HIG-20-018

HIG-20-018

# Search for light Higgs bosons from supersymmetric cascade decays in $\Pp\Pp$
collisions at $\sqrt{s}=13\TeV$

###### Abstract

A search is reported for pairs of light Higgs bosons ($\PH_{1}$) produced in
supersymmetric cascade decays in final states with small missing transverse
momentum. A data set of LHC $\Pp\Pp$ collisions collected with the CMS
detector at $\sqrt{s}=13\TeV$ and corresponding to an integrated luminosity of
138is used. The search targets events where both $\PH_{1}$ bosons decay into
$\bbbar$ pairs that are reconstructed as large-radius jets using substructure
techniques. No evidence is found for an excess of events beyond the background
expectations of the standard model (SM). Results from the search are
interpreted in the next-to-minimal supersymmetric extension of the SM, where a
“singlino” of small mass leads to squark and gluino cascade decays that can
predominantly end in a highly Lorentz-boosted singlet-like $\PH_{1}$ and a
singlino-like neutralino of small transverse momentum. Upper limits are set on
the product of the squark or gluino pair production cross section and the
square of the $\bbbar$ branching fraction of the $\PH_{1}$ in a benchmark
model containing almost mass-degenerate gluinos and light-flavour squarks.
Under the assumption of an SM-like $\PH_{1}\to\bbbar$ branching fraction,
$\PH_{1}$ bosons with masses in the range 40–120arising from the decays of
squarks or gluinos with a mass of 1200 to 2500are excluded at 95% confidence
level.

##  0.1 Introduction

This paper presents a search for pairs of light Higgs bosons ($\PH_{1}$)
produced in supersymmetric (SUSY) [1, 2, 3, 4, 5, 6, 7, 8] cascade decays in
final states with small missing transverse momentum (). Such events can arise
from the pair production of squarks () and gluinos () in the next-to-minimal
supersymmetric extension of the standard model (SM) [9] when the lightest SUSY
particle (LSP) is a singlino-like neutralino ($\PSGc_{\text{S}}^{0}$) of small
mass [10]. The $\PSGc_{\text{S}}^{0}$ mass eigenstate is dominated by the
singlino component and has only small couplings to other SUSY particles,
suppressing direct squark or gluino decays to the $\PSGc_{\text{S}}^{0}$.
Squarks and gluinos decay via the next-to-LSP into a $\PSGc_{\text{S}}^{0}$
and a Higgs, , or boson [10, 11]. The case of a singlet-like $CP$-even
$\PH_{1}$, shown in Fig. 1, is the focus of this search. When the
$\PSGc_{\text{S}}^{0}$ has a far smaller mass than the $\PH_{1}$ and the phase
space for the decay $\PSGczDt\to\PH_{1}+\PSGc_{\text{S}}^{0}$ is small, the
$\PH_{1}$ carries much larger momentum than the $\PSGc_{\text{S}}^{0}$. In
such -suppressed scenarios, the key signature for the pair production of
squarks and gluinos is a pair of Lorentz-boosted $\PH_{1}$ bosons.

Figure 1:  Diagram of squark pair production and subsequent cascade decay in
the benchmark signal model. The particle is the next-to-LSP,
$\PSGc_{\text{S}}^{0}$ is the singlino-like LSP, and $\PH_{1}$ is the
$CP$-even singlet-like Higgs boson.

This search targets events with two highly boosted $\PH_{1}$ bosons that decay
into $\bbbar$ pairs that are reconstructed as large-radius jets using
substructure techniques. This is the first search at the LHC to focus on this
type of event, where particles invisible to the detector have only small
transverse momentum () and therefore the events are not selected by searches
requiring significant [12, 10]. Previous searches by the ATLAS and CMS
experiments with similar final states have considered events with two boosted
SM Higgs bosons and large values of [13, 14], or two SM Higgs bosons in
resolved final states where each of the four quarks is reconstructed as a
separate jet, with either small [15] or large [16, 17, 15, 14] values of .
This search uses data from $\Pp\Pp$ collisions collected by the CMS detector
at $\sqrt{s}=13\TeV$ during 2016–2018, corresponding to an integrated
luminosity of 138 [18, 19, 20].

##  0.2 Benchmark signal model

A benchmark signal model is established following the work of Ellwanger and
Teixeira [10, 11]. The eight light-flavour squarks are assumed mass-degenerate
at the mass $m_{\text{SUSY}}$, and the gluino mass is set at 1% larger. The
small gluino-squark mass gap means that the kinematics of the final-state
particles are very similar in the $\PSq\PSq$, $\PSq\PSg$, and $\PSg\PSg$
production modes, as little momentum is transferred to the quark in the
$\PSg\to\PSq+\cPq$ decay. All SUSY particles other than gluinos and those
shown in Fig. 1 are assumed decoupled.

