\%$ decrease in the nominal observed limits, depending on $n$.
Figure~\ref{fig:add} and table~\ref{tab:add} present the results.
Values of $M_D$ below $7.7~\TeV$ at $n=2$ and below $4.8~\TeV$ at $n=6$ are excluded at
95$\%$~CL,
which improve on the exclusion limits from previous results using 3.2~$\ifb$ of $13~\TeV$ data~\cite{Aaboud-ml-2016tnv}.
As discussed in refs.~\cite{ATLAS-ml-2012ky, Aad-ml-2015zva},
the analysis partially probes the phase-space region with $\hat{s} > M_D^2$,
where $\sqrt{\hat{s}}$ is the
centre-of-mass energy of the hard interaction. This challenges the validity of the model implementation and the lower bounds
on $M_D$, as they depend on the unknown ultraviolet behaviour of the effective theory.
The observed 95$\%$ CL limits are recomputed after
suppressing, with a weighting factor $M_D^4/\hat{s}^2$, the signal events with $\hat{s} > M_D^2$, here
referred to as damping. This results in a negligible decrease of the quoted 95$\%$ CL lower limits on $M_D$,
as also shown in table~\ref{tab:add_limits}.
\begin{table}
\centering
\begin{footnotesize}\renewcommand\arraystretch{1.2}
\begin{tabular}{|@{\ }lccc@{\ }|} \hline
\multicolumn{4}{|c|}{{\bf\boldmath ADD Model Limits on $M_{D}$
} (95\% CL)} \\ \hline
& Expected [TeV]& Observed [TeV]& Observed (damped) [TeV]\\ \hline
$n = 2$ & 9.2$^{+0.8}_{-1.0}$ & 7.7$^{+0.4}_{-0.5}$ & 7.7 \\
$n = 3$ & 7.1$^{+0.5}_{-0.6}$ & 6.2$^{+0.4}_{-0.5}$ & 6.2 \\
$n = 4$ & 6.1$^{+0.3}_{-0.4}$ & 5.5$^{+0.3}_{-0.5}$ & 5.5 \\
$n = 5$ & 5.5$^{+0.3}_{-0.3}$ & 5.1$^{+0.3}_{-0.5}$ & 5.1 \\
$n = 6$ & 5.2$^{+0.2}_{-0.3}$ & 4.8$^{+0.3}_{-0.5}$ & 4.8 \\ \hline
\end{tabular}
\end{footnotesize}
]]>
M_D^2$ (see text)
are quoted.
]]>
M_D^2$.
The results from this analysis are compared to previous results from the ATLAS
Collaboration
using $3.2 \ifb$ of $\sqrt{s} = 13~\TeV$ data~\cite{Aaboud-ml-2016tnv}.
]]>
ConclusionsAcknowledgmentshttps://arxiv.org/abs/1604.07773https://doi.org/10.1007/JHEP07(2017)014https://arxiv.org/abs/1707.03263https://doi.org/10.1146/annurev.aa.25.090187.002233https://arxiv.org/abs/hep-ph/0404175https://arxiv.org/abs/1003.0904https://doi.org/10.1016/0550-3213(85)90537-1
E.W. Kolb and M.S. Turner, The early Universe, Front. Phys. 69 (1990) 1
[https://inspirehep.net/search?p=find+J+%22Front.Phys.,69,1%22].
https://arxiv.org/abs/1502.01582https://arxiv.org/abs/1212.5226https://arxiv.org/abs/1506.03116https://arxiv.org/abs/1507.00966https://doi.org/10.1007/JHEP01(2015)037https://arxiv.org/abs/1502.01518https://arxiv.org/abs/1008.1783https://arxiv.org/abs/1307.2253https://arxiv.org/abs/1209.0231https://doi.org/10.1007/JHEP11(2014)024https://doi.org/10.1007/JHEP05(2016)112https://doi.org/10.1143/PTP.36.1266https://doi.org/10.1103/PhysRevD.3.2415
Yu.A. Golfand and E.P. Likhtman, Extension of the algebra of Poincaré group generators and
violation of
invariance, JETP Lett. 13 (1971) 323 [https://inspirehep.net/search?p=find+J+%22JETPLett.,13,323%22].
