refname refsname

DESY-23-014

EFI-22-10

A new LHC search for dark matter produced via
heavy Higgs bosons using simplified models

Danyer Perez Adana***email<EMAIL_ADDRESS>Henning Bahlb†††email:
<EMAIL_ADDRESS>Alexander Grohsjeanc‡‡‡email<EMAIL_ADDRESS>Victor Martin Lozanod§§§email<EMAIL_ADDRESS>Christian
Schwanenbergera,c¶¶¶email<EMAIL_ADDRESS>Georg
Weigleina,c∥∥∥email<EMAIL_ADDRESS>
a Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
b Department of Physics and Enrico Fermi Institute, University of Chicago,
5720 South Ellis Avenue, Chicago, IL 60637 USA
c Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
d Departament de Física Teòrica and IFIC, Universitat de València-CSIC,
E-46100, Burjassot, Spain

###### Abstract

Searches for dark matter produced via scalar resonances in final states
consisting of Standard Model (SM) particles and missing transverse momentum
are of high relevance at the LHC. Motivated by dark-matter portal models, most
existing searches are optimized for unbalanced decay topologies for which the
missing momentum recoils against the visible SM particles. In this work, we
show that existing searches are also sensitive to a wider class of models,
which we characterize by a recently presented simplified model framework. We
point out that searches for models with a balanced decay topology can be
further improved with more dedicated analysis strategies. For this study, we
investigate the feasibility of a new search for bottom-quark associated
neutral Higgs production with a $b\bar{b}Z+{p_{\text{T}}^{\text{miss}}}$ final
state and perform a detailed collider analysis. Our projected results in the
different simplified model topologies investigated here can be easily
reinterpreted in a wide range of models of physics beyond the SM, which we
explicitly demonstrate for the example of the Two-Higgs-Doublet model with an
additional pseudoscalar Higgs boson.

###### Contents

  1. 1 Introduction
  2. 2 Simplified models for mono-$Z$ plus missing momentum final states
  3. 3 MC samples and event reconstruction
  4. 4 Analysis of the $pp\to b\bar{b}\Phi(\to Z+{p_{\text{T}}^{\text{miss}}})$ process
    1. 4.1 Event selection
    2. 4.2 Signal selection efficiency
    3. 4.3 Background expectation
    4. 4.4 Limit extraction method
  5. 5 Expected sensitivity
    1. 5.1 Limit Scan in 1D
    2. 5.2 Limit Scan in 2D
    3. 5.3 2HDMa interpretation
  6. 6 Conclusions

##  1 Introduction

The discovery of a scalar boson ten years ago marked a milestone for particle
physics [1, 2]. Within the current experimental and theoretical uncertainties,
it agrees remarkably well with the Standard Model (SM) Higgs boson. Besides
further characterizing the discovered boson, searching for additional beyond
the Standard Model (BSM) scalars is one of the main efforts within the LHC
physics program.

Additional Higgs bosons could provide ways to address various unexplained
experimental observations like dark matter (DM). Higgs bosons can constitute
DM or act as a mediator between the visible and invisible sectors [3, 4].
Scenarios involving DM particles can be tested by direct DM detection
experiments (searching for the scattering of DM particles with e.g. nucleons),
by indirect detection experiments (searching for the annihilation of DM
particles), or collider experiments (searching for the production of DM
particles at colliders) [5, 6, 7].

Two complementary strategies are pursued at colliders to search for DM.
Besides the search for the decay of the mediator particle into DM particles,
giving rise to a missing transverse momentum signature, searches are also
performed for decays of the mediator particles into SM particles. Concerning
the former type of searches, since the DM particles experimentally only
manifest themselves in the form of a missing transverse momentum, the presence
of at least one additional SM particle in the final state is required.

Most of the “mono-X plus missing momentum” searches [8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21, 22, 23, 24] — with X being for example a jet, a
photon, a Higgs boson, or a $Z$ boson — are motivated by simplified scalar or
vector portal models [25, 26, 27]. In these portal models, a heavy resonance
decays invisibly into dark matter particles and is produced in association
with SM particles. As a result of this event topology, the missing transverse
momentum recoils against the visible transverse momentum resulting in an
“unbalanced” missing momentum distribution peaking at high values.

In general, however, also other event topologies with a more “balanced” (i.e.,
softer) missing momentum distribution can appear in well-motivated BSM models.
In order to classify the different decay topologies, a simplified model
framework for scalar resonance searches with missing transverse momentum final
states has been developed in Bahl:2021xmy, which allows one to cover a wider
class of BSM models compared to a dedicated search within a particular model.

The aim of the present study is to demonstrate this approach by applying it to
a potential search for DM in bottom-quark associated neutral Higgs production
with a $b\bar{b}Z+{p_{\text{T}}^{\text{miss}}}$ (where
${p_{\text{T}}^{\text{miss}}}$ is the missing transverse momentum) final state
and perform a detailed collider study. This channel is so far not well
explored and complementary to many existing $Z+{p_{\text{T}}^{\text{miss}}}$
final states searches, which often explicitly veto $b$-jets. Based on our
analysis setup, we derive expected limits for the various simplified model
topologies. In addition, as an application of our model-independent results we
also provide expected limits for the Two-Higgs-Doublet model with an
additional pseudoscalar DM portal (2HDMa).

This work is structured as follows. In Section 2 we review the simplified
model approach. The production of Monte-Carlo event samples and the event
reconstruction is described in Section 3. We detail the event analysis in
Section 4. In Section 5, we discuss the expected sensitivity of the proposed
search. Our conclusions can be found in Section 6.

##  2 Simplified models for mono-$Z$ plus missing momentum final states

The simplified model considered in the following represents a generic
extension of the SM. Specifically, we focus on a scenario where a heavy scalar
resonance decays into SM particles and transverse missing momentum with
intermediate BSM states.111A detailed description of the simplified model
approach for BSM Higgs searches can be found in Bahl:2021xmy. The possible
experimental signatures are characterised in terms of different simplified
model topologies. The considered simplified model enlarges the SM with a heavy
scalar resonance $\Phi$, a mediator ${M}$ and an invisible particle ${I}$
(with masses $m_{\Phi}$, $m_{M}$, and $m_{I}$, respectively). The spin nature
of the mediator and the invisible particle could be either scalar, fermion or
vector as described in Bahl:2021xmy. It is important to note that for the
different topologies that can occur for the specified matter content we do not
distinguish between the different types of mediators and between the different
types of invisible particles. In this way the results obtained for the
simplified model topologies can be mapped to different classes of explicit
models. The approach of treating the mediator and the invisible particles in a
generic way independently of their spin nature is motivated by the results in
Bahl:2021xmy where it has been shown that the spin nature of the different
particles has only a minor impact on the results for the different simplified
model topologies.

