# Probing mild-tempered neutralino dark matter through top-squark production
at the LHC

Monoranjan Guchait<EMAIL_ADDRESS>Department of High Energy Physics,
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai-400005, India Arnab Roy<EMAIL_ADDRESS>Department of High Energy Physics, Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai-400005, India Seema Sharma<EMAIL_ADDRESS>Indian Institute of Science Education and Research, Pune-411008, India

###### Abstract

The lightest neutralino, assumed to be the lightest supersymmetric particle,
is proposed to be a dark matter (DM) candidate for the mass $\cal{O}$(100)
GeV. Constraints from various direct dark matter detection experiments and
Planck measurements exclude a substantial region of parameter space of minimal
supersymmetric standard model (MSSM). However, a “mild-tempered” neutralino
with dominant bino composition and a little admixture of Higgsino is found to
be a viable candidate for DM. Within the MSSM framework, we revisit the
allowed region of parameter space that is consistent with all existing
constraints. Regions of parameters that are not sensitive to direct detection
experiments, known as “blind spots,” are also revisited. Complimentary to the
direct detection of DM particles, a mild-tempered neutralino scenario is
explored at the LHC with the center of mass energy $\rm\sqrt{s}$=13 TeV
through the top-squark pair production, and its subsequent decays with the
standard-model-like Higgs boson in the final state. Our considered channel is
found to be very sensitive also to the blind spot scenario. Detectable signal
sensitivities are achieved using the cut-based method for the high luminosity
options $\rm 300$ and $\rm 3000\leavevmode\nobreak\ fb^{-1}$, which are
further improved by applying the multi-variate analysis technique.

##  1 Introduction

The quest for a signature of beyond standard model (SM) physics is a very high
priority agenda in high energy physics experiments and it has been going on
for a long time in several laboratories. In particular, at the LHC
experiments, looking for new physics signals is the major thrust area.
Unfortunately, no single direct evidence of new physics signals has been
observed at this point. As a consequence, the absence of experimental
confirmation leads to stringent constraints to various BSM models[1]. On the
other hand, the well-confirmed existence of dark matter (DM) by various
cosmological and astrophysical experiments serves as one of the strong
motivations to propose the existence of BSM physics[2, 3]. Among several
probable candidates of DM, the weakly interacting massive particle (WIMP)
turns out to be the most suitable one for thermal DM, with a correct relic
density measured by the PLANCK experiment which predicts[4],

$\displaystyle\rm\Omega h^{2}=0.12\leavevmode\nobreak\ \pm\leavevmode\nobreak\
0.001.$ (1.1)

Enormous efforts have been in place for a long time to look for DM candidates
via direct and indirect searches in various experiments[5, 6, 7, 8, 9, 10].
However, null results, in particular, from some of the direct detection (DD)
experiments have resulted in strong constraints on DM-nucleon scattering cross
sections in terms of DM (WIMP) masses[11, 12, 13, 14, 15, 16, 17, 18, 19, 20].
The DM-nucleon scattering cross section can be classified into two categories,
namely, spin-independent (SI) and spin-dependent (SD), depending on the
structure of the coupling. Note that, in general, the SI DM-nucleon scattering
cross section is smaller than that of the SD case, and it is more sensitive to
DD experiments[21, 22, 23]. For instance, the most stringent bounds come from
XENON1T experiment, where the DM-nucleon scattering cross section
corresponding to the DM of the mass range $\sim$20–100 GeV is strongly
restricted,
$\rm\sigma_{SI}\buildrel\scriptscriptstyle<\over{\scriptscriptstyle\sim}10^{-46}{\rm
cm}^{2}$[13]. The other experiments such as LUX[11], PANDA[12], PICO-60[17],
Darkside[14] etc. also constrain the DM-nucleon cross section for a wide range
of masses of DM candidates from few GeV to TeV.

The minimal supersymmetric standard model (MSSM) with R-parity conservation
offers the lightest neutralino, assumed to be the lightest supersymmetric
particle (LSP) as the potential DM (WIMP) candidate of the mass $\sim$ 100
GeV[24, 25, 26, 27]. Comprehensive searches of neutralino DM are carried out
at the LHC which lead to various constraints in the absence of any signal[28,
29, 30]. In MSSM, the physical neutralino state is constituted through the
linear superposition of electroweak (EW) gauginos (bino($\rm\widetilde{B}$),
wino($\rm\widetilde{W}$)) and
Higgsinos($\rm\tilde{H}_{u}^{0},\tilde{H}_{d}^{0}$). This composition is
mainly determined by relative values of two EW gaugino mass parameters, $\rm
M_{1}$ and $\rm M_{2}$, corresponding to U(1) and SU(2) gauge transformations
respectively. In addition, the other two parameters, namely Higgsino mass
parameter($\mu$) and $\tan\beta$, the ratio of two vacuum expectation values
of two neutral Higgs bosons also play an important role in determining the
physical masses and composition of neutralino states. A neutralino state with
pure Higgsino or wino composition of the mass
$\rm\sim\mathcal{O}(100)\leavevmode\nobreak\ GeV$ is found not to be a
favorable DM candidate because of its under-abundance of relic density[31].
However, for large masses $\rm\mathcal{O}(TeV)$, those can serve as a DM
candidate[31, 32, 33, 34, 35]. Similarly, a neutralino with pure bino
composition also does not satisfy the right relic density measurement (see Eq.
1.1). Hence, in order to propose LSP as a viable DM candidate, the “tempered
neutralino” scenario is proposed to be the best bet [31], where the neutralino
is no longer a pure state, but has admixtures of more than one composition. A
well-tempered bino-Higgsino[36, 37, 38, 39] or bino-wino[40, 41, 42]
neutralino is found to be the most suitable DM candidate for the mass
$\sim$100 GeV to achieve the right relic density. The Higgsino component is
indispensable to bring down the relic density to the required value (Eq. 1.1)
via resonant Z or Higgs-mediated annihilation, where the Higgs can be the SM-
like Higgs boson as well as heavier Higgs boson states, in the limit of large
sfermion masses. It is to be noted that, the neutralino-nucleon SI scattering
cross section is enhanced with the increase of Higgsino composition in the
neutralino state. Therefore, the strong experimental limits on the SI
scattering cross section restrict the composition of neutralino, in
particular, the Higgsino content[43, 44]. Hence a bino dominated neutralino
with a little mixture of Higgsino component, referred to as “mild-tempered
neutralino”, is expected to be the viable DM candidate for the mass
$\rm\mathcal{O}(100)\leavevmode\nobreak\ GeV$ or little less [45], and
consistent with all existing constraints. In this regard, it is to be noted
that few studies exist in the literature based on the extended supersymmetric
(SUSY) model, which present very light DM candidates ($\rm
m_{\chi}\buildrel\scriptscriptstyle<\over{\scriptscriptstyle\sim}50\leavevmode\nobreak\
GeV$)[46, 47, 48, 49, 50], satisfying all current constraints.

It is worth pointing out here, that there exists a region of MSSM parameter
space where the DM-nucleon SI scattering cross section almost vanishes because
of the interplay among various amplitudes. Consequently, direct detection rate
of DM becomes insensitive corresponding to that region of parameter space,
which is known as the “blind spot”(BS) [51, 52, 53, 54, 55]. As the DD
experiments fail to probe this BS scenario, it is worth finding a
complementary way for DM searches at the LHC.

In this current study, we focus on the mild-tempered scenario, i.e. bino-
Higgsino neutralino with a larger bino component, and of the mass ${\cal
O}$(100) GeV, and then identify the corresponding region of parameter space
consistent with all measurements. The existence of a relatively lighter LSP of
the mass range considered in this study is still not absolutely ruled out by
any SUSY searches at the LHC. Hence, our study will presumably give some idea
about its detectability at the LHC with its high luminosity options. With this
aim, the characteristic signature corresponding to this mild-tempered
neutralino including the BS scenario are discussed for the LHC experiment. We
consider the top-squark pair production and then its cascade decay to SM-like
Higgs boson and an LSP, the DM candidate. Although $\rm
m_{\widetilde{t_{1}}}\buildrel\scriptscriptstyle<\over{\scriptscriptstyle\sim}1.1\leavevmode\nobreak\
TeV$ are ruled out from searches at the LHC in the context of various
simplified models, for low $\rm
BR(\widetilde{t_{1}}\rightarrow\widetilde{\chi}^{0}_{1}+t)\sim 10\%$, $\rm
m_{\widetilde{t_{1}}}<1\leavevmode\nobreak\ TeV$ are found to be still allowed
using statistical analysis. It is be noted that the top-squarks of lower mass
range which are within the reach of current LHC energy, are also motivated in
the context of “naturalness” scenario [56, 57, 58, 59, 60, 61]. A detailed
investigation is carried out performing simulation to explore the feasibility
of finding the signal at the LHC for higher luminosity options, such as
$\rm{\cal L}=300\leavevmode\nobreak\ fb^{-1}$ and 3000 fb-1.

