LPT-Orsay-18-73

We examine scenarios in the Next-to-Minimal Supersymmetric Standard Model
(NMSSM), where pair-produced squarks and gluinos decay via two cascades, each
ending in a stable neutralino as Lightest Supersymmetric Particle (LSP) and a
Standard Model (SM)-like Higgs boson, with mass spectra such that the missing
transverse energy, $E_{\text{T}}^{\text{miss}}$, is very low. Performing two-
dimensional parameter scans and focusing on the hadronic $H\rightarrow
b\bar{b}$ decay giving a $b\bar{b}b\bar{b}$ \+ $E_{\text{T}}^{\text{miss}}$
final state we explore the sensitivity of a current LHC general-purpose
jets+$E_{\text{T}}^{\text{miss}}$ analysis to such scenarios.

# Exploring Sensitivity to NMSSM Signatures with Low Missing Transverse Energy
at the LHC

A. Titterton1,2,3, U. Ellwanger4, H.U. Flaecher1, S. Moretti2,3,
C.H. Shepherd-Themistocleous3 1 H.H. Wills Physics Laboratory, University of
Bristol, Bristol, BS8 1TL,
United Kingdom  2 School of Physics and Astronomy, University of Southampton,
Highfield, Southampton, SO17 1BJ, United Kingdom  3 Particle Physics
Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX,
United Kingdom  4 Laboratoire de Physique Théorique, UMR 8627, CNRS,
Université de Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

##  1 Introduction

After four years of proton-proton collisions at the LHC with a centre-of-mass
energy of $\sqrt{s}=7-8$ TeV and a further three with $13$ TeV, searches for
physics Beyond the SM (BSM) have so far not observed any significant excesses.
Particularly, in searches for Supersymmetry (SUSY) [1, 2, 3, 4], this has
allowed lower bounds to be placed on the masses of supersymmetric particles
such as squarks, gluinos, gauginos and Higgsinos.

Recent LHC analyses such as [5], utilising the $\alpha_{\text{T}}$ kinematic
variable [6, 7], have pushed the lower bounds on the squark mass
$M_{\tilde{q}}$ and gluino mass $M_{\tilde{g}}$ well in excess of 1 TeV and
the mass of a neutralino LSP $M_{\tilde{X}^{0}_{1}}$ also as high as $1$ TeV
for certain regions of parameter space of simplified SUSY models [8, 9, 10,
11, 12, 13]. These experimental limits are of course dependent upon various
properties of the decay cascade such as the masses of other sparticles, the
decay branching fractions and the kinematic distributions of the decay
products, but have still ruled out a large area of parameter space in the
MSSM.

The majority of the SUSY search effort so far has relied upon the notion that
an $R$-parity-conserving supersymmetric model is expected to generate events
featuring large missing transverse energy, $E_{\text{T}}^{\text{miss}}$. In
addition, long SUSY decay cascades often imply many hadronic jets with large
transverse momentum, $p_{\text{T}}$, meaning events whose jet $p_{\text{T}}$
scalar sum, $H_{\text{T}}$, is also very high.

Starting from the NMSSM [14] scenarios proposed in [15], we consider the case
where the Next-to-LSP (NLSP) decays into a LSP plus a SM-like Higgs boson,
$H$. In a scenario where the LSP is very soft in this decay the
$E_{\text{T}}^{\text{miss}}$ is reduced considerably. An example of such a
scenario would be for a very light LSP where the NLSP mass,
$M_{\tilde{\chi}_{2}^{0}}$, is just slightly above $M_{\tilde{\chi}_{1}^{0}}$
+$M_{H}$, since the much heavier Higgs boson would inherit most of the
momentum from the NLSP. However, in the MSSM, most of the heavier sparticles
would prefer to skip this NLSP decay step and decay straight into the LSP
instead, thus still generating high $E_{\text{T}}^{\text{miss}}$.

If, in contrast, the LSP were the singlino of the NMSSM [16], having only weak
couplings to sparticles, then the heavier sparticles will decay into a bino-
like NLSP, which plays the role of the MSSM-like LSP. This NLSP then decays
into a soft, “true” LSP and a Higgs boson, thus allowing for these
low-$E_{\text{T}}^{\text{miss}}$ scenarios. In this SUSY scenario, the
singlino is the fermionic counterpart of a singlet superfield $\hat{S}$, where
$S$ is the gauge singlet field to which the coupling of the two Higgs doublets
of the MSSM solves the $\mu$-problem [17].

Furthermore, in the case where we have $M_{\tilde{\chi}_{2}^{0}}$ not much
smaller than $M_{\tilde{q}}$ or $M_{\tilde{g}}$ but still close to
$M_{\tilde{\chi}_{1}^{0}}$ \+ $125$ GeV/$c^{2}$, the now heavy LSP will gain
fairly little extra momentum compared to the initially produced sparticles,
even though it will inherit more of this than the now (in comparison) lighter
Higgs boson. Additionally, the small mass gaps in the decay cascade will mean
low-$p_{\text{T}}$ jets, implying events with low $H_{\text{T}}$ as well as
low $E_{\text{T}}^{\text{miss}}$, in contrast to the typical signature of a
more minimal SUSY model.

As discussed in [15], these NMSSM scenarios with low
$E_{\text{T}}^{\text{miss}}$ generally have weaker constraints imposed by
experimental searches, however, the focus therein was mainly on Run I of the
LHC, with all sparticle masses in the $1-1.5$ TeV/$c^{2}$ range. In order to
gain understanding of the sensitivity to these models which might be attained
with current search efforts in Run II, the CMS $\alpha_{\text{T}}$-based
general-purpose BSM analysis in [5] is examined, which focuses on an all-
hadronic final state and uses $35.9$ fb-1 of CMS data from Run II of the LHC
at a centre-of-mass energy of $\sqrt{s}=13$ TeV.

A similar quantity to $E_{\text{T}}^{\text{miss}}$ which is frequently used in
searches involving hadronic final states is missing-$H_{\text{T}}$, denoted
$H_{\text{T}}^{\text{miss}}$. $H_{\text{T}}^{\text{miss}}$ is defined as the
norm of the two-dimensional vector sum of the transverse momenta of the
_hadronic jets_ in an event within various acceptance regions, such as
$p_{\text{T}}$, $\eta$ and various isolation requirements. On the other hand
$E_{\text{T}}^{\text{miss}}$ includes all objects within these acceptance
regions, such as leptons. Following the approach of
$H_{\text{T}}^{\text{miss}}$ throughout [5], this will be used in lieu of
$E_{\text{T}}^{\text{miss}}$ throughout this paper, noting that these
quantities should be essentially equivalent in the presence of a sufficiently
tight veto on events containing final state leptons.

Starting from the eight Benchmark Points (BPs), denoted BP1, …, BP8 and
presented in table 1, taken from [15], parameter scans are developed which
envelop these points in order to determine the current sensitivity of this CMS
analysis. Monte Carlo (MC) simulated events are then generated at parton-
level, with the decays, hadronisation and detector response calculated for
each point in these scans.