In this work, we will concentrate on the mono-$Z$ plus missing momentum
signature (in association with additional $b$-jets from the production of the
scalar resonance). A detailed study of this signature in the simplified model
context can be found in Bahl:2021xmy. This final state gives rise to four
different topologies that are shown in Fig. 1 (where we omit the $b$-jets from
the production of the scalar resonance). The first topology can be found in
Fig. 1(a). This topology is dubbed the 1-vs-1 unbalanced topology. In this
case, the scalar resonance decays into a $Z$ boson and an invisible particle
directly. As a consequence of the direct decay of the scalar, the invisible
particle recoils against the $Z$ boson, resulting in a missing transverse
momentum spectrum peaking at high ${p_{\text{T}}^{\text{miss}}}$ values. The
second topology presented in Fig. 1(b) is the 2-vs-1 balanced topology. The
decay products of the scalar resonance are a mediator and an invisible
particle. The mediator subsequently decays into an invisible particle and a
$Z$ boson. Given the fact that the scalar resonance is produced approximately
at rest, the mediator will recoil against the invisible particle in the first
step of the decay process, yielding a balanced missing transverse momentum
spectrum. The third topology can be found in Fig. 1(c). In this case, the
scalar resonance decays into a $Z$ boson and a mediator, which decays into two
invisible particles. As the $Z$ boson recoils against the mediator in the
scalar reference frame, the $Z$ boson is produced in opposite direction with
respect to the missing transverse momentum originating from the decay of the
mediator. This results in a very similar kinematical situation as the 1-vs-1
topology, where the missing transverse momentum spectrum peaks at high
${p_{\text{T}}^{\text{miss}}}$ values. The last topology is the 2-vs-2
balanced topology, shown in Fig. 1(d). In this case the scalar resonance
decays into two mediator particles. One of them decays into a $Z$ boson and an
invisible particle, while the second mediator decays into two invisible
particles. Although it contains two mediators in the decay, this topology is
similar to the 2-vs-1 balanced topology with respect to its kinematics. For
that reason the missing transverse momentum spectrum features a similar
balanced distribution in ${p_{\text{T}}^{\text{miss}}}$.

(a) 1-vs-1 unbalanced

(b) 2-vs-1 balanced

(c) 2-vs-1 unbalanced

(d) 2-vs-2 balanced

Figure 1: Decay topologies of a neutral scalar boson $\Phi$ decaying in its
rest frame to a $Z$ boson plus ${p_{\text{T}}^{\text{miss}}}$.

In Bahl:2021xmy, an additional topology for this specific signature has been
discussed: the initial state radiation topology. In this case, the $Z$ boson
is radiated from the initial state while the scalar resonance decays
completely into invisible particles (directly or indirectly through different
mediators). We do not consider this case in the present study because of the
extremely low cross section resulting from requiring the presence of a
$b\bar{b}$ pair accompanying the heavy resonance and the $Z$ boson as produced
from an initial state radiation process. The details of the different Feynman
diagrams contributing to each topology can be found in Bahl:2021xmy.

In this work, we will concentrate on the four topologies shown in Fig. 1 and
perform a detailed collider analysis. Concretely, we focus on the production
of a neutral scalar resonance via bottom-associated production and the
subsequent decay to a $Z$ boson and invisible particles. No dedicated
experimental search has so far been performed in this channel.

##  3 MC samples and event reconstruction

This analysis is based on simulated $pp$ collisions at a center-of-mass energy
of 13 TeV applying the conditions of the CMS detector [29] during the Run 2
data-taking period, in which an amount of data equivalent to a total
integrated luminosity of 137 fb-1 was collected. Several SM background
processes contribute to the signature explored in this work as detailed in
Section 4.3 below. The most important background sources are $Z$+jets,
$t\bar{t}$, single-top, and di-boson production in final states with two
leptons. Monte Carlo simulated events are used to model the expected signal
and background yields, as well as the relevant distributions of the
observables that are used throughout the entire analysis.

Signal MC samples for the four topologies described in Section 2 have been
generated at leading order (LO) in perturbation theory using MadGraph5_aMC@NLO
2.6.5 [30, 31] and the UFO model simpBSM provided in Bahl:2021xmy. Pythia
8.230 was used to simulate parton shower, hadronization, and the underlying
event [32]. Signal samples have been generated varying two of the model mass
parameters, resulting in a dedicated 2D scan per signal topology. All mass
configurations have been chosen in such a way that none of the resonances ends
up being off-shell in the decay chain. Therefore the mass scan is limited to
the region of kinematically allowed $1\rightarrow 2$ decays. More details
regarding the mass scan implemented in each case are reported in Tab. 1. The
selection of the mass parameter that is fixed in the scan is based on choosing
the one whose variation does not change the kinematics or produces the
smallest effect for the signature under consideration.222 For the case of the
1-vs-1 unbalanced topology, the mass of the mediator $m_{M}$ was formally set
to $m_{M}=600$ GeV throughout this paper, however, this value has no impact on
the results of this topology.

Topology | Mass fixed | Masses varied | Kin. constraints | No. points
---|---|---|---|---
1-vs-1 unbalanced | $m_{M}$ | $(m_{\Phi},m_{I})$ | $m_{\Phi}\geq m_{I}+m_{Z}$ | 300
2-vs-1 balanced | $m_{\Phi}$ | $(m_{M},m_{I})$ | $m_{\Phi}\geq m_{I}+m_{M}$ | 80
$m_{M}\geq m_{I}+m_{Z}$
2-vs-1 unbalanced | $m_{I}$ | $(m_{\Phi},m_{M})$ | $m_{\Phi}\geq m_{Z}+m_{M}$ | 300
$m_{M}\geq 2m_{I}$
2-vs-2 balanced | $m_{\Phi}$ | $(m_{M},m_{I})$ | $m_{\Phi}\geq 2m_{M}$ | 28
$m_{M}\geq m_{I}+m_{Z}$
$m_{M}\geq 2m_{I}$
Table 1: The two-dimensional mass scans that have been performed for the four
signal topologies. The second column indicates which mass parameter has been
fixed in the scan, while the third one specifies the masses that were scanned
for a given topology. The kinematic constraints taken into account when
generating the individual mass grids are shown in the fourth column. In the
last column the total number of mass points generated for each case is given.

The dominant background of $Z/\gamma^{*}\rightarrow ll$, denoted as Z+jets,
has been generated at leading order with MadGraph5_aMC@NLO interfaced to
Pythia using the MLM matching scheme to properly describe hard emissions of up
to four extra jets. The Powheg v.2 [33, 34] generator interfaced to Pythia for
showering is employed to generate top-quark pair production ($t\bar{t}$) and
single-top processes at next-to-leading-order (NLO) in QCD. The various di-
boson processes ($WW$, $WZ$, and $ZZ$) are produced at LO accuracy using
Pythia as both matrix element and parton shower generator.