This search targets squarks and gluinos with $m_{\text{SUSY}}>1200\GeV$. Less
massive squarks and gluinos can be probed by -based searches, owing to their
larger pair-production cross sections [12]. Smaller $m_{\text{SUSY}}$ values
can also lead to smaller of the $\PH_{1}$ than is necessary for the $\bbbar$
pair to be merged in a single jet. The cross sections ($\sigma$) for the
signal probed in this search, calculated at next-to-leading order (NLO)
accuracy in the strong coupling constant () including approximate next-to-NLO
(NNLO) corrections and next-to-next-to-leading logarithmic (NNLL) soft gluon
corrections [21, 22, 23, 24, 25, 26, 27, 28, 29], are shown in Table 0.2.

Inclusive pair-production cross sections calculated at approximately NNLO and
NNLL in [21, 22, 23, 24, 25, 26, 27, 28, 29] for squark mass $m_{\text{SUSY}}$
and gluino mass 1% larger. The quoted uncertainty is obtained from variations
in the choice of scales, parton distribution functions, and .
$m_{\text{SUSY}}$ [] $\sigma(\Pp\Pp\to\PSq\PSq,\PSq\PSg,\PSg\PSg)$ [fb]
Uncertainty 1200 $580\,\\!\\!\,$ $8\%$ 1600 $69\,\\!\\!\,$ $9\%$ 2000
$10\,\\!\\!\,$ $11\%$ 2200 $4\,\\!\\!\,.1$ $13\%$ 2400 $1\,\\!\\!\,.6$ $14\%$
2600 $0\,\\!\\!\,.67$ $16\%$ 2800 $0\,\\!\\!\,.27$ $18\%$

The values considered of the $\PH_{1}$ mass ($m_{\PH_{1}}$) and the
corresponding $\PH_{1}\to\bbbar$ branching fractions ($\mathcal{B}$) are shown
in Table 0.2. Only events where both $\PH_{1}$ bosons decay into $\bbbar$
pairs are used as signal. The $\mathcal{B}$ values are chosen to be those of
an SM-like Higgs boson ($\PH_{\text{SM}}$) of the corresponding mass [10], as
calculated using 6.61 [30, 31]. The $\mathcal{B}$ values decrease for larger
$\PH_{1}$ masses as the virtual $\PW\PW^{*}$ and $\PZ\PZ^{*}$ decay channels,
both of which have sizeable leptonic branching fractions, become more
accessible. The region $m_{\PH_{1}}<m_{\PZ}$ is therefore where the
-suppressed all-jet signature is of greatest experimental importance.
Nevertheless, to preserve generality, this search attempts to probe as much of
the region $m_{\PH_{1}}<125\GeV$ as possible.

The $m_{\PH_{1}}$ values in this search and corresponding $\PH_{1}\to\bbbar$
branching fractions.  $m_{\PH_{1}}$ [] 30 35 40 50 60 70 80 90 100 110 120 125
$\mathcal{B}(\PH_{1}\to\bbbar)$ 0.86 0.86 0.86 0.86 0.85 0.84 0.83 0.81 0.79
0.75 0.65 0.58

In addition to $m_{\PH_{1}}$ and $m_{\text{SUSY}}$, there are two other
unknown masses in the benchmark model: those of the $\PSGc_{\text{S}}^{0}$ and
the . The corresponding degrees of freedom are parameterised by $R_{m}\equiv
m_{\PH_{1}}/m_{\PSGczDt}$ and $\Delta_{m}\equiv
m_{\PSGczDt}-m_{\PH_{1}}-m_{\PSGc_{\text{S}}^{0}}$. The -suppressed signature
arises for values of $R_{m}$ close to unity, provided $\Delta_{m}>0$ to permit
the $\PSGczDt\to\PH_{1}+\PSGc_{\text{S}}^{0}$ decay. In this case, the phase
space for the decay is small and the $\PSGc_{\text{S}}^{0}$ has much smaller
mass than the $\PH_{1}$, so the $\PSGc_{\text{S}}^{0}$ always carries much
less momentum than the $\PH_{1}$. The -suppressed signature probed in this
search is representative of a significant part of the model parameter space
since the momenta of reconstructed objects do not exhibit a strong dependence
on $R_{m}$ and $\Delta_{m}$ in the region $R_{m}>0.9$. Models with smaller
$R_{m}$ can be probed by -based searches [12, 10]. For the benchmark model,
the values $R_{m}=0.99$ and $\Delta_{m}=0.1\GeV$ are assumed.

Branching fractions of unity are assumed for the decays $\PSq\to\cPq+\PSGczDt$
and $\PSGczDt\to\PH_{1}+\PSGc_{\text{S}}^{0}$. In the $R_{m}$ and $\Delta_{m}$
region of the benchmark model, this is true except where
$m_{\PSGczDt}>m_{\PZ}+m_{\PSGc_{\text{S}}^{0}}$. In that case, the
$\PSGczDt\to\PZ+\PSGc_{\text{S}}^{0}$ decay is permitted if the has a higgsino
component [11]. However, the is expected to be mainly bino-like for relevant
values of its mass [10]. For configurations where the $\PH_{1}$ mass is close
to that of the $\PH_{\text{SM}}$, the decay
$\PSGczDt\to\PH_{\text{SM}}+\PSGc_{\text{S}}^{0}$ is also possible. The
signatures for such $\PH_{1}$ and $\PH_{\text{SM}}$ bosons are
indistinguishable in this search. The assumption that the branching fraction
for $\PSGczDt\to\PH_{1}+\PSGc_{\text{S}}^{0}$ decay is 100% can therefore be
relaxed to the assumption that the branching fractions to $\PH_{1}$ and
$\PH_{\text{SM}}$ sum to unity.