The paper is organized as follows. In section 2, the MSSM model set up
providing mild-tempered neutralino and BS scenario is discussed, and then
corresponding allowed region of parameters are identified. In section 3,
signal and background simulations are presented and followed by results.
Finally, we summarize in section 4.

##  2 Mild-tempered neutralino scenario in the MSSM

In this section, we discuss the MSSM model setup and then delineate the region
of parameter space interesting to our scenario which presents a DM candidate
of mass $\sim{\cal O}$(100) GeV consistent with the existing data from Planck
experiment (Eq. 1.1) and direct searches as mentioned above.

In the gauge eigenstate basis
($\rm\widetilde{B},\widetilde{W}_{3},\widetilde{H}_{d}^{0},\widetilde{H}_{u}^{0}$),
the neutralino mass matrix can be written as,

$\displaystyle\rm{M}_{N}=\left(\begin{array}[]{cccc}\rm
M_{1}&0&\frac{-g_{1}vc_{\beta}}{\sqrt{2}}&\frac{g_{1}vs_{\beta}}{\sqrt{2}}\\\
0&\rm
M_{2}&\frac{g_{2}vc_{\beta}}{\sqrt{2}}&\frac{-g_{2}vs_{\beta}}{\sqrt{2}}\\\
\frac{-g_{1}vc_{\beta}}{\sqrt{2}}&\frac{g_{2}vc_{\beta}}{\sqrt{2}}&0&-\mu\\\
\frac{g_{1}vs_{\beta}}{\sqrt{2}}&\frac{-g_{2}vs_{\beta}}{\sqrt{2}}&-\mu&0\end{array}\right).$
(2.6)

Here, $\rm M_{1}(g_{1})$ and $\rm M_{2}(g_{2})$ present the
(U(1))$\rm\widetilde{B}$ and (SU(2))$\rm\widetilde{W}_{3}$ gaugino
mass(coupling) parameters respectively, whereas $\mu$ is defined to be the
Higgsino mass parameter. The two VEVs corresponding to two neutral components
of the two Higgs doublets $\rm H_{u}^{0}$ and $\rm H_{d}^{0}$ are $v_{u}$ and
$v_{d}$ respectively and constrained to be $v_{u}^{2}+v_{d}^{2}=v^{2}$. As
practice, we assume $\tan\beta=\frac{v_{u}}{v_{d}}$, and $\rm s_{\beta}\equiv
sin\beta,\;c_{\beta}\equiv cos\beta$. The symmetric matrix $\rm{M_{N}}$ can be
diagonalized by a unitary matrix $\rm N_{4\times 4}$ to obtain the masses of
four neutralino states $\rm\tilde{\chi}_{i}^{0}(i=1,2,3,4)$ as,

$\displaystyle\rm M_{\tilde{\chi}^{0}}^{D}=\rm NM_{N}N^{\dagger},$ (2.7)

and the corresponding physical neutralino states are given by,

$\rm\widetilde{\chi}_{i}^{0}=N_{i1}{\widetilde{B}}+N_{i2}{\widetilde{W}_{3}}+N_{i3}\widetilde{H}_{d}^{0}+N_{i4}\widetilde{H}_{u}^{0}.$
(2.8)

Among the four neutralino states, two of the lighter states become gaugino-
like ($\rm\widetilde{B}$ and $\widetilde{W}_{3}$), if $\rm|M_{1,2}-\mu|\geq
M_{Z}$ and $\rm|\mu|>M_{2}>M_{1}$ with masses $\rm
m_{\widetilde{\chi}^{0}_{1}}\sim M_{1}$ and $\rm
m_{\widetilde{\chi}^{0}_{2}}\sim M_{2}$ respectively. The masses of Higgsino
dominated states are mostly controlled by $\mu$, and in particular $\rm
m_{\widetilde{\chi}^{0}_{2,3}}\sim\mu$ for a decoupled scenario ($\rm
M_{2}>>\rm\mu>M_{1}$). Further, for $\rm M_{1}<\mu<<M_{2}$ cases, the heaviest
state is expected to be $\rm\sim\widetilde{W}_{3}$-like, whereas intermediate
states become Higgsino dominated with the lightest state almost bino-like with
tiny Higgsino component ($\rm i.e.,\leavevmode\nobreak\
N_{11}^{2}>>N_{13}^{2}+N_{14}^{2}$). Similarly, in the basis ($\rm
i\widetilde{W}^{-},\widetilde{H}_{u}^{-}$) and ($\rm
i\widetilde{W}^{+},\widetilde{H}_{d}^{+}$) the chargino mass matrix is given
by:

$\rm M_{C}=\left(\begin{array}[]{c c}\rm M_{2}&\rm\sqrt{2}M_{W}\sin\beta\\\
\rm\sqrt{2}M_{W}\cos\beta&\mu\end{array}\right),$ (2.9)

which is diagonalized by two unitary matrices U and V. For $\rm M_{2}>>\mu$,
the lighter chargino ($\widetilde{\chi}_{1}^{\pm}$) state becomes Higgsino-
like.

For our considered scenario, the dominant DM annihilation process occurs
through the s-channel mediated by CP-even(h, H) and CP-odd(A) Higgs bosons or
Z,

$\displaystyle\rm\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}\xrightarrow{{\phi/Z}}f\bar{f},\
\ \ \ \phi=h,H,A,$ (2.10)

in the limit of relatively heavier slepton masses. The cross section of the
annihilation process primarily depends on the
$\rm(\phi,Z)$-$\widetilde{\chi}^{0}_{1}$-$\widetilde{\chi}^{0}_{1}$ couplings,
which are of the following form,

$\displaystyle\rm g_{h\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}}$
$\displaystyle\sim$ $\displaystyle\rm g(N_{12}-\tan\theta_{W}N_{11})(sin\alpha
N_{13}+\cos\alpha N_{14})$ (2.11) $\displaystyle\rm
g_{H\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}}$ $\displaystyle\sim$
$\displaystyle\rm g(N_{12}-\tan\theta_{W}N_{11})(sin\alpha N_{14}-\cos\alpha
N_{13})$ (2.12) $\displaystyle\rm
g_{A\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}}$ $\displaystyle\sim$
$\displaystyle\rm g(N_{12}-\tan\theta_{W}N_{11})(\cos\beta N_{14}-sin\beta
N_{13})$ (2.13) $\displaystyle\rm
g_{Z\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}}$ $\displaystyle\sim$
$\displaystyle\rm\frac{g}{2\cos\theta_{W}}(N_{13}^{2}-N_{14}^{2}),$ (2.14)

where $\rm\alpha$ is the mixing angle of the CP-even Higgs sector. Clearly,
the combined effect of bino$\rm(N_{11})$ and Higgsino components($\rm
N_{13},N_{14}$) in $\rm\widetilde{\chi}^{0}_{1}$ determine the annihilation
rate. In addition, a neutralino with a moderate to large amount of Higgsino
content may dominantly co-annihilate with Higgsino-like(large $\rm V_{12}$)
and nearly mass degenerate lighter chargino $\rm\widetilde{\chi}_{1}^{\pm}$,

$\displaystyle\rm\widetilde{\chi}^{0}_{1}\widetilde{\chi}_{1}^{\pm}\xrightarrow{{W^{\pm}}}f\bar{f},$
(2.15)

along with other subdominant contributions, which may enhance the annihilation
cross-section through the following coupling,

$\displaystyle\rm
g_{W^{\pm}\widetilde{\chi}^{0}_{1}\widetilde{\chi}_{1}^{\pm}}=\frac{g\tan\theta_{W}}{\sqrt{2}}(N_{14}V_{12}^{*}-\sqrt{2}N_{12}V_{11}^{*}).$
(2.16)

Hence, in combination of all processes, whichever are viable, the cross
section for annihilation process corresponding to a Higgsino-like LSP goes up
leading to an under-abundance of relic density. Hence one can conclude that an
LSP with a suitable combination of bino and Higgsino composition appears to be
a viable DM candidate around the mass ${\cal O}$(100) GeV. In the case of
wino-Higgsino dominated LSP, various possible annihilation and co-annihilation
processes can occur, which are mediated by SM gauge bosons, and lead to the
under-abundant scenario. In order to achieve the right relic density
prediction, in this case, one needs to lift the mass($\rm\sim M_{2}$) of the
LSP to TeV level and suppress annihilation cross section[31, 32]. This type of
scenario appears naturally in anomaly mediated SUSY breaking model[62, 63,
64]. Hence, a SUSY DM model disfavors the possibility of Higgsino/wino
dominated scenario with DM mass $\rm\sim\cal{O}$(100) GeV.

As pointed out earlier, the composition of the LSP DM candidate is also
constrained by direct detection experiments[13, 11, 12, 16, 17], where DM
candidate scattering off a heavy nucleus mediated by Higgs/gauge bosons or
squarks. The effects due to heavier squarks (${\cal O}$(1) TeV) are very much
suppressed. Hence the main contribution to SI(SD) cross section occurs through
Higgs(Z) boson exchange via t-channel diagram[21, 22]. The dominant
contribution comes from the diagram mediated by the CP-even lightest Higgs
boson, whereas contributions due to other heavier Higgs bosons are suppressed.
Interestingly, this suppression can be compensated by enhanced couplings of
heavier Higgs bosons with the quarks for a certain range of parameters, in
particular, for higher values of $\tan\beta$, which we will discuss later.