The set of parton distribution functions (PDFs) used for simulating all the
above samples is NNPDF 3.1 NNLO [35], which have been accessed through the
LHAPDF interface [36, 37]. All background MC samples have been generated in
the five flavour (5F) scheme, whereas the signal samples were produced in the
4F scheme. The detector response simulation for all samples has been performed
with the Delphes 3.5.0 [38] package using the default configuration for the
case of the CMS detector. For simplicity, simultaneous $pp$ collisions usually
occurring in the same bunch crossing or in nearby bunch crossings, and
commonly known as pileup, are not considered in the simulation. The analysis
described in the next section has been done within the framework of
MadAnalysis5 1.8.45 [39].

##  4 Analysis of the $pp\to b\bar{b}\Phi(\to Z+{p_{\text{T}}^{\text{miss}}})$
process

###  4.1 Event selection

The event selection targets a signal topology in which a substantially boosted
$Z$ boson is produced in association with a pair of relatively forward
$b$-jets. Due to the invisible particles in the final state, events are
moreover characterized by large missing transverse momentum,
${p_{\text{T}}^{\text{miss}}}$. The selection of the final state particles,
i.e. the leptons ($e$ and $\mu$), jets and ${p_{\text{T}}^{\text{miss}}}$, is
designed to be as inclusive as possible with respect to the scanned mass
points.

Electrons and muons are selected if they fall within the pseudorapity range
$|\eta|<2.4$, and if they both have at least a transverse momentum of
$p_{\mathrm{T}}>10$ GeV, here called loose leptons. Signal leptons, referred
to as leptons, are expected to be more energetic due to the boosted $Z$ boson,
hence a higher cut of $p_{\mathrm{T}}>20$ GeV is applied. Additionally, an
isolation requirement is added for both electrons and muons. For electrons the
isolation is calculated using the energy deposited in a cone of $\Delta R<0.3$
around the electron and required to be less than 15% of the electron energy.
For muons the isolation is calculated from the energy of all tracks in a cone
of $\Delta R<0.3$ around the muon and required to be less than 10% of the muon
energy.

Selected jets must have a minimum transverse momentum of $p_{\mathrm{T}}>20$
GeV. Two main jet definitions are used in the analysis; the standard jets,
which are additionally required to have a pseudorapidity value satisfying
$|\eta|<2.4$, and the forward jets, allowed to reach pseudorapidity values of
up to $|\eta|<5$. The latter are relevant given the marked presence of jets
with high pseudorapidity in the signal processes. The standard jets are
further labeled depending on whether they pass the $b$-tagging algorithm or
not. If they pass the criterion, they are called b-tagged jets. All jets are
cleaned by requiring the absence of any type of loose lepton inside a cone of
$\Delta R<0.4$ around the jet momentum.

The base event selection starts by requiring the presence of exactly two
leptons of same flavour and vetoing events with additional loose leptons.
Selected leptons must be oppositely-charged, and their invariant mass must be
within a window of $76\,\text{GeV}<m(l^{+}l^{-})<106\,\text{GeV}$, which
corresponds to the bulk of the distribution of the reconstructed $Z$ boson
mass. In order to reduce the $VV$ and $Z$+jets backgrounds while keeping
almost the entire signal, a cut on the transverse momentum of the leading
lepton of $p_{\mathrm{T}}(l_{\text{lead}})>50$ GeV is applied, as well as on
the transverse momentum of the di-lepton system with the same lower threshold
of $p_{\mathrm{T}}(l^{+}l^{-})>50$ GeV. Moreover, the angular separation
between the two leptons is required to be $\Delta R(l^{+},l^{-})<3$. Given
that in most signal scenarios the largest amount of
${p_{\text{T}}^{\text{miss}}}$ is usually produced when the invisible
particles are back-to-back with respect to the $Z$ boson, a moderate lower
threshold for the difference in azimuthal angle between $p^{\text{
miss}}_{\text{T}}$ and the di-lepton system is included in the selection,
applying $\Delta\phi(\vec{p}^{\text{ miss}}_{\mathrm{T}},l^{+}l^{-})>0.5$. In
all signal topologies there is a relatively heavy intermediate resonance
($\phi$). Thus, a large reconstructed invariant mass of its decay products is
expected. However, as it is only possible to estimate the missing momentum in
the transverse plane, the transverse mass of the $p^{\text{ miss}}_{\text{T}}$
and di-lepton systems, partly encoding the information about the mass of
$\phi$, is used instead in order to further reduce the SM background, imposing
$m_{T}(\vec{p}^{\text{ miss}}_{\text{T}},l^{+}l^{-})>140\,\text{GeV}$.

Two signal regions are constructed based on the information coming from the
jets in the event. The first region, named as Standard-SR, is defined by
requiring at least one $b$-tagged jet in the event on top of the above base
selection. The other signal region, named ForwardJets-SR, is constructed by
demanding no $b$-tagged jets but at least two forward jets with a separation
in pseudorapidity of $|\eta(j_{1})-\eta(j_{2})|>2.5$. If more than two forward
jets are found in the event, the pair combination with the largest value for
this quantity is considered for the above condition. No requirement is imposed
on the ${p_{\text{T}}^{\text{miss}}}$, given that the full distribution is
employed in the statistical analysis, as it will be explained in detail later.
A summary of all the kinematic selections described above can be found in
Table 2.

Quantity | Standard-SR | ForwardJets-SR
---|---|---
$N_{l}$ (opposite-charge, same-flavour) |  $=2$ (with additional lepton veto)
$p_{\text{T}}(l)$ |  $50/20$ GeV leading/trailing
$m(l^{+}l^{-})$ | $76\,\text{GeV}<m(l^{+}l^{-})<106\,\text{GeV}$
$p_{\text{T}}(l^{+}l^{-})$ |  $>50$ GeV
$\Delta R(l^{+},l^{-})$ | $<3$
$\Delta\phi(\vec{p}^{\text{ miss}}_{\text{T}},l^{+}l^{-})$ | $>0.5$
$m_{\text{T}}(\vec{p}^{\text{ miss}}_{\text{T}},l^{+}l^{-})$ |  $>140$ GeV
$N_{\text{b-tag}}$ | $\geq 1$ | $=0$
$|\eta(j_{1})-\eta(j_{2})|_{\text{max}}$ | $-$ | $>2.5$
Table 2: Summary of the kinematic selections for the two defined signal
regions.

###  4.2 Signal selection efficiency

In order to study the efficiency of the above selection for the four
topologies described in Section 2, a scan on the mass parameters
$(m_{\Phi},m_{M},m_{I})$ is carried out as specified in Tab. 1, and the
overall efficiency is determined. For each topology one of the three mass
parameters is kept fixed, while the other two masses are varied simultaneously
in order to obtain a 2D map of the analysis efficiency per topology. This is
performed individually for both signal regions defined above. The obtained
values for the Standard-SR and the ForwardJets-SR are depicted in Fig. 2 and
Fig. 3 respectively.