Point |  $M_{\tilde{q}}$ [GeV/$c^{2}$] |  $M_{\tilde{g}}$ [GeV/$c^{2}$] |  $M_{\tilde{t},\tilde{b}}$ [GeV/$c^{2}$]
---|---|---|---
BP1 | $1000$ | $1010$ | decoupled
BP2 | $1400$ | $1410$ | decoupled
BP3 | $1100$ | $900$ | decoupled
BP4 | $1500$ | $1300$ | decoupled
BP5 | $1400$ | $1410$ | $M_{\tilde{t}}=750$
BP6 | $1100$ | $1110$ | $M_{\tilde{b}}=750$
BP7 | $1500$ | $1300$ | $M_{\tilde{t}}=750$
BP8 | $1400$ | $1200$ | $M_{\tilde{b}}=750$
Table 1: Original BPs in [15].

##  2 Testing scenarios with low $E_{\text{T}}^{\text{miss}}$E(T)**(miss)

Current searches for SUSY have yet to find substantial evidence, increasing
the lower bounds on sparticle masses for simplified models. However, for
certain regions of parameter space, it is possible that a supersymmetric decay
cascade may in fact give a very low $E_{\text{T}}^{\text{miss}}$ signal whilst
still having a LSP mass of only a few GeV/$c^{2}$, weakening the lower bounds
on the masses of the squarks and gluino.

For example, the $E_{\text{T}}^{\text{miss}}$ distributions are shown in
figure 1 for each of the eight BPs in table 1, featuring a LSP mass of $3$
GeV/$c^{2}$ with the squark and gluino masses around 1 TeV/$c^{2}$, along with
a simplified MSSM-like scenario which exhibits typically larger values of
$E_{\text{T}}^{\text{miss}}$. This MSSM-like scenario features the same
sparticle masses as BP1, such as $1$ TeV/$c^{2}$ squarks and a $3$ GeV/$c^{2}$
LSP.

Here, it is clear that the mean $E_{\text{T}}^{\text{miss}}$ is quite low for
these NMSSM scenarios, more akin to that from SM processes such as top quark
pair production. In turn, this suggests current experimental searches
concentrating on a hadronic jets plus $E_{\text{T}}^{\text{miss}}$ final state
will likely not be optimally tuned to this type of SUSY signature.

Figure 1: $E_{\text{T}}^{\text{miss}}$ distribution for the eight benchmark
points defined in [15] along with an MSSM-like simplified scenario.

In [15] the Higgs boson in question is SM-like with a mass of around $125$
GeV/$c^{2}$ and the final state under consideration contains two bottom quark
jets and two $\tau$ leptons, produced when one of the two Higgs bosons decays
to a bottom quark-antiquark pair and the other to a $\tau$ lepton-antilepton
pair. This was chosen in order to suppress SM background processes compared
with an all-hadronic final state such as that where both Higgs bosons decay
into a bottom quark-antiquark pair.

However, since the analysis considered in [5] concentrates specifically on
all-hadronic final states, this paper will focus on the scenario where each
Higgs boson decays into a bottom quark-antiquark pair, with no $\tau$ leptons
produced, thus seeking a $4b$+$E_{\text{T}}^{\text{miss}}$ final state. This
retains the maximum proportion of signal events, since the largest branching
fraction for the Higgs boson decay is that to a bottom quark-antiquark pair.
Likewise, the contribution towards the background from SM events involving
large numbers of hadronic jets formed through Quantum Chromo-Dynamics (QCD)
interactions, i.e., multijet events, will also increase.

Thus denoting this SM-like Higgs boson as $H$, our final state decays will
appear as

NLSP $\displaystyle\rightarrow H+\text{LSP}$ $\displaystyle H$
$\displaystyle\rightarrow b\bar{b}\text{ (jets)}.$ (1)

###  2.1 Other factors affecting signal processes

Whilst the masses of the neutralinos and Higgs boson will dictate the
behaviour of some of the kinematical variables, these have no real effect on
the initial sparticle production cross-section, which is to a large extent
dependent only upon the masses of the squarks and gluino.

As the squark and gluino masses increase, so does the mass gap between these
and the NLSP. This in turn will lead to high-$p_{\text{T}}$ jets from the SUSY
decay cascade as well as increased NLSP momentum, resulting in higher
$H_{\text{T}}$ and larger Higgs boson $p_{\text{T}}$.

##  3 Simulation techniques

Firstly, the mass spectra are chosen in order to exploit these light-LSP,
low-$E_{\text{T}}^{\text{miss}}$ scenarios. In order to generate simulated
events for processes calculated at matrix element level, MadGraph [18], which
has built-in support for NMSSM processes at Leading Order (LO), is used.
However MadGraph cannot generate NMSSM events at Next-to-LO (NLO), therefore,
the cross-section value stated by MadGraph is not used. Instead, squark and
gluino production cross-sections are calculated (inclusively) using Prospino
[19] at NLO.

The initial squarks, antisquarks and gluinos, plus up to two additional hard
jets, are generated by MadGraph at LO, after which Pythia8 [20] decays the
particles according to their respective Branching Ratios (BRs). A fast
simulation of the CMS detector is then performed using Delphes [21].

Taking, for example the, first two BPs in [15], denoted BP1 and BP2 in table
1, we see that gluinos are in both cases around $10$ GeV/$c^{2}$ heavier than
squarks. The gluinos thus decay first into squarks, with each squark decaying
into a NLSP and a correspondingly flavoured quark:
$\tilde{g}\rightarrow\tilde{q}+q$;
$\tilde{q}\rightarrow\tilde{\chi}_{2}^{0}+q$.

BP3 and BP4 differ in that the gluino is $200$ GeV/$c^{2}$ lighter than the
squarks. In these scenarios the left-handed squarks always decay into the
gluino and a correspondingly flavoured quark, whilst the right-handed squarks
decay either into a gluino-quark combination or skip this step entirely and
decay directly into a NLSP and a quark, with corresponding BRs of 70% and 30%,
respectively, with these fractions close to those estimated by NMSDECAY [22,
23].

For BP5 and BP6 the squarks are lighter than the gluino, as in points BP1 and
BP2. However, the respective stop/sbottom-type squark is now lighter than the
gluino, sufficiently so that gluino two-body decays are possible. In these two
BPs the gluino is assumed to always decay into a stop (BP5) or sbottom (BP6)
squark and corresponding top/bottom quark, which in turn decays into a NLSP
and correspondingly flavoured quark. The first- and second-generation squarks
decay with 100% BR into the NLSP and corresponding quark as in BP1 and BP2.

BP7 and BP8 also involve the stop (BP7) or sbottom (BP8) squark, but with the
gluino lighter than the first two generation squarks, as in BP3 and BP4. Much
like in BP3 and BP4, the left-handed squarks always decay into a gluino and a
correspondingly flavoured quark, whilst the right-handed squark decays with
70% and 30% BR into either a gluino and a quark or directly into a NLSP and
quark, respectively. In both of these points the gluino always decays into the
respective stop/sbottom squark and top/bottom quark, with the third generation
squark decaying furthermore into a NLSP and corresponding top/bottom quark.