https://doi.org/10.1016/0550-3213(71)90448-2https://doi.org/10.1103/PhysRevD.4.1109https://doi.org/10.1016/0550-3213(71)90351-8https://doi.org/10.1016/0370-2693(73)90490-5https://doi.org/10.1016/0370-2693(74)90578-4https://doi.org/10.1016/0550-3213(74)90355-1https://doi.org/10.1016/0550-3213(88)90171-Xhttps://doi.org/10.1016/0370-2693(76)90319-1https://doi.org/10.1016/0370-2693(77)90852-8https://doi.org/10.1016/0370-2693(78)90858-4https://doi.org/10.1016/0370-2693(79)91229-2https://doi.org/10.1016/0550-3213(81)90522-8https://arxiv.org/abs/hep-ph/9803315https://doi.org/10.1088/1748-0221/3/08/S08003
ATLAS collaboration, ATLAS insertable B-layer technical design report,
ATLAS-TDR-19 (2010).
https://arxiv.org/abs/1611.09661https://arxiv.org/abs/1005.4568https://doi.org/10.1016/S0168-9002(03)01368-8https://doi.org/10.1088/1126-6708/2006/05/026https://doi.org/10.1007/JHEP06(2010)043https://doi.org/10.1088/1126-6708/2007/11/070https://doi.org/10.1088/1126-6708/2004/11/040https://doi.org/10.1007/JHEP12(2013)007https://doi.org/10.1007/JHEP06(2015)078https://doi.org/10.1007/JHEP04(2015)040http://cds.cern.ch/record/1966419https://doi.org/10.1007/JHEP07(2014)079https://arxiv.org/abs/1207.1303https://doi.org/10.1007/JHEP03(2012)019https://arxiv.org/abs/hep-ph/9710451https://doi.org/10.1007/JHEP08(2010)098https://arxiv.org/abs/1105.1110https://arxiv.org/abs/1407.5066https://doi.org/10.1088/1126-6708/2009/02/007https://arxiv.org/abs/1111.5206https://doi.org/10.1088/1126-6708/2008/12/039https://doi.org/10.1088/1126-6708/2008/03/038https://doi.org/10.1007/JHEP04(2013)027https://arxiv.org/abs/0903.2120https://arxiv.org/abs/hep-ph/0703012https://arxiv.org/abs/0901.0002https://arxiv.org/abs/1705.04664https://arxiv.org/abs/1702.05725https://doi.org/10.1088/1126-6708/2007/09/126https://arxiv.org/abs/1007.2241https://doi.org/10.1016/S0168-9002(01)00089-4https://arxiv.org/abs/0803.0883https://doi.org/10.1007/JHEP07(2011)018https://doi.org/10.1088/1126-6708/2008/04/063https://arxiv.org/abs/1111.6097https://arxiv.org/abs/1112.6426http://cds.cern.ch/record/1700870https://doi.org/10.1088/1748-0221/11/04/P04008http://cds.cern.ch/record/2160731http://cds.cern.ch/record/1706245https://arxiv.org/abs/1603.05598http://cds.cern.ch/record/2037700https://arxiv.org/abs/1608.03953http://cds.cern.ch/record/2037702https://doi.org/10.1088/1748-0221/8/07/P07004https://arxiv.org/abs/1208.0949https://arxiv.org/abs/1007.1727http://cds.cern.ch/record/2157687https://arxiv.org/abs/1407.5063http://cds.cern.ch/record/2261937http://cds.cern.ch/record/2261938http://cds.cern.ch/record/2261933https://arxiv.org/abs/1412.3989https://doi.org/10.1088/0954-3899/28/10/313https://doi.org/10.1007/JHEP02(2016)016https://arxiv.org/abs/1603.04156https://arxiv.org/abs/1505.04190https://arxiv.org/abs/1702.07666https://arxiv.org/abs/1605.03814https://doi.org/10.1007/JHEP04(2013)075http://cds.cern.ch/record/2202407