Figure 2: Analysis efficiency (including detector acceptance) for the
selection corresponding to the Standard-SR (for a sample produced with the
charged lepton decays of the Z boson). The horizontal and vertical axes
indicate the mass combination for which the efficiency is measured, while the
color coding indicates the efficiency value obtained for this mass
combination. The results are shown for the 1-vs-1 unbalanced (upper left
panel), 2-vs-1 balanced (upper right panel), 2-vs-1 unbalanced (lower left
panel), and 2-vs-2 balanced (lower right panel) topologies. The kinematic
constraints for each topology are indicated by solid red lines, whereas the
fixed mass value is specified in the legend.

Figure 3: Analysis efficiency (including detector acceptance) for the
selection corresponding to the ForwardJets-SR (for a sample produced with the
charged lepton decays of the $Z$ boson). The horizontal and vertical axes
indicate the mass combination for which the efficiency is measured, while the
color coding indicates the efficiency value obtained for this mass
combination. The results are shown for the 1-vs-1 unbalanced (upper left
panel), 2-vs-1 balanced (upper right panel), 2-vs-1 unbalanced (lower left
panel), and 2-vs-2 balanced (lower right panel) topologies. The kinematic
constraints for each topology are indicated by solid red lines, whereas the
fixed mass value is specified in the legend.

First, one can notice that the Standard-SR has an overall larger efficiency
for all signal topologies compared to the ForwardJets-SR, though the
contribution of the latter is clearly non-negligible. The highest efficiency
value for the Standard-SR occurs for the 2-vs-1 unbalanced topology and for a
mass combination of about ($2100$ GeV, $1500$ GeV, $10$ GeV) reaching up to
$0.168\pm 0.002$333A value that is consistent within the statistical
uncertainty is obtained for the 1-vs-1 unbalanced topology for ($2100$ GeV,
$600$ GeV, $1500$ GeV)., where the reported uncertainty is purely statistical.
Similarly high values of the efficiency are also found for various points
along the approximate line $m_{\Phi}-m_{M}=600$ GeV for the 2-vs-1 unbalanced
topology, and for points near $m_{\Phi}-m_{I}=600$ GeV in the 1-vs-1
unbalanced topology. For the ForwardJets-SR, the highest efficiency is also
reached for the 2-vs-1 unbalanced topology, but this time for a mass
combination of ($2500$ GeV, $1900$ GeV, $10$ GeV), resulting in an efficiency
of $0.128\pm 0.002$. This demonstrates that the analysis is highly efficient
for signal scenarios with a semi-boosted regime, which can be deduced from the
event selection using relatively energetic leptons coming from the $Z$ boson.
In the case of extremely boosted $Z$ bosons, the two lepton signatures
overlap, impacting on their reconstruction and causing the isolation criteria
to reject most of those events. An additional feature that is observed in the
ForwardJets-SR for the two unbalanced topologies is that the efficiency gets
larger for increasing mass $m_{\Phi}$ of the scalar resonance (for a fixed
mass difference $m_{\Phi}-m_{I}$ (for 1-vs-1 unbalanced) or $m_{\Phi}-m_{M}$
(for 2-vs-1 unbalanced)). This is caused by the fact that the jets point more
into the forward or backward direction as the mass of the heavy resonance is
enhanced, which implies that they are more likely to pass the pseudorapidity
difference cut included in the definition of the ForwardJets-SR. With regard
to the variation in the signal kinematics for the various topologies, one can
observe that the two unbalanced cases closely resemble each other, whereas the
main qualitative difference occurs when comparing the balanced with the
unbalanced cases. For the balanced topologies, the variation in the selection
efficiency is less pronounced as one moves across the scanned phase space,
given that here $m_{\Phi}$ has been fixed. The most visible variation in the
2-vs-1 balanced topology occurs (besides kinematic edges) where the difference
$m_{M}-m_{I}$ is increased, which results in a slightly more boosted $Z$ boson
and a more sizable imbalance between the $Z$ boson and the $p^{\text{
miss}}_{\text{T}}$. In the 2-vs-2 balanced topology, the variations in
$m_{M}-m_{I}$ can barely modify the above-mentioned imbalance, since an
invisible decay of the mediator occurs in both legs of the diagram.

###  4.3 Background expectation

The multiple background processes contributing to the selection described in
Section 4.1 are estimated using simulation, which is detailed in Section 3.
The main SM processes that pass the selection are $Z+\text{jets}$, $t\bar{t}$,
single-top ($tW$ channel), and di-boson production. The $Z+\text{jets}$
process enters in the Standard-SR selection if a relatively boosted $Z$ boson
is produced in association with a $b$-quark, whereas if a similarly energetic
$Z$ boson is produced through di-boson production it becomes more likely that
it will contribute to the ForwardJets-SR. The $t\bar{t}$ production with di-
leptonic decay also poses a substantial background component, given the
presence of $b$-quarks in the final state and the fact that
${p_{\text{T}}^{\text{miss}}}$ is generated by neutrinos. The production of a
single top quark, specifically in the $tW$ channel with di-leptonic decay,
exhibits a very similar signature compared to $t\bar{t}$, only differentiated
at Born level by having one less $b$-quark. In both cases, if the $b$-quark(s)
are not tagged as $b$-jet(s) during the selection, the event could end up in
the ForwardJets-SR, with possible contributions of other jets arising from QCD
initial or final state radiation. $WW$, $WZ$, and $ZZ$ production with
additional jets can also enter both signal regions. For $WZ$, if the lepton
from the $W$ boson is not reconstructed, this background resembles the signal
signature; this also happens if one of the $Z$ bosons in the $ZZ$ process
decays into a pair of neutrinos while the other decays into a lepton pair. In
the case of the $WW$ process, the signature is similar to that of the
$t\bar{t}$ and $tW$ processes, where additional ($b$-)jets can arise from QCD
radiation.

A summary of the expected event yields for the various background components
assuming an integrated luminosity of 137 fb-1 444This is approximately the
amount of luminosity collected by the CMS experiment during the Run 2 data
taking period (see Run2:Luminosity), and it will be used as reference for most
of the results presented in this work. is reported in Tab. 3.