The SI scattering cross section is also sensitive to couplings $\rm
g_{h\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}}$(Eq. 2.11). The presence
of a larger Higgsino component in $\rm\widetilde{\chi}^{0}_{1}$ enhances the
SI DM-nucleon scattering cross section mediated mainly by the CP even lightest
Higgs boson, which is tightly constrained by the existing limits on DM-nucleon
scattering cross section from the XENON1T experiment[13]. On the other hand,
the composition of the $\rm\widetilde{\chi}^{0}_{1}$ state is also constrained
by relic density. Hence, the bino-Higgsino content of a mild-tempered
neutralino state is severely restricted by the combined effect of relic
density measurements and DM-nucleon cross section limits. This feature of
mild-tempered neutralino is reflected in Fig. 1(left), where the variation of
relic density with the relative size of bino and Higgsino composition of the
LSP is presented in terms of $\rm N_{11}^{2}/(N_{13}^{2}+N_{14}^{2})$. It is
to be noted that this figure is subject to the condition $\mu>0$ to avoid
effects from “blind spots,” which occur for $\mu<0$ when $\rm M_{1}$ is
assumed to be positive. It will be discussed in detail later. In Fig.
1(right), we present the ranges of $\rm\mu$ and $\rm M_{1}$ allowed by relic
density, limits from DD experiments along with some other constraints as
described in section 2.1. These figures are obtained by performing a numerical
scan of parameters (Eq.2.22), which will be discussed later.

Figure 1: (left) Relic density with the variation of $\rm\tilde{B}/\tilde{H}$
components in $\rm\widetilde{\chi}^{0}_{1}$. Allowed points by DD
measurements(yellow) and relic density(black band); (right) Ranges of $\mu$
and $\rm M_{1}$ along with the Higgsino component of the LSP allowed by relic
density and DD constraints.

Fig. 1(left) indicates that the $\rm\widetilde{\chi}^{0}_{1}$, with relatively
higher Higgsino composition and tiny bino content, makes under-abundance of
relic density. In this case, along with DM annihilation (Eq. 2.10), the co-
annihilation process(Eq. 2.15) also takes place resulting in a larger DM
annihilation cross section. Towards the rightmost region of Fig. 1(left), due
to the absence of sufficient Higgsino-components in the LSP, the DM-nucleon
scattering cross section goes down because of the couplings(Eq. 2.11) and
becomes consistent with DD limits. This region is presented(yellow) in Fig.
1(left) at the higher values of ratio $\rm
N_{11}^{2}/(N_{13}^{2}+N_{14}^{2})$. Hence, it can be concluded that the bino
dominated LSP with little admixtures ($\sim 1\%$) of Higgsino component is the
most favoured option in a decoupled scenario ($\rm M_{2}$ is very large). We
referred to this as a scenario of “mild-tempered” neutralino in the previous
section. In this scenario, relatively higher values $\rm\mu$ are found to be
allowed with light to moderate values of $\rm M_{1}$. It is clearly seen in
Fig. 1(right) that, for $\mu>0$, the Higgsino fraction in the LSP is tiny.
However, for $\mu<0$, there exist parameter spaces with a comparatively higher
amount of Higgsino components that are still allowed. It occurs mainly due to
the effect of “blind spots”, which is discussed next.

The blind spot is an interesting scenario where the DM-nucleon scattering
cross section is found to be very insensitive for a certain range of relevant
parameters in the MSSM, and the corresponding region of parameters is called
“blind spot”. It may happen for various reasons. For instance, the tree-level
scattering cross section may vanish either for a pure gaugino (i.e $\rm
N_{13},N_{14}\sim 0$) or Higgsino (i.e $\rm N_{11}\sim 0$) neutralino state.
Moreover, scattering takes place via one and two loop diagrams mediated by
gauge bosons, and an accidental cancellation among various scattering
amplitudes for pure Higgsino and gaugino LSP state, lead the total cross
sections too small and beyond the sensitivity of DD experiment(
$\rm\sigma_{SI}<<10^{-46}{\rm cm}^{2}$)[65, 66, 51]. Finally, BS may also
arise at the tree level due to cancellation among various amplitudes. The
dominant contribution to DM-nucleon cross section comes from the diagram
mediated by the CP even lightest Higgs boson, whereas contributions due to
other heavier Higgs bosons are found to be very small for the decoupling
scenario($\rm m_{A}>>M_{Z}$). Interestingly, at the tree level, the
suppression of contribution mediated by heavier Higgs bosons can be
compensated by its enhanced coupling with the (down type) fermions for the
range of moderate to higher values of $\tan\beta$. Additionally, the coupling
between heavier Higgs bosons and neutralinos, $\rm
H$-$\widetilde{\chi}^{0}_{1}$-$\widetilde{\chi}^{0}_{1}$(Eq. 2.12) may receive
similar kind of enhancement for a larger value of $\rm N_{13}$, the down type
of Higgsino content in the LSP. Consequently, the amplitudes mediated by
heavier Higgs bosons turn out to be comparable or at the same level of the CP
even SM-like Higgs boson exchange diagram. Depending on the relative signs of
$\mu$ and $\rm M_{1}$, the interference between these two diagrams, may become
destructive or constructive[53]. Incidentally, for a certain range and
combination of related parameters, these two contributions almost cancel each
other leading to the scattering cross section insensitive[53]. A detailed
analytical study shows that the combination of parameters corresponding to the
BS for moderate to larger values of $\tan\beta$ follow the relation among
$\mu$, $\rm m_{A}$, $\rm tan\beta$, and $\rm m_{\widetilde{\chi}^{0}_{1}}$
($\rm\sim M_{1}$), as [53],

$\displaystyle\rm\frac{M_{1}}{\mu}\sim-\left(\sin
2\beta+tan\beta\frac{m_{h}^{2}}{2m_{A}^{2}}\right).$ (2.17)

Corresponding to this parameter space, naturally a larger Higgsino component
$\sim\cal{O}$$(10\%)$ can be accessible without violating DD bounds in
contrast to the requirement of $\sim\cal{O}$$(1\%)$ or less for a mild-
tempered neutralino case. The above condition for BS connects the gaugino mass
parameter with the Higgs sector.

Figure 2: Contour plots of $\rm\mu/m_{\widetilde{\chi}^{0}_{1}}$ for various
values corresponding to BS scenario in the $\rm tan\beta$ and $\rm m_{A}$
plane along with the exclusion lines from $\rm h,A\to\tau\tau$ searches in
ATLAS(red) and CMS(blue) experiments.

Note that a substantial region of $\rm\tan\beta$ and $\rm m_{A}$ plane is
excluded from the Higgs searches in the channel, $\rm h,A\to\tau\tau$ [67,
68]. This $\rm m_{A}$-$\tan\beta$ exclusion can be traded to obtain
constraints on $\rm\mu/m_{\widetilde{\chi}^{0}_{1}}$, by using Eq. 2.17 in the
$\rm m_{A}$-$\tan\beta$ plane. In Fig. 2, following Eq. 2.17 the contour plots
of $\rm\frac{\mu}{m_{\widetilde{\chi}^{0}_{1}}}\sim\frac{\mu}{M_{1}}$ are
shown in the $\rm m_{A}$, $\rm tan\beta$ plane[53]. The region above the red
and blue lines are excluded due to the non observation of any signal events in
the $\rm h,A\to\tau\tau$ searches by
ATLAS[67]($\rm\mathcal{L}=139.5\leavevmode\nobreak\ fb^{-1}$) and
CMS[68]($\rm\mathcal{L}=35.9\leavevmode\nobreak\ fb^{-1}$) experiments
respectively. Depending on the value of $\rm m_{A}$, the BS condition, i.e.
the ratio $\rm\frac{\mu}{M_{1}}$ may vary from -1.5 to -3.5. It implies that
the lightest neutralino state is bino like whereas the second and third
heavier states are Higgsino like in the limit of large $\rm M_{2}$, which is
exactly the scenario that we try to explore at the LHC experiment.

