DESY 18-219, KA-TP-01-2019

MSSM Higgs Benchmark Scenarios for
Run 2 and Beyond: the low $\tan\beta$ region

Henning Bahla, Stefan Lieblerb, Tim Stefaniaka

aDESY, Notkestraße 85, D-22607 Hamburg, Germany
bInstitute for Theoretical Physics (ITP), Karlsruhe Institute of Technology,
D-76131 Karlsruhe, Germany

###### Abstract

We propose two new benchmark scenarios for Higgs-boson searches in the Minimal
Supersymmetric Standard Model (MSSM). These scenarios are specifically
designed for the low $\tan\beta$ region. A light Higgs-boson mass prediction
compatible with the observed value of $125$ GeV is ensured in almost the
entire parameter space by employing a flexible supersymmetric (SUSY) mass
scale, reaching values of up to $10^{16}$ GeV. The MSSM Higgs-sector
predictions are evaluated in an effective field theory (EFT) framework that
exhibits a Two-Higgs-Doublet-Model at the low scale. In the first scenario all
SUSY particles are relatively heavy, whereas the second scenario features
light neutralinos and charginos. Both scenarios are largely compatible with
the most recent results from Run 2 of the LHC, and we highlight the main
phenomenological features relevant for future LHC searches. In particular, we
provide a detailed discussion of heavy Higgs-boson decays to neutralinos and
charginos in the second scenario, and the arising collider signatures, in
order to facilitate the design of dedicated LHC searches in the near future.

##  1 Introduction

The last free parameter in the Standard Model (SM) of particle physics, namely
the mass of the Higgs boson that was discovered at the Large Hadron Collider
(LHC) [1, 2], was determined during Run 1 of the LHC to
$M_{H^{\text{{SM}{}}}}^{\rm obs}=125.09\pm 0.24$ GeV [3]. In addition, the
Higgs-boson properties, among them the Higgs-boson couplings to the heavier SM
particles and the Higgs-boson width, were found to be compatible with the SM
predictions within the experimental and theoretical uncertainties [4]. This
experimental information puts strong indirect constraints on beyond-the-SM
(BSM) physics, which become increasingly important since no direct evidence
for BSM physics has yet been found at the LHC.

One of the most compelling models of BSM physics is the Minimal Supersymmetric
Standard Model (MSSM) [5, 6, 7]. Apart from associating a superpartner with
each SM degree of freedom, it also extends the SM Higgs sector by a second
doublet resulting in five physical Higgs states. Assuming $\mathcal{CP}$
conservation in the Higgs sector these are the light and heavy
$\mathcal{CP}$-even Higgs bosons, $h$ and $H$, respectively, the
$\mathcal{CP}$-odd Higgs boson, $A$, and the charged Higgs bosons, $H^{\pm}$.
Due to the underlying supersymmetry (SUSY), the MSSM Higgs sector is highly
predictive. At the tree-level, all masses and couplings are determined by only
two non-SM parameters. Typically, the ratio of the vacuum expectation values
(vevs) of the two doublets, $\tan\beta$, and the mass of the
$\mathcal{CP}$-odd Higgs boson, $M_{A}$, are chosen in the
$\mathcal{CP}$-conserving MSSM.

However, the tree-level predictions receive large quantum corrections. Their
inclusion is especially important in the case of the SM-like Higgs-boson mass,
which we assume to be the $h$ boson in this work (see Refs. [8, 9, 10, 11, 12]
for scenarios in which the $H$ boson plays the role of the Higgs boson
discovered at the LHC). Consequently, much work has been dedicated to the
calculation of these corrections. We refer to Ref. [13] for a recent review.
Through the radiative corrections a large set of parameters enter the
calculation. This makes an interpretation of corresponding experimental
results challenging. Consequently, benchmark scenarios have been proposed to
alleviate experimental analyses and their theoretical interpretation [14, 15,
16, 17, 18, 19]. Due to experimental and theoretical progress much of the
parameter space of these original benchmark scenarios has been ruled out.
Therefore, new benchmark scenarios, taking into account the most recent
experimental limits as well as state-of-art theory predictions, have been
proposed in Ref. [20].