Process | Standard-SR | ForwardJets-SR
---|---|---
$Z+\text{jets}$ | $350147\pm 18557$ | $618659\pm 24667$
$t\bar{t}$ |  $72839\pm 421$0 | $7672\pm 137$
Single-top ($tW$) |  $6380\pm 59$0 | $826\pm 21$
$WW$ |  0$77\pm 13$ | $224\pm 22$
$WZ$ |  $143\pm 6$0 | $749\pm 14$
$ZZ$ |  $149\pm 3$0 |  $462\pm 5$0
Table 3:  Yield estimates in the two defined signal regions for the different
background processes contributing after the selection specified in Section 4.1
for a reference integrated luminosity of 137 fb-1. The reported uncertainty
represents solely the statistical component.

As can be noticed, the remaining background after the selection in both signal
regions is relatively high, and this can be understood if one takes into
account that no requirement has been imposed on
${p_{\text{T}}^{\text{miss}}}$. This has been done on purpose to keep the
selection as inclusive as possible with respect to highly diversified
kinematics resulting from the multiple signal scenarios explored; the strategy
to follow in order to boost the sensitivity for all signal topologies will be
outlined in the next section. Table 3 elucidates the fact that $Z+\text{jets}$
amply dominates the background composition in both signal regions, though this
particular background will be relatively easy to discriminate using
${p_{\text{T}}^{\text{miss}}}$, as it will be illustrated in Section 4.4.
Another clear observation extracted from the above table is that $t\bar{t}$
and $tW$ backgrounds are more prominent in the Standard-SR, something that
would be expected given the $b$-jet requirement in this region and the $b$-jet
veto in the ForwardJets-SR. The consequences of that will be more clear when
evaluating the expected sensitivity of the analysis per signal region, as
despite the analysis having a larger efficiency in the Standard-SR (see Fig. 2
and Fig. 3), the smaller contribution of processes with a substantial tail in
the ${p_{\text{T}}^{\text{miss}}}$ distribution ($t\bar{t}$ and $tW$) provides
the ForwardJets-SR with a solid discriminating power.

###  4.4 Limit extraction method

As mentioned in the previous section, an optimisation of the analysis for a
specific signal topology will lead to a drastic reduction in sensitivity for
other kinematically distinct topologies. Consequently, the strategy devised
for the present analysis was to keep the selection as inclusive as possible
and to try to implement a robust statistical analysis in one of the most
powerful observables to achieve a strong level of discrimination in the
majority of signal regimes. The variable designated to accomplish that task
was the ${p_{\text{T}}^{\text{miss}}}$, given the huge discrimination against
the dominant $Z+\text{jets}$ background (which does not have a genuine
${p_{\text{T}}^{\text{miss}}}$ contribution) and the moderate separation
against all the other backgrounds mentioned in Section 4.3. The statistical
inference is then performed using a shape scanning over the binned
${p_{\text{T}}^{\text{miss}}}$ distribution. The selected binning, which has
been chosen according to both statistical and sensitivity considerations, is
shown in Table 4 for both signal regions.

Region | Number of ${p_{\text{T}}^{\text{miss}}}$ bins | Bin edges in ${p_{\text{T}}^{\text{miss}}}$ [GeV]
---|---|---
Standard-SR | 10 | $[0,20,40,70,100,135,190,280,400,550,1000]$
ForwardJets-SR | 8 | $[0,20,40,70,100,150,240,360,1000]$
Table 4:  Binning in ${p_{\text{T}}^{\text{miss}}}$ chosen for each of the two
signal regions. All events with ${p_{\text{T}}^{\text{miss}}}>1000\text{ GeV}$
are added to the last bin of the respective region.

The corresponding ${p_{\text{T}}^{\text{miss}}}$ distributions for all
background processes and for a few benchmark signal points are presented in
Fig. 4. It can be noticed there that the $Z+\text{jets}$ process has a
negligible contribution in bins with high signal expectation, therefore weakly
impacting the full significance of the analysis. The other processes, however,
do present relatively large ${p_{\text{T}}^{\text{miss}}}$ due to the genuine
presence of invisible particles, and are the contributions that determine in
the end the overall analysis sensitivity. In terms of signal shapes, one can
see a clear difference between the balanced and the unbalanced cases, but
among signal topologies of the same kind (e.g. 1-vs-1 unbalanced compared to
2-vs-1 unbalanced), the distinction is much less pronounced, in agreement with
what was perceived from the signal efficiency maps obtained in Section 4.2.

Figure 4:  Binned ${p_{\text{T}}^{\text{miss}}}$ distributions for both signal
regions, Standard-SR (left panel) and ForwardJets-SR (right panel),
constructed to perform the statistical analysis corresponding to the limit
extraction procedure. All processes, including the benchmarks chosen for the
signal topologies, have been normalized to an integrated luminosity of 137
fb-1, where for all the signal benchmark scenarios shown (dashed histograms),
a common cross section of 1 pb has been used for their normalization. For all
signal topologies, the mass combination used was ($1000$ GeV, $300$ GeV, $100$
GeV), except for the 1-vs-1 unbalanced topology, where $m_{M}$ is irrelevant
(see above), and the 2-vs-1 unbalanced topology, where $m_{I}=10$ GeV was
used; it should be noted that these modifications do not significantly alter
the shape of the ${p_{\text{T}}^{\text{miss}}}$ distribution. The various
background processes have been stacked up to illustrate the overall background
contribution. The various di-boson processes ($WW$, $WZ$, and $ZZ$) have been
grouped under the label $VV$.

The statistical model is built using the template shapes displayed in Fig. 4
for each given process. On top of the statistical uncertainty resulting from
the limited number of MC events in the samples per bin, various systematic
uncertainties affecting the normalization have been incorporated to make the
results more realistic. An uncertainty has been assigned to the integrated
luminosity value used, corresponding to 2.5%, where we refer to the measured
uncertainty value by CMS in 2018 [41]. An uncertainty on the normalization of
the $t\bar{t}$ process, and consequently affecting only this template, with a
value of 5% is included, assuming the latest precision achieved by the
theoretical calculations of the cross section [42]. Similarly, a value of also
5% [43] is considered for the single-top production through the $tW$ channel.
For the case of the $Z+\text{jets}$ process, and given the more specific
configuration used to generate events, we have used the uncertainty value
obtained after running the FEWZ 3.1 program presented in Li:2012wna, which
corresponds to a total uncertainty of 2.5% on the cross section. For $VV$, and
taking into account the combination of multiple individual processes into this
template, a conservative 15% uncertainty is assumed, which is close to the
uncertainty value delivered by most NLO MC generators like MC@NLO and POWHEG
for these processes.

The limits are computed using the RooStats package [45] by means of the
HistFactory interface [46] that is implemented in ROOT [47]. The calculation
is made using the asymptotic approximation in RooStats, which is an
implementation of the results obtained in Cowan:2010js, and also considering
the CLs method described in Read:451614. Two categories corresponding to the
two signal regions are constructed. Thus, limits for each individual category
as well as for the combination of both categories are provided. A confidence
level (CL) of 95% has been used to compute all the limits that will be
presented in this work.