##  0.3 The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. A silicon pixel and
strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a
brass and scintillator hadron calorimeter, each composed of a barrel and two
endcap sections, reside within the solenoid volume. Forward calorimeters
extend the pseudorapidity ($\eta$) coverage provided by the barrel and endcap
detectors. Muons are measured in gas-ionisation detectors embedded in the
steel flux-return yoke outside the solenoid. Events of interest are selected
using a two-tiered trigger system. The first level, composed of custom
hardware processors, uses information from the calorimeters and muon detectors
to select events at a rate of around 100kHz within a fixed latency of about 4
[32]. The second level, known as the high-level trigger, consists of a farm of
processors running a version of the full event reconstruction software
optimised for fast processing, and reduces the event rate to around 1kHz
before data storage [33]. A more detailed description of the CMS detector,
together with a definition of the coordinate system and the kinematic
variables, can be found in Ref. [34].

##  0.4 Event simulation

The primary background in this search originates from multijet production.
Simulated multijet events are used to validate the multijet background
estimation based on data (described in Section 0.6), but are not used for any
of the final predictions. The remaining significant background is from events
with vector bosons that decay into quark-antiquark pairs. Simulated events are
used to determine the contributions from , +jets, and +jets production. The
expected yields from all other SM sources of background are found to be
negligible.

The multijet, +jets, and +jets processes are simulated at leading order (LO)
in perturbative quantum chromodynamics (QCD) using 2.4.2 [35] with up to four
additional partons at the matrix element (ME) level. Simulated signal events
for each pair of $m_{\PH_{1}}$ and $m_{\text{SUSY}}$ values of the benchmark
model are generated at LO at the ME level with up to one additional parton
using 2.3.3. The MLM [36] prescription is used to match partons from the LO ME
calculations to those from the parton showers. Simulated events are produced
at NLO in QCD at the ME level with the $\text{v}2.0$ [37, 38, 39, 40]
generator. The NNPDF2.3, NNPDF3.0, and NNPDF3.1 [41, 42, 43, 44] parton
distribution functions (PDFs) are used for the signal, 2016 background, and
2017–2018 background simulations, respectively. The parton shower and
hadronisation are performed via 8.2 [45]. The CUETP8M1 [46, 47] tune is used
for the signal and 2016 background simulations, while the CP5 tune [48] is
used for the 2017 and 2018 background simulations. The cross section used to
normalise the simulation is calculated at NNLO+NNLL in QCD [49], and those for
+jets and +jets are calculated at NNLO in QCD [50, 51, 52]. Additional
$\Pp\Pp$ interactions within the same or nearby bunch crossings (pileup) are
simulated for all events according to the distribution of the number of
interactions observed in each bunch crossing [53]. The interactions of
particles with the CMS detector are simulated using [54].

##  0.5 Object reconstruction and event selection

The data are collected using triggers based on the scalar sum of jet (), with
a requirement of $\HT>900\GeV$ (2016) and $\HT>1050\GeV$ (2017 and 2018).
Events are reconstructed offline using a particle-flow (PF) algorithm [55]
that reconstructs and identifies each individual particle (PF candidate) in an
event using an optimised combination of information from the components of the
CMS detector.

Jets are reconstructed by clustering the PF candidates using the anti-
clustering algorithm [56], as implemented in the package [57]. A distance
parameter of 0.4 or 0.8 is used for standard- and large-radius jets, referred
to as AK4 and AK8 jets, respectively. The jet momentum is defined as the
vectorial sum of all particle momenta in the jet. To mitigate the effect of
pileup, constituent charged PF candidates identified to be originating from
vertices other than the primary $\Pp\Pp$ interaction vertex are not used in
the clustering algorithm. The primary vertex is taken to be the vertex
corresponding to the hardest scattering in the event, evaluated using tracking
information alone, as described in Section 9.4 of Ref. [58]. For AK4 jets, an
offset correction is applied to correct for remaining pileup contributions.
For AK8 jets, the pileup-per-particle identification algorithm [59, 60] is
used to rescale the momenta of constituent neutral particles according to the
probability they originated from the primary vertex. This probability is based
on a local shape variable that distinguishes between collinear and soft
diffuse distributions of the surrounding charged particles that are compatible
with the primary vertex. For all jets, jet energy corrections are derived from
simulation to bring the measured average response of jets to that of particle-
level jets. In situ measurements of the momentum balance in dijet, photon+jet,
+jet, and multijet events are used to account for any residual differences in
jet energy scale and resolution between data and simulation [61, 62].
Additional criteria are imposed to reject jets from spurious sources, such as
electronics noise and detector malfunctions [63, 64].