In all the original benchmark scenarios as well as in the new scenarios
presented in Ref. [20] the supersymmetric partners of the SM fermions
(sfermions) are tied to the TeV scale. In this case, the parameter region
$\tan\beta\lesssim 5$ is ruled out because the mass of the SM-like Higgs
boson, $M_{h}$, is predicted to be lower than the measured value. On the other
hand, experimental searches for heavy Higgs bosons decaying into bottom quarks
and $\tau$ leptons [21, 22] rule out the parameter space at large $\tan\beta$
up to high values of $M_{A}$ beyond the TeV scale. At low $\tan\beta$ the
searches for heavy Higgs bosons are much less sensitive, i.e. still allow for
lower values of $M_{A}$. In this region, the Higgs bosons decay into a variety
of final states, which are more difficult to handle experimentally. To re-open
the parameter region of low $\tan\beta$ values, the “low-$\tan\beta$-high”
scenario was proposed in Ref. [18] raising the sfermion mass scale,
$M_{\text{{SUSY}}}$, up to $100$ TeV in order to reach $M_{h}\sim 125$ GeV
also for low $\tan\beta$. In case of such a large hierarchy between the
electroweak scale and the sfermion scale, large logarithms, involving
$M_{\text{{SUSY}}}$ and e.g. the top-quark mass, appear in the calculation of
$M_{h}$. These can be resummed by integrating out the sfermions at
$M_{\text{{SUSY}}}$ and then evolving the couplings in the effective field
theory (EFT) below $M_{\text{{SUSY}}}$ using renormalization group equations
(RGEs) down to the electroweak scale at which the SM-like Higgs-boson mass is
calculated. In the simplest approach the SM is used as EFT [23, 24, 25, 26,
27, 28, 29, 30, 31]. Also the “low-$\tan\beta$-high” scenario was based on
this setup. However, if we assume all Higgs-boson masses to be close to the
electroweak scale, i.e. below a few TeV, the Two-Higgs-Doublet Model (2HDM)
has to be used as low-energy EFT to ensure a correct resummation. Such setups
were published in Refs. [32, 33, 34, 20, 35]. Those works show that a
substantial part of the parameter space in the “low-$\tan\beta$-high” scenario
yields a prediction for the light Higgs-bosons mass, $M_{h}$, which is much
lower than the measured value and hence the “low-$\tan\beta$-high” scenario is
meanwhile ruled out. It is the goal of this paper to define new scenarios
valid at low values of $\tan\beta$ in the framework of a low-energy 2HDM.

Moreover, this region of low $\tan\beta$ is the region of validity of the
hMSSM [36, 37, 38], an approximation of the MSSM Higgs sector, which assumes
that the dominant correction to Higgs boson masses and mixing have a common
origin: they stem from the top-quark and its SUSY partners, the stops,
entering a single element of the neutral $\mathcal{CP}$-even Higgs-boson mass
matrix only. As indicated this assumption is only valid at low values of
$\tan\beta$ and in addition for low values of $\mu/M_{\text{{SUSY}}}$, and
then allows to trade the loop corrections as a function of the light Higgs
boson mass $M_{h}$ (for specific values of $M_{A}$ and $\tan\beta$) such that
the explicit dependence of the Higgs masses and mixing on the SUSY parameters
can be ignored. For low $\tan\beta$ the original hMSSM approach is known to
approximate Higgs masses and mixing quite well, see e.g. Refs. [39, 18, 33],
though for the Higgs-boson couplings, entering e.g. the important decay $H\to
hh$, further refinements [40] are needed. In comparison with our suggested
scenarios the quality of the hMSSM approximation and its region of validity
can be tested. As a first step, we compare the $\mathcal{CP}$-even Higgs-boson
mixing angle, $\alpha$, and the heavy $\mathcal{CP}$-even Higgs-boson mass,
$M_{H}$, between the two approaches, but leave a discussion of more elaborate
quantities, including the prediction of the $H\to hh$ partial width, to future
work.