##  5 Expected sensitivity

The expected sensitivity of this analysis is evaluated by setting limits in
the absence of a signal on the product of the production cross section times
the full branching fraction for a given topology, i.e.
$\sigma(b\bar{b}\Phi)\times\mathcal{B}(\Phi\rightarrow
Z+{p_{\text{T}}^{\text{miss}}})\times\mathcal{B}(Z\rightarrow l\bar{l})$.
Here, the term $\mathcal{B}(\Phi\rightarrow Z+{p_{\text{T}}^{\text{miss}}})$
depends on the specific decay case covered by the signal topology; as an
example, for the 2-vs-1 unbalanced topology (Fig. 1(c)) that terms read
$\mathcal{B}(\Phi\rightarrow
Z+{p_{\text{T}}^{\text{miss}}})\equiv\mathcal{B}(\Phi\rightarrow
ZM)\times\mathcal{B}(M\rightarrow II)$.

Two sets of results are presented in terms of limits on the cross section. The
first group corresponds to 1D projections, where two of the mass parameters
are fixed and the remaining mass is varied. In those results the sensitivity
of the two defined signal regions can easily be compared with each other and
with the combined sensitivity. Furthermore, we will indicate the bands
corresponding to one and two standard deviations from the reported central
value. The second set of results are 2D limit scans corresponding to the ones
presented in Figs. 2 and 3 for the efficiency case. In those results we
display the central limit value obtained from the combination of the two
signal regions.

###  5.1 Limit Scan in 1D

Figure 5: Expected upper limits on the cross section times branching fraction
(as defined in the text) for a 1D variation of one of the mass parameters in
each topology. The horizontal axis indicates the varied mass parameter, while
the vertical axis represents the upper limit obtained at 95% CL for various
scenarios: the central limit obtained using only the Standard-SR (red dotted
line), the central limit obtained using only the ForwardJets-SR (blue dotted
line), and the central limit obtained combining the two signal regions (black
solid line). The green and yellow uncertainty bands correspond to the 68% and
95% interval coverage for the combined limit, respectively. The results are
shown for the 1-vs-1 unbalanced (upper left panel), 2-vs-1 balanced (upper
right panel), 2-vs-1 unbalanced (lower left panel), and 2-vs-2 balanced (lower
right panel) topologies. The choice for the two mass parameters that have been
kept fixed is indicated in the legend for each signal topology.

Figure 6: As in Fig. 5, but for different choices of the varied and fixed mass
parameters.

The 1D limit projections are shown in Figs. 5 and 6. The first observation to
be made is with respect to the individual sensitivity reached by the two
signal regions. The individual limits are close to each other for all
different variations presented in the figures, which points to the fact that
the two regions are similarly important with respect to the overall
sensitivity of the analysis. This is explained by the limited efficiency of
identifying one $b$-tagged jet for the signal scenarios that are investigated
here, caused by both the forward kinematics of the jets and the performance of
the $b$-tagging algorithm. On the other hand, the low rate of forward jets in
the background processes dominating for this di-lepton selection makes the
ForwardJets-SR highly competitive despite having a slightly lower overall
signal efficiency, as this signal region benefits from a drastic reduction of
the overwhelming high-${p_{\text{T}}^{\text{miss}}}$ top background. This
becomes particularly evident in the $m_{I}$ and $m_{M}$ scans for the
unbalanced topologies in Fig. 5, where one can see that the ForwardJets-SR
provides almost identical sensitivity to the Standard-SR in the entire mass
range.

Another interesting piece of information that can be extracted from these
results, and that was also asserted in the analysis of the efficiencies in
Sec. 4.2, is that there is no intrinsic difference in the signal kinematics
for the two unbalanced topologies; in good approximation these two topologies
can be treated such that they yield identical results, and this is verified in
both projections shown in Figs. 5 and 6. This means that any experimental
analysis optimized for one of those two topologies is automatically optimal
for the other one as well. In the case of the analysis presented in this work,
it can be corroborated from the limits that our analysis is highly sensitive
to scenarios with semi-boosted $Z$ bosons, occurring for a mass difference
$m_{\Phi}-m_{I}$ (for 1-vs-1 unbalanced) or $m_{\Phi}-m_{M}$ (for 2-vs-1
unbalanced) of around 1 TeV. The situation for the balanced topologies is
slightly more involved. Even though the results are very close to each other
if $m_{M}$ is sufficiently small (see Fig. 6 right panel), with increasing
mediator mass the limits depart from each other substantially, and the limits
for the 2-vs-1 balanced topology are found to be up to a factor of two
stronger compared to the 2-vs-2 balanced topology for the same mass
parameters. This effect can be explained from the discussion of the efficiency
results in Sec. 4.2. It arises from the fact that the $Z$ boson becomes more
boosted for the 2-vs-1 balanced case if the difference $m_{M}-m_{I}$
increases.

###  5.2 Limit Scan in 2D

Analogously as it was done for the signal efficiency in Section 4.2, a scan in
the 2D plane formed by the two mass parameters that are varied is performed to
get the cross section limit map for each signal topology. The results are
shown in Fig. 7, where the limit obtained from the combination of the two
signal regions is depicted.

Figure 7: Expected upper limits on the cross section times branching fraction
(as defined in the text) for a 2D variation of the mass parameters in each
topology. The horizontal and vertical axes indicate the mass combination for
which the limit is calculated, while the color coding represents the central
value obtained at 95% CL combining the two signal regions for that specific 2D
point. The results are shown for the 1-vs-1 unbalanced (upper left panel),
2-vs-1 balanced (upper right panel), 2-vs-1 unbalanced (lower left panel), and
2-vs-2 balanced (lower right panel) topologies. The kinematic constraints for
each topology are indicated by solid red lines, whereas the fixed mass value
is specified in the legend.