As explained before, the main focus of this study is to explore the
feasibility of finding mild-tempered neutralino scenario at the LHC. The added
advantage of our proposed channel is its sensitiveness to the region of
parameters corresponding to the BS scenario, which can also be probed at the
LHC. As we know, the content of bino and Higgsino in the LSP depends on the
splitting between $\rm\mu$ and $\rm M_{1}$. Therefore, mild-tempered scenario
appears with the condition
$\rm|\mu|-M_{1}\buildrel\scriptscriptstyle>\over{\scriptscriptstyle\sim}100\leavevmode\nobreak\
GeV$, which provides also an LSP of mass $\cal O$(100) GeV. The scenario with
little Higgsino admixture along with the dominant bino composition in
$\rm\widetilde{\chi}^{0}_{1}$ presumably predicts Higgsino-dominated
$\widetilde{\chi}^{0}_{2,3}$ and $\widetilde{\chi}_{1}^{\pm}$ states that are
degenerate in mass $\sim\mu$, for a decoupled wino state (i.e large $\rm
M_{2}$). In such cases, heavier states $\widetilde{\chi}^{0}_{2,3}$ prefer to
decay to a Z boson and an LSP, and $\widetilde{\chi}_{1}^{\pm}$ decays to a W
and an LSP. The coupling involved in $\widetilde{\chi}^{0}_{2,3}$ decays is
$\rm Z$-$\widetilde{\chi}^{0}_{2,3}$-$\widetilde{\chi}^{0}_{1}\propto$ $\rm
N_{13}N_{23}-N_{14}N_{24}$, and since $\widetilde{\chi}^{0}_{1}$ is primarily
bino dominated (i.e $\rm N_{13},N_{14}$ very tiny), it is suppressed. Thus
$\rm\widetilde{\chi}^{0}_{2,3}$ preferably decay as,

$\displaystyle\rm\widetilde{\chi}^{0}_{2,3}\to h+\widetilde{\chi}^{0}_{1},$
(2.18)

and a larger Higgsino composition in $\widetilde{\chi}^{0}_{2,3}$ state(Eq.
2.11) makes its rate higher. This decay channel of
$\widetilde{\chi}^{0}_{2,3}$ is found to be the characteristic feature for the
mild-tempered neutralino scenario. Hence testing of this scenario can be
performed by studying $\widetilde{\chi}^{0}_{2,3}$ and
$\widetilde{\chi}_{1}^{\pm}$ production at the LHC[69, 70] and their
subsequent decays. Earlier, this channel is thought to be a “spoiler” mode
corresponding to trilepton signal in
pp$\to\widetilde{\chi}^{0}_{2}\widetilde{\chi}_{1}^{\pm}\to\ell^{+}\ell^{-}\ell\widetilde{\chi}^{0}_{1}\widetilde{\chi}^{0}_{1}$
production[71, 72]. In this study, instead of considering the
$\rm\widetilde{\chi}^{0}_{2}\widetilde{\chi}_{1}^{\pm}$ production via
electroweak interaction, we consider the production of
$\widetilde{\chi}^{0}_{2}$ through lighter top-squark production via strong
interaction, where $\rm\widetilde{t_{1}}$ dominantly decays to Higgsino-like
$\rm\widetilde{\chi}^{0}_{2,3}$ and $\chi_{1}^{\pm}$[73, 70]. The decay
$\rm\widetilde{t_{1}}\to t+\widetilde{\chi}^{0}_{2,3}$, is governed by the
interactions,

$\displaystyle\rm\mathcal{L}_{t\bar{\tilde{t}}\tilde{\chi}_{i}^{0}}=\bar{t}\left(g_{L}^{\tilde{\chi}_{i}^{0}}P_{L}+g_{R}^{\tilde{\chi}_{i}^{0}}P_{R}\right)\widetilde{\chi}^{0}_{i}\tilde{t},$
(2.19)

where,

$\displaystyle g_{L}^{\tilde{\chi}_{i}^{0}}$ $\displaystyle=$
$\displaystyle-\left[\frac{g_{2}}{\sqrt{2}}N_{i2}+\frac{g_{1}}{3\sqrt{2}}N_{i1}\right]\cos\theta_{\tilde{t}}-\frac{m_{t}}{v}N_{i4}\sin\theta_{\tilde{t}}$
(2.20) $\displaystyle\sim$
$\displaystyle\frac{g_{1}}{3\sqrt{2}}N_{i1}\cos\theta_{\tilde{t}}-\frac{m_{t}}{v}N_{i4}\sin\theta_{\tilde{t}}$
$\displaystyle g_{R}^{\tilde{\chi}_{i}^{0}}$ $\displaystyle=$
$\displaystyle\frac{2\sqrt{2}}{3}g_{1}N_{i1}\sin\theta_{\tilde{t}}-\frac{m_{t}}{v}N_{i4}\cos\theta_{\tilde{t}}.$
(2.21)

Here $\theta_{\tilde{t}}$ is the mixing angle in the top-squark sector.
Evidently, the $\rm m_{t}$ dependent term becomes dominant for Higgsino($\rm
N_{i4}$)-like neutralino states leading higher branching ratio (BR) for
$\rm\widetilde{t_{1}}\to\widetilde{\chi}^{0}_{2,3}+t$. Due to large enough
splitting between $\mu$ and $\rm M_{1}$, it is natural to have $\rm
m_{\widetilde{\chi}^{0}_{2,3}}-m_{\widetilde{\chi}^{0}_{1}}>125\leavevmode\nobreak\
GeV$, resulting in the $\rm\widetilde{\chi}^{0}_{2,3}\rightarrow
h+\widetilde{\chi}^{0}_{1}$ decay to be dominant. Hence the mild-tempered
neutralino DM can be indirectly produced from the decay of Higgsino-like
$\rm\widetilde{\chi}^{0}_{2,3}$ producing those in the lighter top-
squark($\rm\widetilde{t_{1}}$) production. It is be noted that, this type of
scenario can also be probed through the associated production, such as $\rm
pp\to\widetilde{\chi}^{0}_{2,3}\widetilde{\chi}_{1}^{\pm}$ and with the three
lepton final states along with missing energy[74, 75, 76]. However, we observe
that for the same set of parameters, the rates corresponding to signal final
states are higher for top-squark pair production via strong interaction than
the case of electroweak associated production.

###  2.1 Numerical scan

In order to identify the region of parameter space of our interest we perform
an illustrative numerical scan of all relevant parameters. This scan is
carried out using SUSPECT[77] to calculate the spectrum for a given set of
input parameters, and then interfacing with SUSYHIT[78] to obtain respective
branching fractions of SUSY particle decays. Also micrOMEGAs[79, 80, 81, 82]
is interfaced for the calculation of DM related observables and then checking
the constraints.

We have set the ranges of the most relevant parameters, including third
generation soft squark masses ($\rm M_{Q_{3}},\leavevmode\nobreak\
M_{t_{R}}$), in the random scan (every unit is in GeV, wherever applicable):

$\displaystyle\rm 1.5\leq{tan\beta}\leq 60,30\leq M_{1}\leq 1000,100\leq
M_{2}\leq 3000,\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ $ $\displaystyle\rm 100\leq|\mu|\leq
1500,100\leq m_{A}\leq 1500,600\leq M_{Q_{3}}\leq 2500,600\leq M_{t_{R}}\leq
2500,$ (2.22)

while the other gaugino mass parameter is fixed as,

$\displaystyle\rm M_{3}=3\leavevmode\nobreak\ TeV.$ (2.23)

First two generations squark masses are assumed to be,

$\displaystyle\rm M_{Q_{1,2}}=3\leavevmode\nobreak\ TeV.$ (2.24)

The A-term corresponding to the third generation quark($\rm A_{t}$) plays an
important role in determining the lightest CP even SM-like Higgs boson mass,
and it is varied in the range,

$\displaystyle\rm-6\leavevmode\nobreak\ TeV\leq A_{t}\leq
6\leavevmode\nobreak\ TeV.$ (2.25)

All the slepton masses of the first two generations are fixed to 2 TeV. While
performing the scan, each model point is tested with PLANCK[4] data (Eq. 1.1)
and limits from direct searches[11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. We
focus only on the LSP of the mass range $\sim$50-500 GeV. The presence of SM-
like Higgs boson (h), with mass 125$\rm\pm 3\;GeV$ is also ensured. Other
absolute constraints from LEP[83], for example, $\rm
m_{\rm\tilde{\chi}_{1}^{\pm}}\geq 103.5\;GeV$ and $\rm m_{\rm
H^{\pm}}>78.6\leavevmode\nobreak\ GeV$ are imposed. In addition,
Higgsbounds-5.5.0[84, 85, 86, 87, 88] is used to check the Higgs couplings and
related measurements. The exclusion of top-squark-neutralino mass plane
predicted by CMS[89, 90, 91, 92] and ATLAS[93, 94, 95, 96] experiments are
also examined using the SModelS-1.2.3 package [97, 98]. Generally the SMS
model with $\rm
BR(\widetilde{t_{1}}\rightarrow\widetilde{\chi}^{0}_{1}+t)=100\%$ is used to
interpret data. Whereas, in our scenario, $\rm
BR(\widetilde{t_{1}}\rightarrow\widetilde{\chi}^{0}_{1}+t)\sim 10\%$ implies
much weaker exclusion limits and consequently relatively light top-squarks
($\rm m_{\widetilde{t_{1}}}\sim 700\leavevmode\nobreak\ GeV$) are also found
to be allowed. Performing the scan, Fig.1(left) is plotted, where mainly the
relic density and DD constraints are relaxed to show the effect of the
compositions of $\rm\widetilde{\chi}^{0}_{1}$ on the relic density and DD
measurements.