We shall define two scenarios: One scenario in which all non-2HDM states are
decoupled and one featuring light neutralinos and charginos, to which we refer
as electroweakinos. The first scenario resembles the $M_{h}^{\text{125}}$
scenario, the other the $M_{h}^{125}(\tilde{\chi})$ scenario, which were
defined in Ref. [20]. In order to allow for $M_{h}\sim 125$ GeV also at low
$\tan\beta$, a very high sfermion mass scale of up to $10^{16}$ GeV is needed.
We employ a state-of-the-art calculation of the Higgs-boson masses and
branching ratios using a yet unpublished version of FeynHiggs [41, 42, 43, 44,
24, 28, 30, 45]. This version implements the results of Ref. [46]: The
effective 2HDM (and a 2HDM+EWinos) as EFT below the sfermion scale includes
full two-loop renormalization group equations as well as full one-loop and
partial two-loop threshold corrections. This EFT calculation is combined with
a state-of-the-art fixed-order calculation. For more details we refer to Ref.
[46]. We obtain the production cross sections of the neutral Higgs bosons from
SusHi [47, 48] for gluon fusion and re-weight matched predictions published in
Refs. [49, 50, 51, 52] for bottom-quark associated production. We explore the
known experimental constraints on the MSSM Higgs sector using HiggsBounds [53,
54, 55, 56] and HiggsSignals [57].

The paper is set up as follows: We explain our theoretical setup in detail in
Section 2. We proceed with an explanation of the experimental constraints in
Section 3. Finally we define and discuss our two benchmark scenarios in
Section 4 including a first comparison with the hMSSM approach and conclude
thereafter.

##  2 Theory setup

In this Section, we provide details about the calculation of the Higgs-boson
masses and branching ratios as well as of the Higgs-boson production cross
sections.

###  2.1 Higgs-boson masses and branching ratios

For the calculation of the Higgs-boson properties (masses and branching
ratios), we rely on the code FeynHiggs. Since the scenarios presented in this
work include a large hierarchy between the scale of non-SM-like Higgs bosons
and scalar fermions, we use a yet not public FeynHiggs version111Until its
official release the employed version of FeynHiggs can be obtained from the
authors upon request. which implements a low-energy 2HDM as well as a low-
energy 2HDM+EWinos as effective field theories [46],222We corrected the
renormalization group equations used in Ref. [46] according to the findings of
Refs. [58, 59]. The numerical effect is negligibly small. which is merged with
a one-loop diagrammatic fixed-order calculation [60, 61, 62, 44]. The two-loop
diagrammatic fixed-order corrections implemented in FeynHiggs are switched
off, see below.

For future reference, we list the FeynHiggs flags set to obtain the result
presented in this work,

mssmpart = 4, higgsmix = 2, p2approx = 4, looplevel = 1,

loglevel = 4, runningMT = 1, botResum = 1, tlCplxApprox = 0.

Setting loglevel = 4 enables the 2HDM as low-energy theory. This flag choice
is not yet available in the most recent public FeynHiggs version 2.14.3, but
will become available in an upcoming version.

In order to provide a numerical stable prediction for very high SUSY scales of
up to $10^{16}$ GeV, the code has to be compiled using quadruple precision. To
improve numerical stability, also an improved solving algorithm for the
renormalization group equation was implemented. In addition, we have to
deactivate the diagrammatic two-loop corrections to the Higgs-boson self-
energies, which are numerically unstable in this parameter region even in case
of quadruple precision. Note that two-loop terms which are not suppressed by
the SUSY scale, re-enter via the EFT calculation.333This includes corrections
involving only 2HDM particles. The missing suppressed terms are completely
negligible. For the same reason, the used one-loop Higgs-boson self-energies
are expanded in the limit of large sfermion masses. We want to point out that
with this FeynHiggs configuration $\tan\beta$ is defined in the 2HDM at the
scale $M_{A}$. In contrast, in the benchmark scenarios defined in Ref. [20],
$\tan\beta$ is evaluated at the scale of the top-quark mass, $M_{t}$.