Figure 3 shows example decay cascades for each of these BPs. BP2 and BP4 have
been omitted, since the possible diagrams do not differ from those for BP1 and
BP3, however, extra diagrams are included for BP3 and BP7 to illustrate the
possible routes by which the right-handed squarks may decay. Additionally, the
alternative BP7 decay chain may apply to BP8 by simply switching each of the
stop/top for the corresponding sbottom/bottom squark/quark.

(a) BP1 possible decay cascade.

(b) BP3 possible decay cascade.

(c) BP3 alternative decay cascade.

(d) BP5 possible decay cascade.

(e) BP6 possible decay cascade.

(f) BP7 possible decay cascade.

The Feynman diagrams in figure 3 show examples of the processes by which we
may produce a final state with two LSPs and two Higgs bosons. In each of these
diagrams we produce one squark and one gluino directly, with each decaying via
an example cascade, however, both squark-squark and gluino-gluino pair
production processes are included additionally in the event generation. These
processes may also involve extra hadronic jets produced along with the initial
sparticles or typically softer radiated jets.

(a) BP7 alternative decay cascade.

(b) BP8 possible decay cascade.

Figure 3: Feynman diagrams showing example processes by which we may produce
two singlino LSP along with two Standard Model-like Higgs bosons. An example
diagram is given for each of the BPs in [15] which contain unique mass
hierarchies. Here, BP1, BP3, BP5, BP6, BP7 and BP8 are shown in (a), (b,c),
(d), (e), (f,g) and (h), respectively.

Considering the diagram in figure 2(a), the initial gluino and squark may be
produced at parton-level in MadGraph, with the second squark produced by
Pythia from the decay of the gluino, shown in figure 4(a). However, if one
were to direct MadGraph to produce two squarks, allowing the production of
extra jets, some of the subprocesses considered would involve a squark
stemming from the decay of a gluino, all of which would be calculated at
parton-level, as in figure 4(b). Thus there is an overlap between the events
generated by MadGraph when asked for two squarks and those generated when
producing gluinos, which are in turn decayed by Pythia into squarks.

(a) Gluino decays in Pythia.

(b) Gluino decays in MadGraph.

Figure 4: MadGraph event generation of two squarks and one jet (left) and one
squark and one gluino (right), sharing the same Feynman diagram after Pythia
has performed the gluino decay.

In order to remove the possibility of subprocesses being counted more than
once in the overall calculation, it is required that any squark or gluino
whose decay is performed at parton-level must be off-shell. Since any squarks
or gluinos whose decay is performed by Pythia will have been treated as _final
state_ particles by MadGraph, they must be on-shell. Thus, by summing the
complementary on- and off-shell terms, the entire momentum space over which
the squarks and gluinos may decay is obtained.

##  4 Mass scans and event selections

###  4.1 Two-dimensional mass scans

Considering each of the existing BPs in [15], where
$M_{\tilde{\chi}_{2}^{0}}$$=130$ GeV/$c^{2}$ and
$M_{\tilde{\chi}_{1}^{0}}$$=3$ GeV/$c^{2}$, a two-dimensional mass scan is
constructed. The mass gaps $M_{\tilde{q}}-M_{\tilde{g}}$ and
$M_{\tilde{\chi}_{2}^{0}}-M_{\tilde{\chi}_{1}^{0}}$ are kept constant, with
$M_{\tilde{q},\tilde{g}}$ and $M_{\tilde{\chi}_{1}^{0},\tilde{\chi}_{2}^{0}}$
now treated as two independent parameters.

However, it may be noted that BP1 and BP2 are essentially the same, but for
$M_{\tilde{q},\tilde{g}}$ being $400$ GeV/$c^{2}$ heavier in the latter.
Therefore, one would find that a mass scan about BP1 would encapsulate BP2
anyway. This is also the case for BP3 with respect to BP4, however, BP5 to BP8
transform into four independent scans, since for BP5 and BP7 the stop squark
is involved in the decay cascades but not the sbottom squark. For BP6 and BP8
the converse applies.

Whilst it is expected that the sensitivity to these NMSSM scenarios be lowest
for the lightest LSP, due to the suppressed $H_{\text{T}}^{\text{miss}}$
distribution, the masses of the NLSP and LSP in each scan are increased as
high as is possible whilst remaining below the mass of the lighter of the
squark and gluino. This is done in order to cover the entirety of the
available sparticle mass range, such that it is possible to compare the same
NMSSM scenario with a range of LSP masses. Thus, the six independent mass
scans are defined as in table 2.

|  $M_{\tilde{q}}$ [GeV/$c^{2}$] |  $M_{\tilde{g}}$ [GeV/$c^{2}$] |  $M_{\tilde{\chi}_{1}^{0}}$ [GeV/$c^{2}$] |  $M_{\tilde{\chi}_{2}^{0}}$ [GeV/$c^{2}$] |  $M_{\tilde{t},\tilde{b}}$ [GeV/$c^{2}$]
---|---|---|---|---|---
BP1/BP2 | $1200\rightarrow 3000$ | $M_{\tilde{q}}+10$ | $3\rightarrow\\{M_{\tilde{q}}-20\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | decoupled
BP3/BP4 | $1200\rightarrow 3000$ | $M_{\tilde{q}}-200$ | $3\rightarrow\\{M_{\tilde{g}}-20\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | decoupled
BP5 | $1200\rightarrow 3000$ | $M_{\tilde{q}}+10$ | $3\rightarrow\\{M_{\tilde{t}}-200\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | $M_{\tilde{t}}=M_{\tilde{q}}-250$
BP6 | $1200\rightarrow 3000$ | $M_{\tilde{q}}+10$ | $3\rightarrow\\{M_{\tilde{b}}-20\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | $M_{\tilde{b}}=M_{\tilde{q}}-250$
BP7 | $1200\rightarrow 3000$ | $M_{\tilde{q}}-200$ | $3\rightarrow\\{M_{\tilde{t}}-200\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | $M_{\tilde{t}}=M_{\tilde{g}}-250$
BP8 | $1200\rightarrow 3000$ | $M_{\tilde{q}}-200$ | $3\rightarrow\\{M_{\tilde{b}}-20\\}$ | $M_{\tilde{\chi}_{1}^{0}}+127$ | $M_{\tilde{b}}=M_{\tilde{g}}-250$

Table 2: Table showing various mass ranges in the scans.

For the first two scans the NLSP mass is increased up to just below the
lighter of the squark and gluino masses whilst still allowing for on-shell
decay. For the remaining four scans, where the respective stop or sbottom
squark is non-decoupled, its mass is set to be $250$ GeV/$c^{2}$ lower than
the lightest of the squark and gluino, such that the gluino may still decay
into the relevant third generation squark, along with an appropriate quark. In
these cases, the NLSP mass may still be increased, so long that the involved
third generation squark may still decay in an on-shell fashion into its
respectively flavoured quark and a NLSP.