The identification of AK8 jets originating from two collimated quarks (double-
tagging) is integral to the reconstruction of the $\PH_{1}$. A discriminant is
calculated for each jet using a double-tagging algorithm that combines
tracking and vertexing information in a multivariate approach with no
significant dependence on jet mass or [65].

The event preselection requires two AK8 jets with $\pt>170\GeV$ and
$|\eta|<2.4$ (so that they are within the acceptance of the tracker). If there
are more than two candidate AK8 jets, the two with the largest double- tag
discriminants are selected as most likely to have originated from
$\PH_{1}\to\bbbar$ decays. For the offline analysis, is defined as the scalar
sum of all AK4 jets with $\pt>40\GeV$ and $|\eta|<3.0$, including AK4 jets
with PF candidates clustered into AK8 jets. The distributions for various
simulated signal and background processes are shown in Fig. 2, after
implementing all preselection requirements. Since the final state contains
only jets, the average signal event depends significantly on
$m_{\text{SUSY}}$, and signal events with $m_{\text{SUSY}}>1200\GeV$ tend to
have $\HT>1500\GeV$.

Figure 2:  The distribution in signal events with different values of
$m_{\text{SUSY}}$, and in the simulated SM backgrounds, normalised to unit
area. The uncertainties are statistical. All events satisfy the preselection.

Additional requirements based on the expected kinematic properties of signal
events are applied after the preselection. They define the kinematic event
selection:

  1. 1.

Both selected AK8 jets must have $\pt>300\GeV$ and $|\eta|<2.4$, typical of
jets originating from $\PH_{1}\to\bbbar$ decays.

  2. 2.

There must be at least one AK4 jet with $\pt>300\GeV$ and $|\eta|<3.0$,
typical of quarks produced in the squark decays illustrated in Fig. 1. Such
jets must be separated by $\Delta
R\equiv\sqrt{\smash[b]{(\Delta\phi)^{2}+(\Delta\eta)^{2}}}>1.4$ from both
selected AK8 jets, to avoid being constructed from the same PF candidates.

  3. 3.

The event must exceed 1500.

Although the offline resolution is better than that of the trigger-level
variable, the offline threshold is comfortably above the trigger-level
requirements. The trigger efficiency for this analysis is measured using
events collected with a single muon trigger with a muon threshold between 24
and 27. The efficiency for each data-taking year is nearly 100%. For the 2018
data, the $|\eta|$ selection for the AK4 jets is reduced from 3.0 to 2.4 to
avoid a region of the endcap electromagnetic calorimeters affected by large
losses in crystal transparency, and therefore increased energy-equivalent
electronics noise [66]. This change has a negligible effect on signal
acceptance for all considered masses.

The fraction of signal events that satisfy the kinematic selection is
essentially independent of $m_{\PH_{1}}$. It increases from about 60 to 80% as
$m_{\text{SUSY}}$ increases from 1200 to 2000, after which it remains
approximately constant.

###  0.5.1 Double-tag based event selection

The two AK8 jets that are classified as the $\PH_{1}\to\bbbar$ candidates in
each event are randomly assigned the labels “A” and “B”. Their double- tag
discriminants define a two-dimensional (2D) parameter space, as shown in Fig.
3 for simulated signal and multijet events. The signal events are expected to
contain two $\PH_{1}\to\bbbar$ decays and therefore accumulate in the region
where both double- tag discriminants are large. The tag region (TR) is defined
as the region where the sum of the two double- tag discriminants exceeds 1.3,
illustrated by the shaded triangle in Fig. 3. Two additional regions are
defined in Fig. 3: the control region (CR), a multijet-dominated region with
negligible signal; and the validation region (VR), a more signal-like region
where one of the two jets has a large double- tag discriminant. The VR is
defined sufficiently far from the TR for the signal contamination to be
negligible.

Figure 3:  Distributions of simulated signal and multijet events in the 2D
double- tag discriminant plane, where the fractions of events in each bin are
represented by the areas of the filled red and open blue squares,
respectively. The signal parameters are $m_{\PH_{1}}=70\GeV$ and
$m_{\text{SUSY}}=2000\GeV$. The kinematic selection is implemented with the
masses of the two AK8 jets required to be within the set of signal and
sideband mass regions defined in Section 0.5.2. The green, yellow, and orange
shaded areas represent the tag region (TR), control region (CR), and
validation region (VR), respectively. Of the plotted signal events, 65% fall
within the TR.

About 50% of the signal events that satisfy the kinematic selection populate
the TR, with variation at the level of $\pm 10\%$ across the $m_{\PH_{1}}$ and
$m_{\text{SUSY}}$ parameter space considered. Since the multijet background is
dominated by light-flavour quark and gluon initiated jets, only about 3% of
these events populate the TR. For the , +jets, and +jets backgrounds, the
corresponding figures are 13, 6, and 3%, respectively.