Few representative benchmark points (BP) are chosen (see Table 1), which are
consistent with all constraints mentioned above. These BPs are used to obtain
the signal sensitivities by performing the simulation of our proposed signal
process. These BPs primarily represent two scenarios, namely “mild-tempered
neutralino” and “blind spots”. But under these broad pictures, they also
encompass compressed and non-compressed spectrum corresponding to various
choices of mass differences, $\rm\Delta
m_{1}=m_{\widetilde{t_{1}}}-(m_{t}+m_{\widetilde{\chi}^{0}_{2,3}})$ and
$\rm\Delta m_{2}=m_{\widetilde{\chi}^{0}_{2,3}}-m_{\widetilde{\chi}^{0}_{1}}$.

Table 1: Masses, branching fractions, DM observables for a few representative
BPs and labeled those corresponding to the BS scenario. Energy units are in
GeV, wherever applicable.

| BP1 | BP2 | BP3 |  BP4(BS) |  BP5(BS) | BP6 | BP7 |  BP8(BS) |  BP9(BS)
---|---|---|---|---|---|---|---|---|---
$\rm M_{1}$ | 60.8 | 58.5 | 274.2 | 334.1 | 296.4 | 204.9 | 352.7 | 238.4 | 248.4
$\rm M_{2}$ | 2784.4 | 2102.4 | 2719.2 | 1438.5 | 1494.1 | 1093.6 | 1860.2 | 1561.4 | 1071.0
$\rm\mu$ | 655.6 | 793.6 | 984.1 | -789.8 | -717.5 | -489.1 | -610.2 | -414.2 | -539.9
$\rm m_{A}$ | 1252.7 | 953.2 | 584.1 | 712.7 | 585.6 | 453.9 | 762.1 | 459.3 | 543.8
$\rm tan\beta$ | 7.5 | 6.0 | 6.6 | 6.1 | 6.2 | 5.0 | 5.8 | 6.3 | 6.7
$\rm M_{Q_{3}}$ | 856.2 | 1102.2 | 2277.6 | 1024.8 | 1544.2 | 770.1 | 824.4 | 765.8 | 811.5
$\rm M_{t_{R}}$ | 3552.0 | 1889 | 1688.8 | 2403.3 | 2061.9 | 2381.8 | 2596.2 | 2088.9 | 2634.1
$\rm m_{\widetilde{t_{1}}}$ | 954 | 1059 | 1675 | 1038 | 1475 | 688 | 804 | 635 | 765
$\rm m_{\widetilde{\chi}^{0}_{3}}$ | 666 | 802 | 996 | 800 | 729 | 494 | 620 | 424 | 550
$\rm m_{\widetilde{\chi}^{0}_{2}}$ | 666 | 800 | 994 | 796 | 725 | 499 | 618 | 422 | 545
$\rm m_{\widetilde{\chi}^{0}_{1}}$ | 59 | 58 | 272 | 335 | 295 | 207 | 354 | 238 | 249
$\rm m_{\tilde{\chi}_{1}^{\pm}}$ | 664 | 799 | 993 | 795 | 725 | 495 | 618 | 420 | 545
$\rm m_{h}$ | 125 | 123 | 123 | 125 | 124 | 123 | 123 | 124 | 125
$\rm m_{H}$ | 1253 | 953 | 584 | 713 | 584 | 454 | 763 | 460 | 544
$\rm N_{11}^{2}$ | 0.995 | 0.996 | 0.996 | 0.996 | 0.996 | 0.99 | 0.99 | 0.976 | 0.99
$\rm N_{13}^{2}+N_{14}^{2}$ | 0.005 | 0.003 | 0.003 | 0.004 | 0.004 | 0.01 | 0.01 | 0.023 | 0.01
$\rm\Omega h^{2}$ | 0.129 | 0.122 | 0.119 | 0.112 | 0.121 | 0.110 | 0.117 | 0.119 | 0.110
$\rm\sigma_{SI}(10^{-11}\>pb)$ | $5.1$ | $5.2$ | $10$ | $0.009$ | $0.02$ | $1.9$ | $2.4$ | $0.69$ | $0.002$
$\rm\sigma_{SD}(p)(10^{-7}\>pb)$ | $7.2$ | $3.2$ | $1.6$ | $5.2$ | $7.5$ | $32$ | $21$ | $100$ | $26$
$\rm\sigma_{SD}(n)(10^{-7}\>pb)$ | $5.7$ | $2.5$ | $1.3$ | $4.1$ | $5.8$ | $25$ | $12$ | $78$ | $20$
$\rm BR(\tilde{t}_{1}\rightarrow\tilde{\chi}_{1}^{0}+\>t)$ | 0.05 | 0.11 | 0.16 | 0.08 | 0.05 | 0.11 | 0.15 | 0.08 | 0.08
$\rm BR(\tilde{t}_{1}\rightarrow\tilde{\chi}_{2}^{0}+\>t)$ | 0.49 | 0.31 | 0.20 | 0.37 | 0.34 | 0.32 | 0.33 | 0.34 | 0.33
$\rm BR(\tilde{t}_{1}\rightarrow\tilde{\chi}_{3}^{0}+\>t)$ | 0.42 | 0.51 | 0.22 | 0.49 | 0.43 | 0.49 | 0.45 | 0.52 | 0.50
$\rm BR(\tilde{\chi}_{2}^{0}\rightarrow\tilde{\chi}_{1}^{0}+\>h)$ | 0.70 | 0.73 | 0.70 | 0.73 | 0.72 | 0.85 | 0.83 | 0.78 | 0.75
$\rm BR(\tilde{\chi}_{3}^{0}\rightarrow\tilde{\chi}_{1}^{0}+\>h)$ | 0.28 | 0.27 | 0.12 | 0.24 | 0.25 | 0.04 | 0.12 | 0.09 | 0.19

Notice also that for all cases of BPs, $\rm m_{\widetilde{t_{1}}}$ varies from
600-1700 GeV and for all cases $\rm
BR(\widetilde{t_{1}}\rightarrow\widetilde{\chi}^{0}_{1}+t)$ is subdominant,
while $\rm\widetilde{\chi}^{0}_{2,3}\rightarrow\widetilde{\chi}^{0}_{1}+h$ is
dominant. Performing the simulation of signal and backgrounds, signal
sensitivities are presented for all these BPs.

##  3 Signal and Background

As discussed before, we consider the following process where the lightest
neutralino originates from the decay of second and third lightest
neutralino($\widetilde{\chi}^{0}_{2,3}$) produced via top-squark production as
shown below,

Since in this scenario, the
$\rm\widetilde{\chi}^{0}_{2}/\widetilde{\chi}^{0}_{3}$ are dominantly
Higgsino-like, hence BR$\rm(\widetilde{t_{1}}\to
t+\widetilde{\chi}^{0}_{2,3})$ is larger than the BR($\rm\widetilde{t_{1}}\to
t+\widetilde{\chi}^{0}_{1}$). Subsequently, the higher neutralino state
(either $\rm\widetilde{\chi}^{0}_{2}$ or $\rm\widetilde{\chi}^{0}_{3}$)
dominantly decays to SM-like Higgs boson and $\rm\widetilde{\chi}^{0}_{1}$.
Here $\rm X\equiv\widetilde{\chi}^{0}_{1},\widetilde{\chi}^{0}_{2,3}$ leads to
a $\rm\widetilde{\chi}^{0}_{1}$ accompanied by either Z or $\rm h$ in the
final state. We focus only on single Higgs boson in the final state. However,
we found that the contribution of di-Higgs boson events in the signal is
negligible. The $\rm b\bar{b}$ channel of Higgs boson decay is considered
owing to its higher BR and comparatively easy to reconstruct its mass. The
pair of lightest neutralinos escape the detector leading to a huge amount of
missing energy in the final state. Moreover, there is another pair of b-jets
originating from two top quarks. Hence, the final state of the signal event is
characterized by,

$\displaystyle\rm h_{b\bar{b}}+\ell+E{\\!\\!\\!/}_{T}+(\geq
1)\leavevmode\nobreak\ b-jets;\ \ \ell=e,\mu.$ (3.26)

We found that the contribution of di-Higgs production to the signal event is
negligible. It is known that QCD is the main source of background
corresponding to any pure hadronic final state. Hence, in order to eliminate
it, the leptonic decay of one of the top quarks is considered. We require the
presence of only one lepton in the final state. The other dominant SM
backgrounds are:

$\displaystyle\rm p\leavevmode\nobreak\ p\rightarrow
t\bar{t}(1\ell),\leavevmode\nobreak\ t\bar{t}(2\ell),\leavevmode\nobreak\
t\bar{t}h,\leavevmode\nobreak\ t\bar{t}Z,\leavevmode\nobreak\
t\bar{t}b\bar{b}$ (3.27)

where, the combination of two b’s coming from the top, $\rm h$, Z, or gluon
splitting mimics the signal b-jets from Higgs decay. The lepton and $\rm
E{\\!\\!\\!/}_{T}$ arise from the semi-leptonic decay of one of the top
quarks, while the other top decays hadronically.