###  4.2 Event selections

The considered experimental analysis [5] contains many measurement bins for
various observables in the data, background and signal channels, in particular
for the number of hadronic jets ($N_{\text{jets}}$), the number of $b$-tagged
hadronic jets ($N_{b\text{-jets}}$), $H_{\text{T}}$ and
$H_{\text{T}}^{\text{miss}}$. Focusing on a
$b\bar{b}b\bar{b}+$$E_{\text{T}}^{\text{miss}}$ final state, with plenty of
jets from both cascades, we consider the bin with the highest number of jets,
i.e., the one for which $N_{\text{jets}}\geq 6$. Anticipating a high chance of
bottom quarks being mis-identified, especially if the Higgs bosons are
boosted, we consider both the $N_{b\text{-jets}}=2$, $N_{b\text{-jets}}=3$ and
$N_{b\text{-jets}}\geq 4$ bins. Additionally, since we are primarily
interested in topologies generating high $H_{\text{T}}$, we focus on the
upper-most $H_{\text{T}}$ $>1200$ GeV/$c$ bin, with the exception of the case
where we have four or more $b$-tagged hadronic jets, where the only bin in [5]
is $H_{\text{T}}$ $>400$ GeV/$c$.

Furthermore, in this analysis, a cut on ‘biased Delta-phi’
($\Delta\phi^{\star}$) is applied to reduce the QCD background. Additional
cuts in [5] regarding vetoing events containing isolated leptons and photons
are also performed, as well as failing events which contain forward/backward-
oriented hadronic jets. The event selection is therefore detailed as follows:

  * •

At least 6 hadronic jets, where any jet must have $p_{\text{T}}$$\geq 40$
GeV/$c$.

  * •

$N_{b\text{-jets}}=2$, $N_{b\text{-jets}}=3$, $N_{b\text{-jets}}\geq 4$, i.e.,
separate bins.

  * •

$N_{b\text{-jets}}$, $H_{\text{T}}$ and $H_{\text{T}}^{\text{miss}}$ binning
defined in table 3.

  * •

$H_{\text{T}}\geq 1200$ GeV/$c$ for events where $N_{b\text{-jets}}\leq 3$, or
$H_{\text{T}}\geq 400$ GeV/$c$ where $N_{b\text{-jets}}\geq 4$.

  * •

$\Delta\phi^{\star}\geq 0.5$.

In addition, event vetoes are defined such that events will fail should they
contain any of the following isolated objects:

  * •

photons with $p_{\text{T}}$ $>20$ GeV/$c$ and $|\eta|<2.5$,

  * •

electrons and muons with $p_{\text{T}}$ $>10$ GeV/$c$ and $|\eta|<2.5$,

  * •

jets with $p_{\text{T}}$ $>40$ GeV/$c$ and $|\eta|>2.4$,

where isolation is defined as being separated from other objects by angular
distance $\Delta R>0.3$ for photons or $\Delta R>0.4$ for electrons, muons and
jets.

Finally an $H_{\text{T}}$-dependent cut on $\alpha_{\text{T}}$ is implemented
as described in table 4, noting that for all but the $N_{b\text{-jets}}\geq 4$
bin there is no $\alpha_{\text{T}}$ cut due to the $H_{\text{T}}$ requirement.

As defined in [6], in the case where an event contains just two hadronic jets,
$\alpha_{\text{T}}$ is calculated as follows:

$\displaystyle\alpha_{T}=\frac{E^{j2}_{T}}{M_{T}},$

where $E^{j2}_{T}$ is the transverse energy of the second-leading hadronic jet
and

$\displaystyle
M_{T}=\sqrt{\left(\sum_{i=1}^{2}E_{T}^{j_{i}}\right)^{2}-\left(\sum_{i=1}^{2}p_{x}^{j_{i}}\right)^{2}-\left(\sum_{i=1}^{2}p_{y}^{j_{i}}\right)^{2}}.$

For events with more than two hadronic jets, the latter are combined to create
_pseudo-jets_ in such a way that the difference in $p_{\text{T}}$ between
these two pseudo-jets is minimised [7].

###  4.3 Signal, background and data event yields

Table 4 contains the data and background yields from [5] for each of the
$N_{b\text{-jets}}$ and $H_{\text{T}}^{\text{miss}}$ bins, satisfying the
remaining event selection criteria.

Bin |  |  $H_{T}$ [GeV/$c$] |  |  $H_{T}^{\rm miss}$ [GeV/$c$] | Data Yield |  | Background Yield
---|---|---|---|---|---|---|---
$=$ 2b |  | 1200– | $\infty$ |  | 200– | 400 | 0 |  |  $2.51$ p m 1.02
$=$ 2b |  | 1200– | $\infty$ |  | 400– | 600 | 0 |  |  $1.65$ p m 0.44
$=$ 2b |  | 1200– | $\infty$ |  | 600– | 900 | 2 |  |  $0.62$ p m 0.32
$=$ 2b |  | 1200– | $\infty$ |  | 900– | $\infty$ | 0 |  |  $0.19$ p m 0.18
$=$ 3b |  | 1200– | $\infty$ |  | 200– | 400 | 1 |  |  $0.40$ p m 0.16
$=$ 3b |  | 1200– | $\infty$ |  | 400– | 600 | 0 |  |  $0.25$ p m 0.08
$=$ 3b |  | 1200– | $\infty$ |  | 600– | 900 | 1 |  |  $0.09$ p m 0.04
$=$ 3b |  | 1200– | $\infty$ |  | 900– | $\infty$ | 0 |  |  $0.02$ p m 0.02
$\geq$ 4b |  | 400– | $\infty$ |  | 200– | $\infty$ | 4 |  |  $2.46$ p m 0.70
Table 3: Data and background yields for the bins used in this analysis, taken from [5]. $H_{\text{T}}$ [GeV/$c$] | $200-250$ | $250-300$ | $300-350$ | $350-400$ | $400-900$ | $900-\infty$
---|---|---|---|---|---|---
$\alpha_{\text{T}}$ | $>0.65$ | $>0.6$ | $>0.55$ | $>0.53$ | $>0.52$ | $>0$
Table 4: Table detailing the $H_{\text{T}}$-dependent $\alpha_{\text{T}}$
cuts.

These data yields and background estimations are then used to calculate lower
bounds on the sparticle masses given the signal yields for each mass point in
each mass scan, with the systematic uncertainty on the signal yields assumed
to be $25$%.

###  4.4 Validation of cut and count analysis tools

In order to check that one may rely on the signal event yields calculated by
the software used to implement the event selection and indeed that the
estimation of the systematic uncertainty is appropriate, it is important to
compare these yields with those in [5]. However of course the experimental
analysis in question does not feature an NMSSM
low-$E_{\text{T}}^{\text{miss}}$ scenario such as those under consideration in
this work, so a reference benchmark model is chosen, $T1bbbb$ [24].