At first glance, a comparison with the patterns observed in the efficiency
maps reveals a quite close similarity between the upper limits and the signal
efficiency. This effect is of course expected given that the signal
normalization is the main factor contributing to the constraint imposed on the
cross section. Nevertheless, a closer look at Fig. 7, in particular at the
limit maps corresponding to the unbalanced topologies (left panel), evidences
a shift of the region with the most stringent limits with respect to the
region with the largest efficiency towards higher mass differences
$m_{\Phi}-m_{I}$ (for 1-vs-1 unbalanced) or $m_{\Phi}-m_{M}$ (for 2-vs-1
unbalanced). The size of this shift for the unbalanced cases ranges from 100
GeV to 400 GeV depending on the heavy scalar mass, and is a consequence of
exploiting the shape of the ${p_{\text{T}}^{\text{miss}}}$ distribution as a
further constraint on the models. For larger mass differences (above $\sim
600\text{ GeV}$) the efficiency tends to drop due to the collimation of the
leptons from the $Z$ boson decay, but at the same time the
${p_{\text{T}}^{\text{miss}}}$ distribution starts to peak at higher values,
which compensates the loss in signal acceptance by an increased significance
in the last bins of the ${p_{\text{T}}^{\text{miss}}}$ distribution (see Fig.
4). This effect is less obvious to discern for the two balanced topologies
where the additional boosting created by more unbalanced configurations is
either almost non-existent (2-vs-2 balanced) or localized in the corners of
the phase space (2-vs-1 balanced). The strongest upper limits obtained for the
1-vs-1 unbalanced and the 2-vs-1 unbalanced topologies are around $3.5\times
10^{-4}~{}\text{pb}$, whereas they are close to $5.5\times
10^{-4}~{}\text{pb}$ and $4.5\times 10^{-3}~{}\text{pb}$ for the 2-vs-1
balanced and 2-vs-2 balanced topologies, respectively. In terms of
similarities among the signal topologies, Fig. 7 confirms once again that the
unbalanced topologies lead to an equivalent kinematic configuration, while the
two balanced scenarios lead to a slight difference in kinematics if they are
compared to each other for the same mass range. Our results presented here and
in Section 5.1 show that a clear distinction can be made between the
unbalanced and the balanced scenarios, which motivate specific experimental
analyses optimized for each case individually.

###  5.3 2HDMa interpretation

After deriving model-independent limits, we here demonstrate how these limits
can be employed to constrain a concrete BSM model. As an exemplary
model,555See Bahl:2021xmy for more examples of models with similar
experimental signatures. we study the Two-Higgs-Doublet model (2HDM) with an
additional pseudoscalar, which serves as a dark matter portal. This model is
usually referred to as 2HDMa.

In addition to the usual 2HDM (see e.g. Branco:2011iw for a review), the 2HDMa
adds the following terms to the Lagrangian [51, 27],

$\displaystyle\mathcal{L}_{\text{2HDMa}}={}$
$\displaystyle\mathcal{L}_{\text{2HDM}}+\bar{\chi}(\not{\partial}+m_{\chi})\chi-
y_{\chi}a_{0}\bar{\chi}i\gamma^{5}\chi$
$\displaystyle+\frac{1}{2}\partial_{\mu}a_{0}\partial^{\mu}a_{0}-\frac{1}{2}m_{a_{0}}^{2}a_{0}^{2}+i\kappa
a_{0}\Phi_{1}^{\dagger}\Phi_{2}+\text{h.c.}+\ldots,$ (1)

where $a_{0}$ is the additional gauge-singlet pseudoscalar of mass
$m_{a_{0}}$, $\chi$ is a Dirac fermion dark matter candidate of mass
$m_{\chi}$, and $\Phi_{1,2}$ are the two 2HDM doublets. The dark sector Yukawa
coupling is denoted as $y_{\chi}$. The portal coupling $\kappa$ and the
pseudoscalar mass $m_{a_{0}}$ are parameters with mass dimension one. The
ellipsis denotes additional quartic interactions which are not relevant for
our discussion here. After electroweak symmetry breaking, the 2HDM
pseudoscalar, which we denote by $A_{0}$, will mix with $a_{0}$ (with the
mixing angle $\theta$) leading to the mass eigenstates $a$ and $A$.

This model has been used as a possible explanation for the gamma ray Galactic
Centre excess observed by the Fermi-LAT space telescope [52, 53, 54] and for
the baryon asymmetry of the Universe [55]. Moreover, this model is often used
as a benchmark model for LHC dark-matter searches [27]. As discussed in
Tunney:2017yfp, the LHC signature

$\displaystyle pp\to b\bar{b}H\to b\bar{b}Za\to
b\bar{b}l^{+}l^{-}\chi\bar{\chi}$ (2)

could be a promising way to test this explanation of the Galactic Centre
excess, which so far cannot be probed by other constraints.

This signature can be straightforwardly mapped to our 2-vs-1 unbalanced
simplified model topology: $H$ plays the role of the scalar resonance $\Phi$;
$a$ is the neutral mediator $M$; and $\chi$ is the invisible particle $I$.
This mapping allows us to easily reinterpret the model-independent expected
limits derived above within the 2HDMa parameter space.

We calculate the cross section for the process in Eq. 2 at the leading order
using MadGraph5_aMC@NLO (v2.6.5). These cross section values are then compared
to the expected limits presented in the lower left panel of Fig. 7. We also
show projections for increased luminosities by simply rescaling the limits by
the square root of the relative increase in luminosity.

Figure 8:  Projected expected limits on the 2HDMa parameter space in the
$(m_{a},s_{\theta})$ parameter plane (upper left), in the $(m_{H},m_{a})$
parameter plane (upper right), in the $(s_{\theta},\tan\beta)$ parameter plane
(lower left), and in the $(m_{H},\tan\beta)$ parameter plane (lower right).
The limits are shown for three different luminosities: $137\;\text{fb}^{-1}$
(blue), $300\;\text{fb}^{-1}$ (red), and $3000\;\text{fb}^{-1}$ (green). For
the lower right parameter plane, we also show the limit presented in
ATLAS:2021gcn.

Fig. 8 shows the resulting constraints on the 2HDMa parameter space in four
different parameter planes. In the upper left panel, we show the
$(m_{a},s_{\theta})$ parameter plane with $m_{H}=600\;\text{GeV}$ and
$\tan\beta=10$. With a luminosity of $137\;\text{fb}^{-1}$, pseudoscalar
masses of up to $300\;\text{GeV}$ can be probed; $s_{\theta}$ can be probed
down to values of $\sim 0.15$.666For $s_{\theta}\to 1$ the cross section for
the process in Eq. 2 goes to zero resulting in a rapid loss of sensitivity.
Increasing the luminosity enhances the sensitivity, especially in the low
$s_{\theta}$ region. Our projected limit is in good agreement with the
projection obtained in Tunney:2017yfp confirming the potential to probe models
that provide explanations for the Galactic Centre excess.777Small differences
can be explained by the inclusion of a $K$ factor of 1.4 for the bottom-
associated Higgs production cross section and by a more simplified treatment
of detector effects in Tunney:2017yfp. The selection cuts in Tunney:2017yfp
are, moreover, optimized for the unbalanced topology.

The limits are shown in the $(m_{H},m_{a})$ parameter plane fixing
$s_{\theta}=0.35$ and $\tan\beta=10$ in the upper right panel of Fig. 8. The
gray line delimits the physical region for which $m_{H}\geq m_{a}+m_{Z}$. With
a luminosity of $137\;\text{fb}^{-1}$ the proposed search can probe scalar
masses up to $\sim 1.1\;\text{TeV}$. Increasing the luminosity to
$300\;\text{fb}^{-1}$ ($3000\;\text{fb}^{-1}$), masses up to $1.2\;\text{TeV}$
($1.4\;\text{TeV}$) are tested.