###  0.5.2 Soft-drop mass based signal and sideband regions

In signal events, both selected AK8 jets are likely to originate from
$\PH_{1}\to\bbbar$ decays and therefore have a jet mass close to
$m_{\PH_{1}}$. The multijet background has no resonant mass peak, while the
other backgrounds are only expected to exhibit peaks near the known top quark
and vector bosons masses, which means that an accurate reconstruction of the
jet mass is important in distinguishing signal from background. The AK8 jet
masses are evaluated using the “soft-drop” algorithm [67] (with a soft-drop
threshold of $z_{\textrm{cut}}=0.1$ and angular exponent of $\beta=0$), in
which wide-angle soft radiation is removed recursively from a jet. In signal
events this algorithm achieves a relative jet mass resolution from 10% for
$m_{\PH_{1}}=125\GeV$ to 20% for $m_{\PH_{1}}=30\GeV$.

The soft-drop masses of the two AK8 jets define a 2D parameter space, shown in
Fig. 4, in which 10 signal regions ($S_{i}$) and 10 sideband regions ($U_{i}$)
are defined. The $S_{i}$ contain events in which the two $\PH_{1}$-candidate
jets have approximately the same soft-drop mass. The width of each $S_{i}$
corresponds to about four times the experimental soft-drop mass resolution for
the relevant simulated value of $m_{\PH_{1}}$.

Figure 4:  Map of mass regions used in the 2D soft-drop mass plane. The
regions labelled $S_{i}$ are the signal mass regions, and the disjoint regions
$U_{i}$ form the corresponding sidebands.

Figure 5:  The normalised distribution of events in the 2D soft-drop mass
plane overlaid by the map of mass regions. The upper left, upper right, and
middle left panels correspond to signal events for $m_{\text{SUSY}}=2000\GeV$
and $m_{\PH_{1}}$ values of 40, 70, and 125, respectively. The panels at
middle right, lower left, and lower right correspond to simulated multijet, ,
and vector boson backgrounds, respectively. All events satisfy the TR
requirement and the kinematic selection.

The event distributions for a set of signal models with different
$m_{\PH_{1}}$ values are shown in Fig. 5, with the signal and sideband mass
regions overlaid. The peaks in the signal distributions where one or both AK8
jets have a soft-drop mass close to zero result from a selected jet
originating from a single parton or one of the $\PH_{1}\to\bbbar$ decays lying
outside the acceptance of the jet reconstruction algorithm. The latter can
happen when the angular separation of the quarks exceeds the AK8 jet distance
parameter, or when the ratio of the quark values is larger than 9 (such that
the softer quark would not satisfy the $z_{\textrm{cut}}$ threshold in the
soft-drop algorithm). For signal models with $40<m_{\PH_{1}}<125\GeV$,
$\approx\\!50\%$ of the events that satisfy the kinematic and TR selection
fall within any of the $S_{i}$. However, for $m_{\PH_{1}}<35\GeV$ the bulk of
the distribution is lower in mass than $S_{1}$, leading to a rapid decrease in
signal acceptance.

The distributions of background events are also shown in Fig. 5. The majority
of multijet events contain at least one AK8 jet evaluated to have a small
soft-drop mass, reflecting the characteristic one-prong structure of quark and
gluon jets. After applying the kinematic and TR selection criteria,
approximately 5% of multijet events fall within any of the $S_{i}$, with
greater probability at small masses. For the vector boson and backgrounds the
corresponding figures are 7 and 19%, respectively, concentrated in the $S_{i}$
corresponding to masses between the boson and top quark masses.

For each $S_{i}$ there are two corresponding sideband regions, $U_{i}$, used
for the multijet background estimation described in Section 0.6. The sideband
regions $U_{1}$ have a triangular form to avoid the region of very small soft-
drop masses, where the density from multijet events increases sharply.

###  0.5.3 Categorisation in and expected yields

The selected events are classified according to three categories: 1500–2500,
2500–3500, and above $3500\GeV$. Each category is divided into the 10 mass
signal regions $S_{i}$ defined in Fig. 4, resulting in a total of 30 search
regions for each data-taking year. As can be seen in Fig. 6 for TR data summed
over the three data-taking years, the search region yields can be visualised
through a 30-bin histogram where bins 1–10 represent the $S_{i}$, in ascending
order, for the first category. The subsequent two sets of 10 bins represent
the results for the second and third categories. The primary background is
from multijet events, estimated from data using the method described in
Section 0.6. The expected contribution from events is also significant,
particularly in the larger soft-drop mass regions populated by jets from
hadronic top quark or boson decays. This prediction is validated in a
dedicated -enriched control region in data. The yields from +jets and +jets
production are small in comparison. All expected SM backgrounds tend to
exhibit small values of compared to signal.