Figure 5: Feynman diagram showing gluino pair production and decay in the
$T1bbbb$ benchmark model.

$T1bbbb$ is a simplified Supersymmetric model whereby pair produced gluinos
each undergo a three-body decay into a bottom quark-antiquark pair and an LSP
neutralino, shown in figure 5. In this example the gluino has a mass of $1900$
GeV/$c^{2}$ and the LSP $100$ GeV/$c^{2}$. In addition to the pair produced
gluinos, up to two hard jets are considered at parton level in the event
generation, as was done with the NMSSM signal mass points.

Event Selection | Benchmark Model
---|---
T1$bbbb$: $M_{\tilde{q}}=1900$ GeV, $M_{\chi^{0}_{1}}=100$ GeV
Efficiencies from [5] | Delphes & own software
Before selection | 100.0 | 100.0
Isolated muon, electron, photon vetos | 99.4 | 98.2
$p_{T}^{j_{1}}>100$ | 98.7 | 98.1
$0.1<f_{h^{\pm}}^{j_{1}}<0.95$ | 93.9 | 98.1
$H_{\text{T}}>200$ GeV | 93.9 | 98.1
$H_{\text{T}}^{\text{miss}}>200$ GeV | 88.5 | 92.2
Event veto for forward jets ($|\eta|>2.4$) | 69.9 | 74.4
$H_{\text{T}}^{\text{miss}}$/$E_{\text{T}}^{\text{miss}}<1.25$ | 69.3 | 73.7
$n_{\text{jet}}$\- and $H_{\text{T}}$-dependent $\alpha_{\text{T}}$ thresholds | 69.2 | 73.7
$\Delta\phi^{*}_{\text{min}}>0.5$ | 25.1 | 23.7
Table 5: Cumulative percentages of events passing the event selections
compared with those from [5] for a standard reference benchmark model,
$T1bbbb$ [24].

As shown in table 5 it is clear that the respective efficiencies of each of
the event selections are all within a few percent of those taken directly from
[5] for the same example benchmark model. Therefore, in order to take into
account other sources of uncertainty such as Initial State Radiation (ISR),
the choice of $25$% appears to be appropriate.

##  5 Signal properties

We examine the observable properties of these BPs, in order to explore which
event selections have the greatest impact on the experimental sensitivity.
Additionally we also consider the MC _truth_ values, i.e., the generated
values without detector simulation being applied, for quantities such as $b$
jet angular separation, since this quantity taking a value below the
resolution of the detector will have a large effect on the efficiency of
bottom quark tagging and the ability to resolve both $b$ jets stemming from
the decay of each Higgs boson.

First consider the BP1-BP8-type mass scans, taking from each two mass points
where one has the lightest $3$ GeV/$c^{2}$ LSP and the other a mid-range $953$
GeV/$c^{2}$ LSP more typical of simplified SUSY models, choosing an example
squark mass of $2$ TeV/$c^{2}$. Plotting quantities of interest for all
events, before any event selection is applied, and normalising to unity for
comparison, it can be shown how many of the cuts in [5] will likely thwart
most of the signal events generated in the low-$M_{\tilde{\chi}_{1}^{0}}$
regions. These are then overlayed with the corresponding normalised
distributions for background processes containing QCD multijet events and
background contributions from top quark pair production.

Additionally, a simplified MSSM-like model is presented for comparison. This
scenario is derived from the BP1-type scan, with the difference being that the
NLSP is dropped, with the squarks and gluinos decaying instead directly to the
LSP. Thus no Higgs bosons are produced and the LSP momentum is no longer
suppressed, removing the possibility of a low $E_{\text{T}}^{\text{miss}}$ and
Higgs boson enriched scenario. In this model the squark mass is set at $2$
TeV/$c^{2}$ and the effective “LSP” has mass $3$ GeV/$c^{2}$.

###  5.1 Total scalar $H_{\text{T}}$

A dominant feature of many SUSY cascades is high $H_{\text{T}}$, due to the
large number of jets produced in the many decays. We note that these low-LSP
mass scenarios deliver an $H_{\text{T}}$ distribution with mean well over $2$
TeV/$c$.

Figure 6 shows the $H_{\text{T}}$ distributions for two example points from
each of the six mass scans. Whilst it is clear that the mean $H_{\text{T}}$
for both QCD multijet and top pair production background processes is far
lower than that for the signal processes, their respective cross-sections are
much higher. Therefore, whilst the peaks of these distributions are well
separated, it would be expected for the tails of both background processes to
still be significant compared with the signal processes when considering the
event yields in an analysis.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 6: $H_{\text{T}}$ distributions for low and mid-range $M_{\text{LSP}}$
near the observed limit in the BP1-type scan, compared with QCD and $t\bar{t}$
background processes and an MSSM-like scenario with a light LSP.

In fact, considering the fraction of events passing the $1200$ GeV/$c$ minimum
$H_{\text{T}}$ requirement across the BP1-type mass scan range, shown in
figure 7, it becomes clear that for many of the mass points essentially all
events pass this cut. The regions where this is not the case are generally
limited to those where the LSP mass is close to the masses of the squarks and
gluinos, thus reducing the $p_{\text{T}}$ of the jet(s) emitted as the squark
or gluino decays.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 7: Fraction of events with total $H_{\text{T}}>1200$ GeV for the
BP1-BP8-type mass scans.

However, it is also apparent, in figure 7, that the mean $H_{\text{T}}$ is
much lower where the LSP mass approaches that of the squarks and gluinos. This
is the case since the mass gaps in the decay cascade are reduced and so the
$p_{\text{T}}$ of any emitted quark is suppressed.

###  5.2 $H_{\text{T}}^{\text{miss}}$

Whilst of course the existence of these LSP with non-zero momenta dictates
there must also be some missing net transverse energy, so long that the two
LSPs are exactly not back-to-back.

In figure 8 rather distinct distributions between the two mass points may be
observed. The heavy LSP scenarios give a fairly wide spread of
$H_{\text{T}}^{\text{miss}}$ values due to the presence of such a heavy,
boosted and invisible LSP. The light-LSP scenarios however suppress this,
since the considerably heavier Higgs boson will inherit most of the momentum
from the NLSP decay, leaving a soft LSP.