It is to be noted that in the signal events, the angular separation between
two b-jets depends on the boost of Higgs boson, which is determined by the
mass differences, $\rm\Delta
m_{1}=m_{\widetilde{t_{1}}}-(m_{t}+m_{\widetilde{\chi}^{0}_{2,3}})$ and
$\rm\Delta m_{2}=m_{\widetilde{\chi}^{0}_{2,3}}-m_{\widetilde{\chi}^{0}_{1}}$.
Accordingly, we simulate signal events in resolved and non-resolved categories
depending on the boost of Higgs boson. In Table 1, BP1-BP5 correspond to the
non-resolved category while BP6-BP9 represent the resolved one. For the
boosted case, two b-jets likely to appear as a single fat jet, which we refer
to as the “Higgs jet(HJ)” now onwards.

The PYTHIA8 [99, 100] is used to generate $\rm
t\bar{t}(1\ell),\leavevmode\nobreak\ t\bar{t}(2\ell)$ events, while the other
background processes are generated using<EMAIL_ADDRESS>interfacing with PYTHIA8, for showering and hadronization. Signal events are
generated in<EMAIL_ADDRESS>using UFO for the MSSM (MSSM-SLHA2),
where the parameter card is generated from SLHA file [102], obtained from
SUSYHIT, corresponding to each BP. The same SLHA file is used for subsequent
showering of signal events in PYTHIA8. Detector effects are taken into account
by passing all signal and background events through Delphes-3.4.2[103] using
the CMS detector card111Results are checked with ATLAS card as well, and no
appreciable change is observed..

In the simulation, the following selections are imposed, where objects are
selected using Delphes inputs.
(1) Lepton selection : Leptons are selected with $\rm
p_{T}>20\leavevmode\nobreak\ GeV$ and $|\eta|<2.5$. Isolation is ensured using
mini-isolation criteria by checking e-flow objects of Delphes as follows
[104]:

$\displaystyle\rm\frac{\sum p_{T}^{R<r}}{p_{T,\ell}}<I,\;\;\ell=e,\mu.$ (3.28)

Here $\rm r=\frac{10.0}{p_{T,\ell}}$ and $\rm I=0.12$ and 0.25 for e and $\mu$
respectively.

(2) Missing transverse momentum ($\rm E{\\!\\!\\!/}_{T}$) : The missing
transverse momentum is constructed by taking the resultant momenta of all
visible particles and then reversing the direction, i.e. ${\vec{\rm p}_{\rm
T}}=-\sum\vec{\rm p}_{\rm T}^{\leavevmode\nobreak\ i}$, where $i$ runs over
all constructed visible collection from the detector. A cut $\rm
E{\\!\\!\\!/}_{T}>200(150)\leavevmode\nobreak\ GeV$ is imposed for events in
the non-resolved(resolved) category.

(3) HJ selection: The reconstruction of HJ is performed in two ways depending
on the boost of the Higgs boson, i.e., resolved and non-resolved categories,
as described below.

  * •

HJ in non-resolved category: At first, fat jets are constructed taking inputs
from Delphes, using Fastjet3.3.2[105] with Cambridge-Aachen[106] algorithm and
R=1.0. Minimum $\rm p_{T}$ of the fatjets is set to be 100 GeV. These fat jets
are then passed through mass-drop Tagger (MDT)[107, 108] with $\mu$ =0.667 and
$\rm y_{cut}>0.09$ to remove contamination due to soft radiation. The subjets
of the ‘tagged fat jet’ are further matched with the b-quarks of the event
which are selected within $|\eta|<2.5$ and with a matching cone $\rm\Delta
R<0.3$. When both the subjets are found to be b-like, we call the tagged
fatjet as the HJ ($\rm J_{bb}$). We also checked the presence of B-hadron in
the b-like subjets and found that for about 95$\%$ cases, it exists.

  * •

Resolved category: In this case, jets, subject to cuts $\rm p_{T}^{j}>$20 GeV
and $|\eta|<$4.0, are constructed from e-flow objects of Delphes, using
Fastjet3.3.2[105], but with the Anti-$\rm k_{T}$[109] algorithm with a jet
size parameter R=0.5. Using the same technique as above, by matching jets with
b-quarks of the event, b-like jets are identified. The pair of b-like jets
that construct the invariant mass closest to Higgs boson mass within the range
100 GeV$\rm\leq m_{HJ}\leq$150 GeV, is identified as HJ, and the resultant
four-momentum of the two jets is regarded as the momentum of HJ.

(4) Other jets and b-jets: This selection also differs according to two
categories.

  * •

Jets in non-resolved category: Once HJ is constructed, the remaining hadrons
are used to construct regular QCD jets through Fastjet3.3.2 with Anti-$\rm
k_{T}$ algorithm setting R=0.5. Out of these jets, b-like jets are identified
by matching technique with the remaining set of b-quarks in the event, which
are not part of $\rm J_{bb}$.

  * •

Jets in resolved category: The two b-jets, which are found to be related to
the HJ, are removed from the list of jets and b-jets, and this new list is
used further.

Furthermore, to suppress backgrounds, we impose few more selection cuts. For
example, the transverse mass between lepton and $\rm E{\\!\\!\\!/}_{T}$,
defined as,

$\displaystyle\rm m_{T}(\ell,E{\\!\\!\\!/}_{T})=\sqrt{2\times
p_{T}^{\ell}\times
E{\\!\\!\\!/}_{T}\times(1-\cos\phi(\ell,E{\\!\\!\\!/}_{T}))},$ (3.29)

is restricted by $\rm M_{W}$ for all semileptonic $\rm t\bar{t}$ background
events as seen in the $\rm m_{T}$ distribution presented in Fig. 3(left) along
with signal events corresponding to two BPs. On the contrary, for signal
events, having a large $\rm E{\\!\\!\\!/}_{T}$ due to neutralinos, which is
also not correlated with the lepton coming from $\rm t\bar{t}$ decay, is
expected to have a more wide $\rm m_{T}$ distribution without any peaks (see
Fig. 3 (left)). Hence a cut $\rm m_{T}(\ell,E{\\!\\!\\!/}_{T})\geq
110\leavevmode\nobreak\ GeV$ turns out to be very effective in eliminating a
certain fraction of the background.

Figure 3: Transverse mass between (Eq. 3.29)lepton and $\rm E{\\!\\!\\!/}_{T}$
(left) and $\rm H_{T}$ (right) for BP1, BP7 and dominating backgrounds.

Another discriminating variable is $\rm H_{T}$, defined as the scalar sum of
$\rm p_{T}$ of all jets except those that constitute HJ. For signal events,
larger number of harder jets exist leading to higher $\rm H_{T}$ as seen from
the distribution shown in Fig. 3 (right). A cut $\rm H_{T}\geq
500\leavevmode\nobreak\ GeV$ turns out to be useful to reject background
events substantially.

Figure 4: Reconstructed mass of Higgs Jet (HJ) for a representative
signal(BP5) point and dominant backgrounds.

In the case of the non-resolved category, the mass distribution of $\rm
J_{bb}$ shows a clear peak at $\sim$125 GeV, which is absent in most of the
backgrounds, and very small for $\rm t\bar{t}h$ as shown in Fig. 4. Thus the
selection of $\rm m_{J_{bb}}>100\leavevmode\nobreak\ GeV$ is found to be
useful in eliminating significant background events. In the resolved category
case, this mass requirement is already imposed while constructing HJ. The
presence of HJ with a specific mass requirement is a very important feature of
our signal and helps to eliminate almost all the $\rm t\bar{t}$ backgrounds by
enormous amount except $\rm t\bar{t}h$ process where the source of $\rm
J_{bb}$ is same as the signal.

Signal events are simulated for 9 BPs which are chosen in such a way that
BP1-BP5 represent the non-resolved cases, whereas BP6-BP9 correspond to the
resolved category. The BPs labeled as ‘BS’ in the parenthesis correspond to BS
scenario. In Table 2, the cross-section yields for the signal and background
processes for the non-resolved categories are presented after imposing
selection cuts. The first row presents the LO cross-sections of each
processes, computed by<EMAIL_ADDRESS>at the center of mass energy
$\rm\sqrt{s}=13\leavevmode\nobreak\ TeV$, using NNPDF23LO [110] for parton
distribution and choosing the dynamic QCD scale ($\rm
Q^{2}=\sqrt{[m_{\widetilde{t_{1}}}^{2}+p_{T}^{2}(\widetilde{t_{1}})][m_{\bar{\widetilde{t_{1}}}}^{2}+p_{T}^{2}(\bar{\widetilde{t_{1}}})]}$
). Higher order effects are taken into account by multiplying respective
K-factors($\rm K=\frac{\sigma_{NLO}}{\sigma_{LO}}$). A K-factor of 1.4 is used
for top-squark pair production(for NNPDF31LO)[111] and $\rm t\bar{t}$ [112,
113]. Whereas, for $\rm t\bar{t}h$, $\rm t\bar{t}Z$ and $\rm t\bar{t}b\bar{b}$
K-factors are considered to be 1.2 [114], 1.35 [115] and 1.8 [116]
respectively. As indicated in the table, the $\rm m_{J_{bb}}$ cut is very
useful to eliminate backgrounds significantly. In addition, the $\rm m_{T}$
cut also kills backgrounds substantially.