We outlined the history of EFT calculations of the Higgs-boson mass already in
the introduction. Apart from FeynHiggs there are two other codes implementing
the 2HDM as low-energy EFT. These are MhEFT [33] and FlexibleSUSY [63,
34].444They do provide predictions for the Higgs-boson masses but not (yet)
for their branching ratios. Among these codes, the prediction of the light
Higgs-boson mass, $M_{h}$, is in good agreement. A comparison of these codes
with FeynHiggs, however, yields discrepancies of a few GeV in the prediction
of $M_{h}$ in the region of $M_{A}\sim 200$ GeV, $\tan\beta\sim 1$, $\mu\sim
200$ GeV and $M_{\text{{SUSY}}}$ above $10^{10}\;{\rm GeV}$, where FeynHiggs
predicts higher $M_{h}$ values.555In contrast to the other codes, the EFT
calculation implemented in FeynHiggs takes into account all effective
couplings as well as full one-loop threshold corrections, see Ref. [46] for
more details. This may be the origin of the observed numerical discrepancies.
Thus using the other codes instead could exclude parts of this region of the
parameter space by a too low prediction of $M_{h}$. As we will show in Section
4, this region is already excluded by the Higgs-boson signal-strength
measurements. For higher $\tan\beta$ or $M_{A}$ values $M_{\text{{SUSY}}}$ can
be adjusted to get $M_{h}\sim 125$ GeV without changing the low-energy
phenomenology. Therefore, while it will be still important to understand the
observed discrepancy between the FeynHiggs and MhEFT/FlexibleSUSY predictions,
the outcome of this discussion will hardly affect the phenomenology of the
scenarios presented in this work.

###  2.2 Production cross sections

For the calculation of the gluon-fusion cross sections of the neutral Higgs
bosons we employ SusHi 1.7.0 [47, 48], which we directly link to FeynHiggs at
quadruple precision. We take into account the Higgs-boson mixing by
implementing the full $\mathbf{Z}$ matrix as explained in Ref. [64]. The
$\mathbf{Z}$ matrix relates the tree-level mass eigenstates to the external
physical states and is calculated by FeynHiggs including a resummation of
large logarithms by the means of the EFT calculation [44, 65, 66]. SusHi
includes top- and bottom-quark contributions at next-to-leading order (NLO)
[67, 68] and for the top-quark contribution adds next-to-NLO (NNLO) effects in
the heavy-quark effective theory [69, 70, 71, 72, 73] as well as next-to-NNLO
(N3LO) contributions, which additionally exploit a threshold expansion [74,
75, 76]. The latter N3LO contributions are only taken into account for the
light SM-like Higgs boson to match the precision of the LHC-HXSWG gluon-fusion
cross section in the SM, see Ref. [77], except from NNLO top-quark mass
effects. The N3LO contribution in the threshold expansion closely matches the
exact result published in Ref. [78]. We also include two-loop electroweak
corrections from light quarks as discussed in Refs. [79, 80]. On the other
hand, we omit corrections from SUSY particles to gluon fusion, both explicit
in the amplitude and through $\Delta_{b}$ corrections. This is justified from
the fact that those contributions quickly decouple for high SUSY masses as
employed in this work. Their inclusion would induce numerical instabilities
due to the high SUSY masses. Keeping $\mu$ at the electroweak scale and fixing
the gluino mass, $M_{3}$, to $2.5$ TeV, this statement also applies to the
dominant $\Delta_{b}$ corrections. We make use of the parton distribution
functions (PDF) named `PDF4LHC15_nlo_mc` and `PDF4LHC15_nnlo_mc` [81] and
choose half of the Higgs-boson mass as central renormalization and
factorization scale.

Instead of employing “Santander-matched” cross sections [82] for the
production of neutral Higgs bosons through bottom-quark annihilation, we
follow the recommendation of the LHC-HXSWG [77] and use the results based on
soft-collinear effective theory [52, 51] and the “fixed order plus next-to-
leading log” (FONLL) approach [50, 49], which both yield identical cross
sections. They are based on the cross sections obtained in the five-flavor
scheme [83] and in the four-flavor scheme [84, 85]. We re-weight the cross
section of the SM Higgs boson proportional to the squared bottom-quark Yukawa
coupling both for the $\mathcal{CP}$-even and $\mathcal{CP}$-odd Higgs bosons
and omit corrections proportional to the top-quark Yukawa coupling.