Figure 6:  Observed and expected yields in the TR for each of the 30 search
regions, summed over the three data-taking years. The multijet background is
estimated from data using the method described in Section 0.6, while the other
backgrounds are simulated. Example signal distributions are shown for
$m_{\PH_{1}}=70\GeV$ and $m_{\text{SUSY}}=1200$, 2000, and 2800. The error
bars represent the statistical uncertainties and the hatched bands the
systematic uncertainties.

The distributions in signal events for $m_{\PH_{1}}=70\GeV$ and
$m_{\text{SUSY}}=1200$, 2000 and 2800are also shown in Fig. 6. Although the
production cross section decreases quickly with increasing $m_{\text{SUSY}}$,
the fraction of events in the larger-categories increases. Within each
category, the distribution of events in the 10 $S_{i}$ bins is described by a
peak with a width of about three bins, centred near the model value of
$m_{\PH_{1}}$.

##  0.6 Multijet background estimation from data

The mass sideband regions $U_{i}$ form a basis for using data to estimate the
multijet background. The density of the multijet background is approximately
uniform within each of the 10 mass regions (spanning $S_{i}$ and $U_{i}$ for
each region $i$ illustrated in Fig. 4). Apart from $U_{1}$, each $U_{i}$ is
constructed to have the same area as $S_{i}$ such that the corresponding
multijet yields, respectively denoted $\hat{U}_{i}$ and $\hat{S}_{i}$, are
approximately equal. The observed ratios of $S_{i}$ to $U_{i}$ yields,
$F_{i}$, are measured in CR data. The $F_{i}$ factors are found to be close to
unity except for the $F_{1}$ values which are approximately 1.5.

The multijet background in the TR is estimated independently for each signal
region $S_{i}$:

$\hat{S}_{i}^{\textrm{TR}}=F_{i}\,\hat{U}_{i}^{\textrm{TR}},$ (1)

where $\hat{U}_{i}^{\textrm{TR}}$ is the observed TR yield in sideband region
$U_{i}$ after subtracting the contributions from the other simulated
backgrounds. In rare cases where the prediction $\hat{S}_{i}^{\textrm{TR}}$ is
negative, it is set equal to zero.

Since the $F_{i}$ factors are measured and applied in different regions of
double- tag discriminant space, any correlation between the soft-drop mass and
the double- tag discriminant of AK8 jets can bias the prediction of Eq. (1).
Using a sample of data satisfying an alternative kinematic event selection
with the requirement for one or more AK4 jets inverted, the variation of
$F_{i}$ between the TR and the CR is found to be less than 10%.

The overall accuracy of the multijet estimation is assessed through closure
tests. First the method is applied to simulated multijet events in the TR
where, within statistical uncertainties, the predicted yields are consistent
with the simulated yields for each data-taking year. Second the method is
applied in the multijet-dominated VR data (defined in Fig. 3) by making the
appropriate modification to Eq. (1):
$\hat{S}_{i}^{\textrm{VR}}=F_{i}\,\hat{U}_{i}^{\textrm{VR}}$. The resulting
predicted and observed VR yields are consistent within uncertainties, as shown
in Fig. 7. Based on the results of the closure tests, a systematic uncertainty
of 15 (30%) is assigned in the lower two categories (upper category).

Figure 7:  A comparison of the predicted and observed multijet yields in the
validation region (VR), after subtraction of the other simulated backgrounds.
The prediction is made separately for the three data-taking years, and the
results are summed. The error bars on the data points represent their
statistical uncertainties. The uncertainties in the predicted yields
(statistical and systematic) are indicated by the hatched bands.

##  0.7 Systematic uncertainties

The simulated events for signal and the , +jets, and +jets backgrounds are
affected by various systematic uncertainties. The efficiency for tagging
(mistagging) a jet originating from two quarks (a light-flavour quark or
gluon) is corrected to match that observed in data [65]. The uncertainty in
this correction corresponds to $\approx\\!10\%$ in the simulated signal and
background yields. The uncertainties related to the jet energy corrections are
applied to the jet properties in bins of and $\eta$. These uncertainties
affect the event , leading to an $\approx\\!4\%$ migration of events between
adjacent categories. The uncertainty in the soft-drop mass scale in simulation
relative to data leads to a migration of events between adjacent $S_{i}$ and
$U_{i}$ regions of up to 10%. The uncertainty in the simulated soft-drop mass
resolution affects the widths of the simulated mass peaks. This effect is
larger for signal models with small $m_{\PH_{1}}$ and can reduce the $S_{i}$
selection efficiency by up to 20%.

The systematic uncertainties are assumed to be fully correlated among the
data-taking years except for the 2016 double-tagging uncertainties, which are
assumed uncorrelated because the CMS pixel detector was upgraded prior to 2017
data-taking. Changing these correlation assumptions is found to have only a
small effect on the final results. Systematic uncertainties related to
integrated luminosity, pileup, PDFs, renormalisation and factorisation scales,
modelling of initial-state radiation, and background cross sections were also
evaluated, along with the statistical uncertainties in the simulation, and
were found to make negligible contributions to the total uncertainty.