In the 2HDMa, the bottom-associated $H$ production is enhanced for large
$\tan\beta$. Correspondingly, stronger limits in the large $\tan\beta$ region
are expected. This is confirmed in the lower left panel of Fig. 8, which shows
the limits in the $(s_{\theta},\tan\beta)$ parameter plane for
$m_{H}=600\;\text{GeV}$ and $m_{a}=150\;\text{GeV}$. As expected from the
dependence of the cross-section on $s_{\theta}$ and $\tan\beta$, the limits
are strongest for $s_{\theta}\sim 0.9$ and large $\tan\beta$. With a
luminosity of $137\;\text{fb}^{-1}$, $\tan\beta$ values down to $\sim 6$ can
be probed for $s_{\theta}\sim 0.9$. Increasing the luminosity to
$300\;\text{fb}^{-1}$ ($3000\;\text{fb}^{-1}$), $\tan\beta$ values down to
$\sim 5$ ($\sim 3$) are tested.

The dependence on $\tan\beta$ is further explored in the lower right panel of
Fig. 8, which shows the limits in the $(m_{H},\tan\beta)$ plane for
$s_{\theta}=0.35$ and $m_{a}=250\;\text{GeV}$. While the proposed search is
not able to probe the region of $\tan\beta\lesssim 3$ even with
$\mathcal{L}=3000\;\text{fb}^{-1}$, the interval $500\;\text{GeV}\lesssim
m_{H}\lesssim 1600\;\text{GeV}$ can be probed for larger $\tan\beta$. For
comparison, we also show the 2HDMa limit set by the search presented by the
ATLAS Collaboration in ATLAS:2021gcn with a luminosity of
$139\;\text{fb}^{-1}$. We observe that this limit is significantly stronger
than our projection for $\mathcal{L}=137\;\text{fb}^{-1}$ and
$\mathcal{L}=300\;\text{fb}^{-1}$. Moreover, it also outperforms our
projection for $\mathcal{L}=3000\;\text{fb}^{-1}$ except for a parameter
region with relatively small $\tan\beta$. This difference in sensitivity is
mainly a consequence of the different final states considered in our analysis
and in ATLAS:2021gcn. In contrast to our proposed search, ATLAS:2021gcn vetoes
$b$-jets in the final state, searching for a $Z+{p_{\text{T}}^{\text{miss}}}$
final state. While the $b\bar{b}Z+{p_{\text{T}}^{\text{miss}}}$ final state,
which our analysis targets, allows one to identify the production mode in case
a signal is detected, the $Z+{p_{\text{T}}^{\text{miss}}}$ final state seems
to have better sensitivity in comparison to the bottom-associated Higgs
production in the case of the 2HDMa. Moreover, it should be noted that our
simplified analysis relies on a simplified detector simulation, is not
optimized for the unbalanced topology, and, moreover, does not use advanced
multivariate analysis techniques.

##  6 Conclusions

While it is expected that the production of DM at colliders will result in an
increased amount of ${p_{\text{T}}^{\text{miss}}}$ in the detectors, the exact
way in which this additional source of missing momentum will manifest itself
is of course not established. Most existing searches are focused on well-
motivated but at the same time specific models with a determined unbalanced
event topology, for which the missing transverse momentum recoils against the
visible particles. This restriction reduces the chance for a discovery, since
other BSM models may predict more balanced event topologies.

In this work, we have studied the capability of a potential new search in the
context of a greater variety of theoretical scenarios based on a flexible
simplified model framework, which covers two unbalanced and two balanced event
topologies. Our detailed collider study focuses on bottom-quark associated
neutral Higgs production with a $b\bar{b}Z+{p_{\text{T}}^{\text{miss}}}$ final
state. The analysis strategy exploited is based on a selection more inclined
towards unbalanced configurations between the ${p_{\text{T}}^{\text{miss}}}$
and the recoiling product.

Our results indicate that in the presence of the $b$-associated production of
a heavy scalar, the inclusion of jets in the forward region of the detectors
plays a very important role in the performance of the analysis. This yields
for the study that is presented here a comparable sensitivity to the one
expected using only the standard central jets with $b$-tagging.

Furthermore, the obtained limits show that the analysis proposed here is well
suited for both unbalanced topologies, yielding almost exactly the same
results in both cases, and thus demonstrating that the kinematics of the two
unbalanced topologies cannot be distinguished with the proposed analysis
(which on the other hand implies that the same search can be applied to a
wider class of theoretical models than the ones addressed by a dedicated
search within a specific model). We showed that the analysis has a significant
sensitivity also for the two balanced topologies, although this sensitivity is
somewhat reduced as compared to the unbalanced case. Such scenarios, where
there is a marked difference in kinematics with respect to the unbalanced
topologies, will probably further profit from a dedicated strategy addressing
the challenges arising when using softer objects and a more relaxed event
selection. In the other extreme, where the $Z$ bosons become highly boosted
and the reconstruction of individual leptons starts to fail, complementary
searches like $b\bar{b}+\text{DM}$ could be of vital importance. As an
additional application of the model-independent results that we have achieved,
we presented projected limits on the 2HDMa parameter space. We find the
projected limits to be not as strong as existing searches that do not require
the presence of $b$-jets in the final state. Those searches are, however, more
optimized for the unbalanced topology and use advanced multivariate analysis
techniques.

In this paper we have demonstrated for the example of the considered search
how results for BSM Higgs searches can be presented in the framework of
simplified models, i.e. within a framework that up to now has been applied
very successfully for direct searches for BSM particles and DM, but so far has
not been used by the experimental collaborations for BSM Higgs searches. We
encourage the experimental collaborations to make use of this framework for
the presentation of their future experimental results.

Finally, we hope that the presented study serves as a starting point for
future experimental efforts which are not restricted to only unbalanced event
topologies. More sophisticated experimental analysis techniques, such as the
inclusion of machine learning and advanced algorithms to discriminate against
the main background processes, could certainly be an important asset when
performing such analyses in a more realistic context.

## Acknowledgements

We thank Jose Miguel No and Katherina Behr for useful discussions. D.P.A.,
A.G., V.M.L., C.S., and G.W. acknowledge support by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s
Excellence Strategy — EXC 2121 “Quantum Universe” — 390833306. H.B.
acknowledges support from the Alexander von Humboldt foundation. V.M.L.
acknowledges the financial support by Ministerio de Universidades and
“European Union-NextGenerationEU/PRTR” under the grant María Zambrano
ZA2021-081, and the Spanish grants PID2020-113775GB-I00
(AEI/10.13039/501100011033) and CIPROM/2021/054 (Generalitat Valenciana). This
work has been partially funded by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) — 491245950.

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