For a detailed discussion of the theoretical uncertainties of neutral Higgs-
boson production in the MSSM we refer to Ref. [86]. We obtain theoretical
uncertainties for gluon fusion and bottom-quark annihilation in the same way
as discussed in Ref. [46], in summary: For gluon fusion we include the
renormalization-scale uncertainty, which is calculated analytically from $100$
scale choices between half and twice the central scale choice following the
approach discussed in Ref. [48]. The difference between the maximal and
minimal cross section is used as symmetric uncertainty. The factorization-
scale uncertainty is subdominant and not further considered. We take into
account relative PDF and $\alpha_{s}$ uncertainties obtained as a function of
the Higgs-boson mass for a SM Higgs boson and for a 2HDM $\mathcal{CP}$-odd
Higgs boson at $\tan\beta=1$, which we employ for $\mathcal{CP}$-even and the
$\mathcal{CP}$-odd Higgs bosons, respectively. The absolute renormalization-
scale and PDF$+\alpha_{s}$ uncertainties are added in quadrature. For bottom-
quark associated production we use the absolute uncertainties provided by the
LHC-HXSWG both for $\mathcal{CP}$-even and $\mathcal{CP}$-odd Higgs bosons,
which include renormalization- and factorization-scale uncertainties,
uncertainties related to the value of the bottom-quark mass and the bottom-
quark matching scale and PDF$+\alpha_{s}$ uncertainties.

Lastly we employ cross sections for charged Higgs-boson production according
to the recommendation of the LHC-HXSWG, which is based upon Refs. [87, 88, 89,
90, 91]. This in particular includes cross sections for charged Higgs bosons
in the mass window of $145$–$200$ GeV at a center-of-mass energy of $13$ TeV.

##  3 Experimental constraints

Searches for additional Higgs bosons at the LHC, as well as the signal-
strength measurements of the observed Higgs boson at the LHC, already
constrain part of the parameter space of our benchmark scenarios. These
constraints are tested in our analysis with the codes HiggsBounds [53, 54, 55,
56] and HiggsSignals [57], respectively. We follow the same procedure as in
Ref. [20], which we summarize briefly in the following.

###  3.1 Constraints from LHC searches for additional Higgs bosons

The program HiggsBounds tests each parameter point against the
$95\%~{}\mathrm{C.L.}$ cross-section limits from neutral and charged Higgs
boson searches at the LEP, Tevatron and LHC experiments. It turns out,
however, that only the LHC Higgs searches are important in our benchmark
scenarios. The code follows a well-defined statistical procedure when applying
these constraints: in a first step, it determines the most sensitive
experimental search for each Higgs boson in the model (as judged by the
expected limit); in the second step only the observed upper limit of this most
sensitive search is compared to the model-predicted signal rate, and the model
is regarded as excluded if the predicted rate exceeds the upper limit. We
refer to Refs. [53, 54, 55, 56] for more details.

The latest version of HiggsBounds, 5.3.0beta, includes results from the
following LHC searches relevant to our scenarios: searches for heavy Higgs
bosons decaying to $\tau^{+}\tau^{-}$ pairs by ATLAS [21] and CMS [22] using
about $36\,\mathrm{fb}^{-1}$ of Run-2 data, as well as the CMS results from
Run 1 [92]; ATLAS [93, 94] and CMS [95, 96] searches during Run-1 and Run-2
for a heavy scalar decaying to a $Z$-boson pair; Run-2 searches by ATLAS [97]
and CMS [98, 99, 100, 101] for a heavy scalar decaying to a pair of SM-like
Higgs bosons. The most relevant charged Higgs-boson searches included in
HiggsBounds are searches for top-quark associated $H^{\pm}$ production, with
subsequent decays to $\tau\nu$ [102, 103, 104, 105] or $tb$ [102, 106, 107]
pairs.

We estimate the theoretical uncertainty in our determination of the excluded
regions by re-evaluating the excluded region with HiggsBounds for (_i_) a most
conservative and (_ii_) a least conservative variation of the gluon-fusion and
bottom-quark annihilation cross sections by their estimated uncertainties, see
Section 2.2 and Ref. [46].

###  3.2 Constraints from the Higgs boson observed at the LHC

We test the compatibility with the observed Higgs-boson signal rates with the
program HiggsSignals (version 2.2.1beta). The program includes the combined
LHC Run-1 ATLAS and CMS measurements of the Higgs-boson signal strengths [4]
as well as recent measurements during LHC Run-2 that became available in
mid-2018, with around $36~{}\mathrm{fb}^{-1}$ of integrated luminosity per
experiment [108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120,
121, 122, 123, 124]. The program evaluates a $\chi^{2}$ value for each
parameter point using in total $100$ individual signal-rate measurements.
Using this $\chi^{2}$ value, we perform an (approximate) log-likelihood ratio
test for model discrimination as follows: within the considered two-
dimensional benchmark plane, we determine the parameter point with minimal
$\chi^{2}$ value, $\chi^{2}_{\text{min}}$, and regard all parameter points
with $\Delta\chi^{2}\equiv\chi^{2}-\chi^{2}_{\text{min}}\leq 6.18$ to be
consistent at the $2\sigma$ level with the best-fit hypothesis (and, hence,
with the observed Higgs rates). We remark that, in both of our proposed
benchmark scenarios, the best fit point is found far in the decoupling limit
($M_{A}\gg M_{Z}$), where the model provides essentially as good a fit to the
observed Higgs rates as the SM.