Table 2: Cross-section (in fb) yields after each set of selection cuts for
signal points in the non-resolved category and background processes.

| BP1 | BP2 | BP3 |  BP4(BS) |  BP5(BS) | $\rm t\bar{t}(1\ell)$ | $\rm t\bar{t}(2\ell)$ | $\rm t\bar{t}h$ | $\rm t\bar{t}Z$ | $\rm t\bar{t}b\bar{b}$
---|---|---|---|---|---|---|---|---|---|---
Cross-secton(LO) (fb) | 6 | 3 | 0.06 | 3 | 0.18 | $178500$ | $36000$ | 400 | 584 | $13700$
$\rm E{\\!\\!\\!/}_{T}>200\leavevmode\nobreak\ GeV$ | $4.9$ | $2.5$ | $0.054$ | $2.4$ | $0.17$ | $2695$ | $592.5$ | $12.6$ | $38.8$ | $186.7$
No. of $\rm\ell=1$ | $1.5$ | $0.73$ | $0.02$ | $0.7$ | $0.05$ | $1419$ | $291.2$ | $5.1$ | $11.5$ | $71.1$
No. of $\rm J_{bb}=1$ | $0.4$ | $0.2$ | $0.004$ | $0.2$ | $0.014$ | $33.8$ | $12.1$ | $1.1$ | $0.8$ | $10.6$
$\rm m_{J_{bb}}>100$ GeV | $0.3$ | $0.15$ | $0.003$ | $0.14$ | $0.01$ | $11.6$ | $2.7$ | $0.7$ | $0.3$ | $2.6$
No. of b-jets$\geq 1$ | $0.15$ | $0.07$ | $0.001$ | $0.07$ | $0.0036$ | $1.0$ | $0.25$ | $0.3$ | $0.1$ | $0.8$
$\rm H_{T}>$500 GeV | $0.1$ | $0.05$ | $0.0008$ | $0.05$ | $0.003$ | $0.25$ | $0.07$ | $0.1$ | $0.05$ | $0.1$
$\rm m_{T}(\ell,E{\\!\\!\\!/}_{T})\geq$110 GeV | $0.08$ | $0.043$ | $0.0007$ | $0.04$ | $0.003$ | $0.04$ | $0.07$ | $0.02$ | $0.006$ | $0.02$
$\rm\sigma\times K$-factor | 0.12 | 0.06 | $0.001$ | 0.056 | $0.004$ | $0.06$ | 0.1 | 0.024 | 0.008 | $0.04$

Table 3: Same as in Table 2, but for resolved category.

| BP6 | BP7 |  BP8(BS) |  BP9(BS) | $\rm t\bar{t}(1\ell)$ | $\rm t\bar{t}(2\ell)$ | $\rm t\bar{t}h$ | $\rm t\bar{t}Z$ | $\rm t\bar{t}b\bar{b}$
---|---|---|---|---|---|---|---|---|---
Cross-secton (fb) | 53 | 19 | 88 | 27 | $178500$ | $36000$ | 400 | 584 | 13700
$\rm E{\\!\\!\\!/}_{T}>150\leavevmode\nobreak\ GeV$ | $36.4$ | $14.1$ | $51.2$ | $20.5$ | $8560$ | $2100$ | $31.3$ | $76.5$ | $555.6$
No. of $\rm\ell=1$ | $9.8$ | $3.8$ | $13.9$ | $5.6$ | $4364$ | $1050$ | $12.2$ | $23.8$ | $204.1$
No. of $\rm J_{bb}=1$ | $3.9$ | $1.5$ | $5.4$ | $2.3$ | $564.2$ | $145.9$ | $4.6$ | $3.9$ | $53.3$
No. of b-jets$\geq 1$ | $2.9$ | $1.1$ | $4.0$ | $1.8$ | $49.5$ | $11.0$ | $3.6$ | $1.3$ | $35.7$
$\rm H_{T}$$>$500 GeV | $1.7$ | $0.7$ | $2.3$ | $1.2$ | $22.3$ | $3.6$ | $1.7$ | $0.6$ | $11.8$
$\rm m_{T}(\ell,E{\\!\\!\\!/}_{T})\geq$110 GeV | $1.2$ | $0.5$ | $1.5$ | $0.9$ | $5.3$ | $2.4$ | $0.4$ | $0.15$ | $2.6$
$\rm\sigma\times K$-factor | 1.7 | 0.7 | 2.1 | 1.22 | 7.5 | 3.36 | 0.43 | 0.20 | 4.7

Similarly, cross section yields for the resolved category are presented in
Table 3. It is clear that the selection of HJ, in this case, is not as
efficient as the non-resolved category, but still having good discriminating
power. In general, overall signal acceptance efficiency is 1-2$\%$; while for
overall backgrounds, it is found to be 0.0001$\%$ for the non-resolved
category and 0.007$\%$ for the resolved category. The total cross-sections of
background events are found to be 0.232 fb for the non-resolved category and
16.2 fb for the resolved cases respectively. Finally, the signal sensitivities
($\rm\frac{S}{\sqrt{S+B}}$) are presented in Table 4 for two high luminosity
options $\rm\mathcal{L}=300\leavevmode\nobreak\ fb^{-1}\leavevmode\nobreak\
and\leavevmode\nobreak\ 3000\leavevmode\nobreak\ fb^{-1}$. It is to be noted
that for the non-resolved category, the sensitivities are $\sim 2-3\sigma$ for
$\mathcal{L}=300\leavevmode\nobreak\ \text{fb}^{-1}$, whereas they are
large($\sim 5-8\sigma$) for the resolved category, mainly because of the high
production cross-sections, due to smaller top-squark masses. The tiny
sensitivities for BP3 and BP5 can be attributed to a very low top-squark
production cross-section because of its higher masses. Assuming 10$\%$
background uncertainty the sensitivity for the BPs in resolved category drops
by $\sim 7\%$ and for the non-resolved category, it reduces by about 0.1$\%$.

Table 4: Signal significances($\rm\frac{S}{\sqrt{S+B}}$) for two luminosity options. | Non-resolved category | Resolved category
---|---|---
Luminosity $\rm(fb^{-1})$ | BP1 | BP2 | BP3 | BP4 | BP5 | BP6 | BP7 | BP8 | BP9
$\rm 300$ | 3.5 | 2.0 | 0.035 | 1.8 | 0.14 | 7 | 2.9 | 8.5 | 5.0
$\rm 3000$ | 11 | 6 | 0.1 | 6 | 0.44 | 22 | 9 | 27 | 16

Though we obtain reasonable signal sensitivity in the resolved category, the
acceptance efficiencies for backgrounds, in that case, are not appreciably
small as in the non-resolved category in the cut-based method. In order to
improve further, we carry out multivariate analysis (MVA) based on boosted
decision tree (BDT) method within the framework of TMVA [117, 118] framework.

###  3.1 Multivariate Analysis

The basic idea of MVA [117, 118, 119, 120, 121] is to examine patterns in
multidimensional data by considering several variables at once. Several
kinematical variables are constructed, keeping in mind the features of signal
events, for training purposes. Depending upon the performances of those
variables, we use 13 of those for the non-resolved category and 15 for the
resolved category to train signal and background samples. The description of
those variables are presented in Tables 5 and 6 corresponding to BP5 for non-
resolved category and BP7 for the resolved category respectively.

Table 5: Rank of variables in MVA for non-resolved category corresponding to
BP5.

Rank | Variable | Description
---|---|---
1 | $\rm m_{h}$ |  Mass of $\rm J_{bb}$
2 | HT |  Scalar sum of $\rm p_{T}$ of all jets outside $\rm J_{bb}$
3 | $\rm E{\\!\\!\\!/}_{T}$ |  Missing $\rm p_{T}$
4 | $\rm\Delta R(E{\\!\\!\\!/}_{T},J_{bb})$ |  $\rm\Delta R$ between $\rm E{\\!\\!\\!/}_{T}$ and $\rm J_{bb}$
5 | $\rm p_{T}(J_{bb})$ |  $\rm p_{T}$ of $\rm J_{bb}$
6 | $\rm p_{T}(\ell)$ |  $\rm p_{T}$ of leading lepton
7 | $\rm\Delta R(b_{1},J_{bb})$ |  $\rm\Delta R$ between leading b-jet (outside $\rm J_{bb}$) and $\rm J_{bb}$
8 | $\rm\Delta R(E{\\!\\!\\!/}_{T},j)$ |  $\rm\Delta R$ between $\rm E{\\!\\!\\!/}_{T}$ and leading jet outside $\rm J_{bb}$
9 | $\rm Njets$ |  Number of jets outside $\rm J_{bb}$.
10 | $\rm M_{T}(\ell,E{\\!\\!\\!/}_{T})$ |  Transverse mass of leading $\rm p_{T}$ lepton and $\rm E{\\!\\!\\!/}_{T}$
11 | $\rm N(\ell)$ | Number of leptons
12 |  $\rm p_{T}$(b-jet) |  $\rm p_{T}$ of leading b-jet outside $\rm J_{bb}$
13 | N(b-jet) |  Number of b-jets, outside $\rm J_{bb}$

The first column of these tables shows the ranking of these variables, which
represents the relative importance in discriminating signal and backgrounds.
The set of variables are the same for all BPs for a given category, but
depending on the kinematics, the ranking of those variables is found to be
little different. While doing MVA for each BP, overtraining tests are
performed to ensure that there are no significant deviations between the
performance of training and testing data.