Even in these light-LSP scenarios, there are still events whose
$H_{\text{T}}^{\text{miss}}$ is quite high. This larger
$H_{\text{T}}^{\text{miss}}$ can arise via Higgs bosons decaying to final
states other than a bottom quark-antiquark pair, though the branching
fractions for decays such as $H\rightarrow
ZZ^{*}\rightarrow\nu\bar{\nu}\nu\bar{\nu}$ are very small. A more likely
phenomenon is for one or more of the bottom quarks stemming from the decays of
the Higgs bosons to decay into a charm quark and an electron or muon, along
with the appropriately-flavoured neutrino, with the neutrino momentum
contributing to the overall $H_{\text{T}}^{\text{miss}}$. Additionally,
hadronic Higgs boson decay final states such as $b\bar{b}$ are difficult to
reconstruct owing to resolution and, given the higher number of jets compared
with, say, a cleaner $H\rightarrow\gamma\gamma$ decay channel, meaning a
larger contribution to the uncertainty in $H_{\text{T}}^{\text{miss}}$ and
$H_{\text{T}}$.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 8: $H_{\text{T}}^{\text{miss}}$ distributions for low and mid-range
$M_{\text{LSP}}$ near the observed limit in the BP1-type scan, compared with
QCD and $t\bar{t}$ background processes.

Here the $H_{\text{T}}^{\text{miss}}$ decreases drastically in the limit of a
light-LSP in the NMSSM, with the peak well below $200$ GeV/$c$, the minimum
$H_{\text{T}}^{\text{miss}}$ requirement used from [5]. It is clear for these
areas of mass space many of the events are lost due to
$H_{\text{T}}^{\text{miss}}$ cuts, thus decreasing experimental sensitivity to
this type of model.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 9: Fraction of events with $H_{\text{T}}^{\text{miss}}$ $>200$ GeV/$c$
for the BP1-BP8-type mass scans.

Additionally, as seen in the colour map plots in figure 9, the fraction of
events with $H_{\text{T}}^{\text{miss}}$ greater than the lower edge of the
minimum $H_{\text{T}}^{\text{miss}}$ bin, $200$ GeV/$c$, rises considerably as
the LSP mass increases. Above a certain threshold, however, this fraction
begins to drop since, as the LSP mass approaches that of the squarks and
gluinos, the mass gaps in the decay cascade shrinks, meaning that we are left
with heavy LSPs with very little kinetic energy, and thus low
$H_{\text{T}}^{\text{miss}}$.

###  5.3 Number of hadronic jets

Typical SUSY decay cascades often involve a large number of hadronic jets
being produced. The model considered in this paper features two such cascades
ending in Higgs boson decays, and some including stop and sbottom-type squarks
whose decays produce even more squarks.

Figure 10 shows the number of hadronic jets as defined in [5], with
$p_{\text{T}}$$>40$ GeV/$c$ and $|\eta|<2.4$, for the usual signal and
background processes.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 10: Number of hadronic jets for low and mid-range $M_{\text{LSP}}$ near
the observed limit in the BP1-type scan, compared with QCD and $t\bar{t}$
background processes and an MSSM-like scenario with a light LSP.

Considering the fraction of events containing at least six hadronic jets, it
can be seen in figure 11 that whilst in general most signal events pass this
selection, the three scans where the gluino is lighter than the squark have a
much higher efficiency with respect to this cut.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 11: Fraction of events with total number of hadronic jets $>5$ for the
BP1-BP8-type mass scans.

The primary reason for this behaviour lies in the decay products of the
sparticles in the various mass hierarchies. The decay cascade for the BP3, BP6
and BP8-type scans involve squarks decaying to a gluino and a quark, where the
gluino decays into two quarks and a neutralino. Conversely, scenarios where
the squark is lighter than the gluino involve the gluino decaying into a
squark and a quark, with the squark decaying into a neutralino and only one
quark.

This three-body gluino decay means that each cascade, of which these scenarios
include two, produces an extra quark, thus increasing the expected number of
hadronic jets per event in the detector.

Additionally in each mass scan the fraction of events passing this selection
is generally highest for a lighter LSP, dropping considerably as the LSP mass
approaches the squark/gluino mass. This drop in efficiency for heavy LSP is
due to the small mass gaps in the decay cascades meaning softer hadronic jets,
such that the $p_{\text{T}}$ of some of these jets will fall below the
$40~{}$GeV/$c$ minimum threshold and so will not be considered.

###  5.4 Number of $b$-tagged hadronic jets

In this NMSSM scenario where the LSP is a singlino, two SM-like Higgs bosons
will be produced. The BRs for SM-like Higgs boson decay dictate that the most
likely decay is that to a bottom quark-antiquark pair, therefore it is
expected that a large number of the hadronic jets in each event will be
_tagged_ as being a bottom quark, or $b$-_tagged_.

Due to uncertainty, of course, not all $b$-tagged jets are necessarily
hadronic jets containing bottom quarks, nor will all bottom quarks form
$b$-tagged jets. However, the efficiency of correctly $b$-tagging a bottom
quark is around $70\%$, whereas the likelihood of $b$-tagging a lighter
flavour quark is only $1\%$ or so. As such the average number of $b$-tagged
jets for each of the example mass points in each mass scan is quite large, as
shown in Figure 12.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 12: Number of $b$-tagged hadronic jets for low and mid-range
$M_{\text{LSP}}$ near the observed limit in the BP1-type scan, compared with
QCD and $t\bar{t}$ background processes and an MSSM-like scenario with a light
LSP.

Considering the efficiency of the binning imposed, taking the fraction of
events with at least two $b$-tagged hadronic jets, it may be noted that in
general at least around half of the events in these signal points contain at
least two $b$-tagged hadronic jets, as shown in figure 13. However it is clear
that in the BP7 and BP8-type scans this efficiency increases to almost 100%,
shown also by the large number of such jets in the example mass points shown
for these scans in figures 12(e) and 12(f).

The high $b$-tag multiplicities in these scans stem from the decay cascades,
shown in figure 3. In the case of the BP7 scan, up to four top quarks are
produced, whose decays may lead to the production of bottom quarks. More
simply, in the case of the BP8-type scan, it is possible to obtain up to four
bottom quarks without even considering the decay of each Higgs boson.

Additionally, it may be noted that whilst the correlations between sparticle
masses and the fraction of events containing at least two $b$-tagged hadronic
jets is not as clear as was seen in figure 9 for $H_{\text{T}}^{\text{miss}}$,
say, there is generally a decrease in efficiency as the LSP mass approaches
the masses of the squark and gluino. Similarly to the case for the number of
hadronic jets, this is likely since the jet $p_{\text{T}}$ distribution is
softer as the mass gaps in the SUSY cascade decrease, meaning some of the
bottom quarks will not have enough transverse momentum required to pass the
$40~{}$GeV/$c$ threshold necessary to be considered.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 13: Fraction of events with total number of $b$-tagged hadronic jets
greater than or equal to 2 for the BP1-BP8-type mass scans.

###  5.5 $\Delta\phi^{*}$

Minimum biased Delta-phi, $\Delta\phi^{*}$, is a variable used in [5] in order
to reduce the background contribution from QCD multijet events, designed in
such a way that events with genuine $E_{\text{T}}^{\text{miss}}$ or
$H_{\text{T}}^{\text{miss}}$ would be expected to have large $\Delta\phi^{*}$
values whereas SM processes should generate small values, typically less than
0.5.