Systematic uncertainties in multijet yields arise from the systematic
uncertainties in the $F_{i}$ factors. As described in Section 0.6, an
uncertainty of $15\%$ is applied to the $F_{i}$ in the lower two categories
and $30\%$ in the upper category, uncorrelated among different $F_{i}$. Except
in the lowest category, the total uncertainty in the multijet yield is
dominated by the statistical uncertainty in $\hat{U}_{i}^{\textrm{TR}}$.

##  0.8 Results

Binned maximum likelihood fits to the data in all 30 search regions $S_{i}$
for each data-taking year are carried out under background-only and
signal+background hypotheses. The corresponding sideband regions $U_{i}$ are
fitted simultaneously, thereby constraining the multijet contributions to the
search region yields through Eq. (1). The likelihood functions are defined
through the product of $90\times 2$ Poisson distributions [68], one for each
search region and one for each sideband region, with additional constraint
terms for the “nuisance” parameters that account for the systematic
uncertainties summarised in Section 0.7. Figure 8 compares the result of the
background-only fit to the yields in the search regions for the combination of
2016, 2017, and 2018 data. There is no evidence for deviations of the data
from the fitted background. The values and uncertainties of most nuisance
parameters are unchanged in the fit, but the ones corresponding to the $F_{i}$
are constrained through Eq. (1) when the yields $\hat{S}_{i}^{\textrm{TR}}$
and $\hat{U}_{i}^{\textrm{TR}}$ are sufficiently large.

Figure 8:  Yields in all search regions after the background-only fit, summed
over the three data-taking years. Example signal contributions used in the
signal+background fits are shown for $m_{\text{SUSY}}=2200\GeV$, and
$m_{\PH_{1}}=50$, 90, and 125. The error bars represent the statistical
uncertainties and the hatched bands the systematic uncertainties.

Signal+background fits are used to set 95% confidence level () upper limits on
the product $\sigma\mathcal{B}^{2}$ for the mass points in the benchmark
signal model. The limits are set using the modified frequentist criterion [69,
70], with the profile likelihood ratio as test statistic [68]. The observed
and expected 95% upper limits on $\sigma\mathcal{B}^{2}$ are shown in Fig. 9,
as functions of $m_{\PH_{1}}$ for constant $m_{\text{SUSY}}$. The upper limits
are weaker for models with $m_{\PH_{1}}<35\GeV$, for which the signal-event
distribution in the 2D soft-drop mass plane peaks outside the signal regions.
The limits have no significant dependence on $m_{\text{SUSY}}$ for models with
$m_{\text{SUSY}}>2000\GeV$, whose signal events mostly populate the upper
category (as shown in Fig. 6).

Figure 9:  Upper limits at 95% on $\sigma\mathcal{B}^{2}$ as a function of
$m_{\PH_{1}}$, for $m_{\text{SUSY}}$ values of 1200 (upper), 2000 (middle),
and 2800(lower). The solid and dashed black lines indicate the observed and
median expected limits, respectively. The inner (green) band and the outer
(yellow) band indicate the regions containing 68 and 95%, respectively, of the
distribution of limits expected under the background-only hypothesis. The
solid and dashed red lines show the theoretical value of
$\sigma\mathcal{B}^{2}$ and its uncertainty [21, 22, 23, 24, 25, 26, 27, 28,
29, 30]. In the upper plot, these $\sigma\mathcal{B}^{2}$ values are beyond
the maximum of the vertical axis.

The $\sigma\mathcal{B}^{2}$ upper limits are used in conjunction with the
theoretical $\sigma$ and $\mathcal{B}$ values from Section 0.2 to exclude
ranges of masses in $m_{\PH_{1}}$ and $m_{\text{SUSY}}$ in the benchmark
model. The observed 95% upper limits on $r$, the ratio of measured and
theoretical values of $\sigma\mathcal{B}^{2}$, are shown in Fig. 10, with the
corresponding exclusion contours at $r=1$. Masses
$1200<m_{\text{SUSY}}<2500\GeV$ are excluded within the range
$40<m_{\PH_{1}}<120\GeV$. Expected exclusion contours for the background-only
scenario agree within one standard deviation with the observed contours. In
the region $110<m_{\PH_{1}}<125\GeV$, $\mathcal{B}$ starts to decrease more
quickly (as shown in Table 0.2), leading to a corresponding reduction in
sensitivity. Most of the sensitivity at large $m_{\text{SUSY}}$ comes from the
$\HT>3500\GeV$ region, where the statistical uncertainties in the observed
yields are dominant over systematic uncertainties. This search does not
explore the region outside of that shown in Fig. 10.

Figure 10:  The observed 95% upper limit on
$\sigma\mathcal{B}^{2}/(\sigma\mathcal{B}^{2})_{\textrm{theory}}$, quantified
by the colour scale as a function of $m_{\PH_{1}}$ and $m_{\text{SUSY}}$. The
solid and dashed red lines indicate the observed excluded region and its
theoretical uncertainty, respectively. The solid and dashed black lines
respectively represent the expected excluded region and its 68% interval,
under the background-only hypothesis.