Table 6: Rank of variables in MVA for resolved category corresponding to BP7.

Rank | Variable | Description
---|---|---
1 | $\rm E{\\!\\!\\!/}_{T}$ |  Missing $\rm p_{T}$
2 | $\rm m_{h}$ |  Mass of $\rm J_{bb}$
3 | $\rm\Delta R(b_{1},b_{2})$ |  $\rm\Delta R$ between two b-jets inside Higgs-jet.
4 | $\rm\Delta R(E{\\!\\!\\!/}_{T},J_{bb})$ |  $\rm\Delta R$ between $\rm E{\\!\\!\\!/}_{T}$ and $\rm J_{bb}$
5 | $\rm p_{T}(b_{1})/p_{T}(b_{2})$ | pT ratio of two b-jets inside Higgs-jet.
6 | $\rm\Delta R(E{\\!\\!\\!/}_{T},j)$ |  $\rm\Delta R$ between $\rm E{\\!\\!\\!/}_{T}$ and leading jet
7 | $\rm\Delta R(b_{1},J_{bb})$ |  $\rm\Delta R$ between leading b-jet (outside $\rm J_{bb}$) and $\rm J_{bb}$
8 | $\rm Njets$ |  Number of outside $\rm J_{bb}$.
9 | HT |  Scalar sum of $\rm p_{T}$ of all jets outside $\rm J_{bb}$
10 | $\rm p_{T}(\ell)$ |  $\rm p_{T}$ of leading lepton
11 | $\rm M_{T}(\ell,E{\\!\\!\\!/}_{T})$ |  Transverse mass of leading pT lepton and $\rm E{\\!\\!\\!/}_{T}$
12 | $\rm p_{T}(J_{bb})$ |  $\rm p_{T}$ of $\rm J_{bb}$
13 | N(b-jet) |  Number of b-jets, outside $\rm J_{bb}$
14 | $\rm N(\ell)$ | Number of leptons
15 |  $\rm p_{T}$(b-jet) |  $\rm p_{T}$ of leading b-jet outside $\rm J_{bb}$

Figure 5: Signal and background yields as a function of threshold on MVA
output discriminator along with the significance of signal corresponding to
$\rm\mathcal{L}=300\leavevmode\nobreak\ fb^{-1}$ for signal point BP1 (left)
and BP6(right).

In Fig. 5, the variation of cross section yields for signal and backgrounds
and the signal significance ($\rm\frac{S}{\sqrt{S+B}}$) as a function of
threshold on MVA output discriminator for luminosity
$\rm\mathcal{L}=300\leavevmode\nobreak\ fb^{-1}$, is presented corresponding
to the BP1 for the non-resolved category and BP6 for the resolved category
case. It indicates that a sensitivity above $\sim 5\sigma$ can be achieved for
luminosity $\rm\mathcal{L}=300\leavevmode\nobreak\ fb^{-1}$ corresponding to a
cut of the classifier $>0.9$.

Evidently, the achievable signal significance for all the BPs are presented in
Table 7 for two luminosity options. Clearly, the signal sensitivities are
found to be well above $5\sigma$ at $\rm\cal{L}$$\rm=300\leavevmode\nobreak\
fb^{-1}$, except for BP3 and BP5, where the production cross-section is too
low due to a heavier top-squark mass.

Table 7: Signal significances($\rm\frac{S}{\sqrt{S+B}}$) for two luminosity options applying MVA. | Non-resolved category | Resolved category
---|---|---
Luminosity $\rm(fb^{-1})$ | BP1 | BP2 | BP3 | BP4 | BP5 | BP6 | BP7 | BP8 | BP9
$\rm 300$ | 6 | 4.5 | 0.14 | 3.6 | 0.35 | 24 | 9.5 | 27 | 15
$\rm 3000$ | 19 | 14 | 0.5 | 11 | 1.1 | 75 | 30 | 85 | 47

##  4 Summary

In the MSSM framework, the lightest neutralino, an LSP of the mass
$\sim\cal{O}$(100) GeV, is found to be one of the best suitable DM candidates.
However, the constraints from direct DM detection experiments and measurement
of the relic density restrict the composition of the physical neutralino
states. It is observed that, instead of a pure state, neutralino DM in MSSM is
“mild-tempered” where it is bino-dominated with a presence of little Higgsino,
providing the best DM solution at this mass range. In this scenario, the DM
annihilation process takes place via Higgs and gauge bosons where Higgsino
content along with dominant bino helps to provide the right relic density. It
is to be noted that, eventually the Higgsino composition in the LSP is
strongly restricted by the limits of SI DM-nucleon scattering cross section
measurements in the direct DM detection experiments, primarily by XENON1T.
Considering this DM solution, a numerical scan is performed to identify the
range of sensitive parameters, in particular, $\mu$ and $\rm M_{1}$ in the
limit of a very large $\rm M_{2}$ value. It is found that, with
$\rm|\mu|-M_{1}>M_{Z}$, the most preferred ranges are $\rm M_{1}\sim 50-600$
GeV and $\rm\mu\sim 400-1000$ GeV. Moreover, there is a region of parameter
space that is blind to the SI scattering cross section due to the interplay of
parameters and cancellation among various amplitudes mediated by the lighter
and heavier Higgs bosons. Consequently, in such cases, the Higgsino content in
the lightest neutralino is not severely constrained. In mild-tempered DM
scenario, $\rm\widetilde{\chi}^{0}_{1}$ is accompanied with Higgsino-like
$\widetilde{\chi}^{0}_{2,3}$ and $\widetilde{\chi}_{1}^{\pm}$ having masses
around $\mu$. It is indeed the case even for the region of parameters
corresponding to the BS scenario. Due to the gaugino-Higgsino-Higgs type of
coupling, $\rm\widetilde{\chi}^{0}_{2,3}\rightarrow
h+\widetilde{\chi}^{0}_{1}$ decay rate gets enhanced, leading to an
interesting phenomenology at the LHC corresponding to our considered scenario.

We focus on the top-squark pair production to explore the mild-tempered
neutralino scenario at the LHC. As $\rm
BR(\widetilde{t_{1}}\rightarrow\widetilde{\chi}^{0}_{1}+t)$ is very small,
$\rm\widetilde{\chi}^{0}_{1}$ is indirectly produced through the production of
$\widetilde{\chi}^{0}_{2,3}$. The presence of SM-Higgs boson in the final
state adds an extra advantage to probe this channel. Interestingly, this
channel also provides an opportunity to probe the BS scenario. The signal is
characterized by one HJ consisting of b-like jets or subjets, large $\rm
E{\\!\\!\\!/}_{T}$, one lepton, plus at least one extra b-like jet. The HJ
tagging turns out to be very efficient to separate out the signal from the
debris of backgrounds. The presence of HJ adds robustness to this signal.

Signal significances are presented for few illustrative BPs including BS
scenario. We observe that for top-squarks of the mass range 600-1700 GeV, for
most of the BPs, a reasonable signal sensitivity($\sim 3-5\sigma$) can be
achieved corresponding to $\rm\cal{L}$ = 300 fb-1 luminosity option, which
goes up roughly by a factor of three for
$\rm\cal{L}$$\rm=3000\leavevmode\nobreak\ fb^{-1}$. Furthermore, we
demonstrate that the sensitivities can be increased by employing MVA
technique. Remarkably, we notice that, for the above luminosity options, and
in particular for the resolved category case, the improvement is significant,
by a factor of $\sim$3-4. The signal is detectable even for $\rm\cal{L}$ = 300
fb-1 option except for BP3 and BP5 for which top-squark masses are $\rm\sim
1.5\leavevmode\nobreak\ TeV$. For the center of mass energy
$\rm\sqrt{s}=14\leavevmode\nobreak\ TeV$, which is the energy option for RUN3
experiment at the LHC, our projected sensitivities are expected to increase by
15-20$\%$ depending on the top-squark masses. A 10$\%$ uncertainty in
background estimation reduces sensitivity by about 7$\%$ and $0.1\%$ for
resolved and non-resolved category respectively. Our analysis shows that both
the “mild-tempered” neutralino providing a DM candidate in the framework of
MSSM and also the BS scenario where the direct search is not sensitive, can be
detected at the LHC with a reasonable sensitivity for projected luminosity
options.

Acknowledgements

The authors are thankful to Shivani Lomte, at affiliation of IISER, Pune, (now
at University of Wisconsin) for collaborating on this project at an earlier
stage. One of the authors, A.R, is thankful to Soham Bhattacharya for useful
discussions and suggestions.

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