This quantity is defined as follows. For each event, first consider the
hadronic jets with $p_{\text{T}}$ $>40$ GeV/$c$ and $|\eta|<2.4$. For each of
these jets the difference in azimuthal angle $\phi$ is calculated between the
jet and the $H_{\text{T}}^{\text{miss}}$ calculated _without that jet_.

The minimum of these $\Delta\phi$ values is then taken as minimum
$\Delta\phi^{*}$, since this would be expected to be most robust against
sources of spurious $H_{\text{T}}^{\text{miss}}$ such as erroneous measurement
of the momentum of hadronic jets.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 14: $\Delta\phi^{*}$ distributions for low and mid-range
$M_{\text{LSP}}$ near the observed limit in the BP1-type scan, compared with
QCD and $t\bar{t}$ background processes and an MSSM-like scenario with a light
LSP.

However, the NMSSM scenarios considered in this paper do not generate many
events containing large $\Delta\phi^{*}$, as shown in figure 14. Considering
the fraction of events with $\Delta\phi^{*}>0.5$, shown in figure 15, it
becomes clear that a large fraction of events are rejected by the event
selection in [5], despite this variable being designed to reject QCD
background events and to allow events with genuine
$E_{\text{T}}^{\text{miss}}$.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 15: Fraction of events with $\Delta\phi^{*}>0.5$ for the BP1-BP8-type
mass scans.

The relatively low $\Delta\phi^{*}$ values produced in these signal mass
points indicates this particular background-reduction variable is not tuned to
the type of scenario under consideration in this paper.

A likely reason for small $\Delta\phi^{*}$ lies in the number of hadronic jets
produced. Without of course assuming a uniform distribution in the direction
of the hadronic jets, it would still be expected to become increasingly
unlikely for the azimuthal angular separation between a hadronic jet and the
$H_{\text{T}}^{\text{miss}}$ value computed without that jet to exceed the cut
of $0.5$ as the number of jets in each event increases.

Accordingly, the regions of parameter space for which the LSP mass is close to
that of the squarks and gluino display a larger fraction of events with
$\Delta\phi^{*}>0.5$, since the calculation of $\Delta\phi^{*}$ only involves
hadronic jets with $p_{\text{T}}$ $>40~{}$GeV/$c$, of which there are fewer in
these regions.

Given the very large average number of jets per event in the light-LSP mass
points presented in this paper, it would be expected that a $\Delta\phi^{*}$
cut would indeed kill much of the signal events in these regions of parameter
space.

###  5.6 Angular separation between bottom quark jets from Higgs boson decays

One such quantity which characterises the BPs in this signal model is the
angular separation $\Delta R$ between the bottom quarks from each Higgs boson
decay, at MC generation (“truth”) level. The bottom quark jets considered in
[5] are standard AK4 jets, formed using the anti-$k_{\text{T}}$ algorithm with
a jet cone radius $R=0.4$. If two such jets from a boosted Higgs boson are
close enough that their angular separation $\Delta R$ is less than the jet
cone radius then it might only be possible to resolve one _fat_ bottom quark
jet.

In order to examine the angular separation of the bottom quark jets stemming
from the Higgs bosons, the MC truth information is examined. This contains the
four-momenta of all individual particles in the event, rather than the
emulated detector measurement of the hadronised jets, allowing for
measurements of angular separation smaller than the jet cone radius of $0.4$.

Considering the BP1-BP8-type mass scans it may be seen in figure 16 how for
example a heavy squark and a light LSP will correspond to a more boosted Higgs
boson, thus decreasing the mean $\Delta R$ value. As the LSP mass increases,
however, the bottom quark jets become more separated, since the LSP momentum
increases relative to that of the associated Higgs boson, resulting in a more
boosted LSP and a less boosted Higgs boson.

(a) BP1

(b) BP3

(c) BP5

(d) BP6

(e) BP7

(f) BP8

Figure 16: $\Delta R$ distributions for low and mid-range $M_{\text{LSP}}$
near the observed limit in the BP1-BP8-type mass scans.

Thus, in the extreme light LSP limit, it is expected that a large fraction of
the bottom quarks stemming from the decay of each Higgs boson will overlap to
the extent that resolving and $b$-tagging both hadronic jets from each Higgs
boson will become very difficult.

Here, it may be noted that the behaviour is essentially the same for each of
these six mass scans, since in all cases heavy quarks combined with a light
LSP leads to a boosted Higgs boson and, as such, small angular separation
between the bottom quark-antiquark pair.

##  6 Results

A fit across the signal, background and data yields in the nine measurement
bins described in table 3 is performed in order to determine the strength
parameter $\mu$, defined as the upper limit placed on the fraction of the
signal cross-section which could not quite be ruled out at $95\%$ Confidence
Level (CL). As such, if for a particular point in parameter space $\mu<1$ this
point may be excluded, whereas if $\mu>1$ the point may not be ruled out.

These limits are calculated given the data and background yields as well as
background uncertainties in table 3, with the systematic uncertainty on the
signal yields assumed as $25$%.

Here we present the contour limit plots for the six scan types performed
within the NMSSM. The $X$\- and $Y$-axis represent the masses of the squark
and LSP, respectively, while the colour scale shows the strength parameter,
$\mu$. The black contour at $\mu=1$ then identifies the areas in parameter
space inside which all mass points are ruled out, and outside which may not be
excluded, given the data yield and the background and signal estimations.

The expected limit, shown as a red contour, is defined as the upper limit we
would observe if the data yields matched the background expectation exactly,
and allows us to quantify any excess or deficit in the observation compared to
what we would expect given the background-only hypothesis.

(a) BP1-type Mass Scan

(b) BP3-type Mass Scan

(c) BP5-type Mass Scan

(d) BP6-type mass scan

(e) BP7-type mass scan

(f) BP8-type mass scan

Figure 17: Observed and expected limits for the BP1-BP8-type mass scans. The
$X$\- and $Y$-axes represent the squark and LSP masses, respectively, whilst
the colour scale represents the upper limit on the strength parameter $\mu$.

In figure 17 it can be seen that both the observed and expected limits are far
weaker for a very light LSP mass, with both contours bending to the left such
that points with much lower squark masses are no longer excluded. As such it
would appear the sensitivity of the analysis in [5] decreases dramatically in
the limit of a light LSP in these NMSSM scenarios, with the lower bound on the
squark mass decreasing from around $2~{}$TeV/$c^{2}$ to as little as
$1~{}$TeV/$c^{2}$ in some cases, as shown in table 6.

Additionally whilst the black observed limit contour is generally further to
the left than the red, expected limit contour, indicating a slight excess in
some of the data yields compared with the background estimation, the agreement
between the two limits is reasonably strong.

These weaker lower bounds on the squark masses for the lightest LSP mass of
$3$ GeV/$c^{2}$ are summarised in table 6.