To aid reinterpretation of the search by reducing the model-dependence, limits
evaluated using only the upper category are presented in Appendix .10.
Tabulated results are provided in the HEPData record for this analysis [71].

##  0.9 Summary

This paper presents a search for pairs of light Higgs bosons ($\PH_{1}$)
produced in supersymmetric cascade decays. The targeted final states have
small amounts of missing transverse momentum and two $\PH_{1}\to\bbbar$ decays
that are reconstructed as large-radius jets using substructure techniques. The
search is based on data from $\Pp\Pp$ collisions collected by the CMS
experiment at $\sqrt{s}=13\TeV$ during 2016–2018, corresponding to an
integrated luminosity of 138.

With no evidence found for an excess of events beyond the background
expectations of the standard model (SM), the results are interpreted in the
next-to-minimal supersymmetric extension of the SM (NMSSM), where a “singlino”
of small mass leads to squark and gluino cascade decays that can predominantly
end in a highly Lorentz-boosted singlet-like $\PH_{1}$ and a singlino-like
neutralino of small transverse momentum.

Upper limits are set on the product of the production cross section and the
square of the $\bbbar$ branching fraction of the $\PH_{1}$ for an NMSSM
benchmark model with almost mass-degenerate gluinos and light-flavour squarks
and branching fractions of unity for the cascade decays ending with the
$\PH_{1}$. Under the assumption of an SM-like $\PH_{1}\to\bbbar$ branching
fraction, $\PH_{1}$ bosons with masses in the range 40–120, arising from the
decays of squarks or gluinos with a mass from 1200 to 2500, are excluded at
95% confidence level.

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##  .10 Simplified analysis for reinterpretation

To aid reinterpretation of the search, a simplified analysis is performed
using only the 10 search regions in the upper category. The value
$A_{\text{kin}}$ is defined as the product of acceptance and efficiency for a
signal event to satisfy the kinematic selection (defined in Section 0.5) and
the $\HT>3500\GeV$ requirement. The value of $A_{\text{kin}}$ is common among
all 10 search regions in the simplified analysis, and is quoted for the
benchmark signal model in Table .10. Upper limits on the product
$\sigma\,\mathcal{B}^{2}\,A_{\text{kin}}$ as a function of $m_{\PH_{1}}$ are
set in Fig. .10.1, from which $\sigma\mathcal{B}^{2}$ limits for different
signal models can be derived through division by the appropriate value of
$A_{\text{kin}}$. Since the upper category provides most of the sensitivity
for $m_{\text{SUSY}}>2000\GeV$ in the nominal analysis, the
$\sigma\mathcal{B}^{2}$ upper limits in this region are not much weaker in the
simplified analysis. This is not the case in the region
$m_{\text{SUSY}}<2000\GeV$, where the lower categories become important.

Reference values of the product of kinematic acceptance and efficiency
($A_{\text{kin}}$) for the $\HT>3500\GeV$ region for the benchmark signal
model with different values of $m_{\text{SUSY}}$. These values are independent
of $m_{\PH_{1}}$ within 2% in the range $30<m_{\PH_{1}}<125\GeV$.
$m_{\text{SUSY}}$ [] 1600 2000 2200 2400 2600 2800 $A_{\text{kin}}$ 0.17 0.46
0.58 0.66 0.71 0.74

10.1.Figure:  The observed and expected 95% upper limit on the product of
$\sigma\mathcal{B}^{2}$ and $A_{\text{kin}}$, the kinematic acceptance and
efficiency for the $\HT>3500\GeV$ region, as a function of $m_{\PH_{1}}$. The
results are independent of $m_{\text{SUSY}}$ within 10% in the range
$1600<m_{\text{SUSY}}<2800\GeV$. The solid and dashed black lines indicate the
observed and median expected limits, respectively. The inner (green) band and
the outer (yellow) band indicate the regions containing 68 and 95%,
respectively, of the distribution of limits expected under the background-only
hypothesis.

The double- tag and mass region selections are not considered in
$A_{\text{kin}}$. This is done for simplicity, and because the fraction of
events satisfying these selections is not found to be strongly model-dependent
(except for the dependence on $m_{\PH_{1}}$, which is accounted for explicitly
in Fig. .10.1). For the benchmark model, this fraction is found to be
independent of $m_{\text{SUSY}}$ within 10% in the region
$1600<m_{\text{SUSY}}<2800\GeV$ and $35<m_{\PH_{1}}<125\GeV$. This approximate
independence does not hold for models with $m_{\text{SUSY}}<1600\GeV$, where
the $\PH_{1}$ distribution has substantial contributions below the necessary
for the $\PH_{1}\to\bbbar$ decay products to be merged in a single AK8 jet.
Only models with typical $\bbbar$ angular separation $\Delta R<0.8$ should be
considered for reinterpretation.