Scan | BP1 | BP3 | BP5 | BP6 | BP7 | BP8
---|---|---|---|---|---|---
$M_{\tilde{q},\text{ min}}$ [GeV/$c^{2}$] | 1000 | 1200 | 1250 | 1000 | 1250 | 1200
$M_{\tilde{g},\text{ min}}$ [GeV/$c^{2}$] | 1010 | 1000 | 1260 | 1010 | 1050 | 1000
Table 6: Approximate lower bounds on the squark mass and corresponding gluino
mass at 95% CL for a $3$ GeV/$c^{2}$ LSP.

It may be noted that the lower bounds on the squark and gluino masses are
considerably weaker for these light-LSP, low-$E_{\text{T}}^{\text{miss}}$
scenarios compared with the simplified models considered in [5].

As the LSP mass is increased above around $100~{}$GeV/$c^{2}$ the converse
becomes true, with the limits being more harsh for these NMSSM scenarios than
for the simplified models. This is expected due to the larger
$H_{\text{T}}^{\text{miss}}$ in these heavier LSP regions.

However, as the LSP mass is increased closer towards the masses of the squarks
and gluinos, the sensitivity appears once again to decrease for heavier
neutralinos. Unlike the light LSP region, however, this lack of sensitivity
for heavy LSP likely arises from the high $H_{\text{T}}$ cut, since few events
in this region pass this cut as shown in figure 7(a). Thus, in order to
explore this area of mass space a wider $H_{\text{T}}$ range would be required
than is considered in this paper.

Similar experimental limits can be placed on the other types of scan. We
recall here that the BP3-type scan has the gluino mass $200$ GeV/$c^{2}$ lower
than the squark mass, rather than $10$ GeV/$c^{2}$ higher, and the BP5/BP6-
and BP7/BP8-type scans are the same as the BP1- and BP3-types, respectively,
but with the appropriate stop or sbottom squark masses $250$ GeV/$c^{2}$
lighter than the squark/gluino, rather than being decoupled.

The observed and expected limits for these remaining mass scans exhibit a
similar behaviour, that is, the cross-section appears to dominate the
sensitivity for points with mid-range LSP mass, where the contours are closer
to vertical. However, in all cases the sensitivity for regions with lower LSP
masses and featuring high $H_{\text{T}}$ and low $H_{\text{T}}^{\text{miss}}$,
to the latter of which the analysis in [5] is not optimised, decreases
dramatically.

###  6.1 MSSM-like scenarios with light LSP

The main feature of the light LSP and low $E_{\text{T}}^{\text{miss}}$
scenarios under consideration relies on the LSP being singlino. In this case
it is possible for the decay cascades to end exclusively in an NLSP decaying
to an LSP and a Higgs boson, which is not the case in the MSSM.

For comparison, figure 18 shows the sensitivity to the simplified MSSM-like
scenario seen previously. Applying the same event selections as in [5], the
observed and expected limits are calculated at 95% CL, akin to the limits in
figure 17.

Figure 18: Observed (black) and expected (red) limits for an MSSM-like
scenario demonstrating the higher sensitivity to regions with low LSP mass.

In the limit plots in figures 17 and 18 it may be observed that the
experimental sensitivity to this simplified MSSM-like model is in fact
strongest for the lightest LSP mass of $3$ GeV/$c^{2}$, contrary to the NMSSM-
specific low-$E_{\text{T}}^{\text{miss}}$ mass scenarios. Conversely, it is
also clear that the overall sensitivity for the regions of parameter space in
which $M_{\tilde{\chi}_{1}^{0}}$ $>200$ GeV/$c^{2}$ is weaker for this model
compared with the NMSSM scenarios considered. Since the decay cascade is
truncated and there are no Higgs boson decays in this model, the expected
numbers of hadronic jets and $b$-tagged jets per event are lower. Therefore,
it is unlikely for as many events to contain more than five hadronic jets or
as many as two $b$-tagged jets, so they will not pass the event selections
which are imposed in this paper. However, exploiting the full 254 bins in [5]
would be expected to increase the sensitivity to this MSSM-like scenario.

##  7 Conclusion

Fairly strong limits of around $2~{}$TeV/$c^{2}$ have been placed on the
squark/gluino masses for a singlino-like LSP in the NMSSM for a LSP mass above
$100$ GeV/$c^{2}$ or so. However, below this mass the limits weaken by a
considerable amount in all cases, as shown in table 6, with limits for some
scenarios decreasing by as much as $1~{}$TeV/$c^{2}$. The eight original BPs
in [15], all featuring a light $3$ GeV/$c^{2}$ LSP, despite having a large
direct production cross-section, are still on or around the limit of
sensitivity of the analysis in [5] with $35.9~{}\text{fb}^{-1}$ data from the
CMS detector at the LHC, thus they cannot be completely excluded at this
stage.

It is clear that these light LSP and low $E_{\text{T}}^{\text{miss}}$
scenarios present further challenges for jets+$E_{\text{T}}^{\text{miss}}$
based searches akin to [5] at the LHC. In order to develop a search for these
stealthy scenarios one might wish to access regions of low
$H_{\text{T}}^{\text{miss}}$, however, this would require careful techniques
so as to not allow yields from background processes to dominate.

Given the expected high $b$-tag multiplicities in these scenarios (cf. figure
12) sensitivity may be boosted, though, if one concentrates on signal regions
with more $b$-_tagged_ jets. One may employ new techniques such as a double
$b$-tagger, one of which being developed by the CMS collaboration [25] and
another by the ATLAS collaboration [26] whereby, in the former, AK8 jets are
formed and, depending on the substructure, a discriminator output is assigned
by a Boosted Decision Tree (BDT), describing how likely the jet is to contain
two bottom quarks originating from the same decay vertex. Here AK8 refers to
the anti-$k_{\text{T}}$ algorithm with a jet cone radius of $0.8$. This tool
thus allows for a way to distinguish between single bottom quark jets and two
overlapping bottom quark jets, such as may be found originating from the decay
of a boosted Higgs boson, a technique employed in [27].

High $b$-tag multiplicities occur also in scenarios where the rôle of the SM
Higgs boson is played by a lighter NMSSM specific Higgs boson $H_{1}$ [16].
Using the double-$b$-tagging method, distributions of the double-$b$-tagged
jet mass can be studied. In any scenario involving SM or NMSSM specific Higgs
bosons, distributions of the double-$b$-tagged jet mass should exhibit
excesses over a smoothly decreasing background from QCD and top quark pair
production around the corresponding Higgs boson mass [16]. This might lead to
a simultaneous discovery of an extra lighter Higgs boson $H_{1}$.

## Acknowledgments

SM, CHS-T and AT are supported in part through the NExT Institute, AT is also
supported by an STFC studentship. SM acknowledges financial support from the
STFC CG ST/L000296/1. H.F acknowledges financial support from STFC CG
ST/N000250/1. SM and U.E. acknowledge support from the the H2020-MSCA-
RISE-2014 grant no. 645722 (NonMinimalHiggs). U.E. also acknowledges support
from the Marie Sklodowska-Curie grant agreement no. 690575 (InvisiblesPlus).

## References

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