##  4 Benchmark scenarios

We subsequently explain our parameter choices and present two benchmark
scenarios for low values of $\tan\beta$ between $1$ and $10$, based on the
previously discussed EFT setup employing a very heavy colored SUSY spectrum.
Both are inspired by two scenarios presented in Ref. [46], which work with a
TeV-scale colored SUSY spectrum and are thus only valid at higher values of
$\tan\beta$.

###  4.1 Input parameters

Following the recommendation of the LHC-HXSWG in Ref. [77], we make use of the
following SM input parameters:

$\displaystyle
m_{t}^{\text{pole}}=172.5~{}\text{GeV},\quad\alpha_{s}(M_{Z})=0.118,\quad
G_{F}=1.16637\cdot 10^{-5}~{}\text{GeV}^{-2},$ $\displaystyle
m_{b}(m_{b})=4.18~{}\text{GeV},\quad M_{Z}=91.1876~{}\text{GeV},\quad
M_{W}=80.385~{}\text{GeV}\,.$ (1)

The other lepton and quarks masses only have a minor influence on the Higgs-
sector observables. Therefore, we stick to the default values of FeynHiggs.
There, however, is a strong dependence of the light Higgs-boson mass, $M_{h}$,
on the value of the employed top-quark pole mass. The value recommended by the
LHC-HXSWG is below the current world average of $173.21\pm 0.51\pm 0.71$ GeV
[125]. In the scenarios considered here, a change of the top-quark pole mass
of $0.7\;{\rm GeV}$ would imply a change of $\sim 0.8\;{\rm GeV}$ in the
prediction for $M_{h}$.

To fix the SUSY parameters, we choose to set all scalar fermion soft-SUSY
breaking masses equal to a common scale $M_{\text{{SUSY}}}$. In both
scenarios, presented here, $M_{\text{{SUSY}}}$ will be adjusted at each point
in the ($M_{A}$, $\tan\beta$) plane such that $M_{h}\sim 125$ GeV is
reached.666Tables listing the $M_{\text{{SUSY}}}{}$ values are available as
auxiliary material to this manuscript. We, however, do not allow
$M_{\text{{SUSY}}}$ to be larger than $10^{16}$ GeV. The minimal value of
$M_{\text{{SUSY}}}$ in both benchmark scenarios is $\sim 6\;{\rm TeV}$, when
restricting to values of $\tan\beta$ between $1$ and $10$ and $M_{A}$ to be
less than $2$ TeV.

In addition, in both scenarios, we choose for the gluino mass and the third-
generation soft-SUSY breaking trilinear couplings,

$\displaystyle M_{3}=2.5~{}\text{TeV}\,,\quad A_{t}=A_{b}=A_{\tau}=0\,,$ (2)

respectively. Typically, large $A_{t}$ values are chosen to reach $M_{h}\sim
125$ GeV for low $M_{\text{{SUSY}}}$ values. In the scenarios considered here,
we are interested most in the region of low $\tan\beta$ and low $M_{A}$. In
this region, very high $M_{\text{{SUSY}}}$ values of up to $10^{16}$ GeV are
needed to reach $M_{h}\sim 125$ GeV. For such high values of
$M_{\text{{SUSY}}}$, there is only a mild dependence of the prediction for
$M_{h}$ on the size of the stop mixing. And due to theoretical fine-tuning
arguments, low $A_{t}$ values are preferred in case of a TeV-scale $M_{3}$ and
TeV-scale electroweakinos. Fixing $M_{3}$ to $2.5$ TeV, the gluino mass is
safely above current bounds from direct searches [126, 127, 128, 129, 130,
131].

###  4.2 $\boldsymbol{M}_{\boldsymbol{h},\text{{EFT}{}}}^{\text{125}}$
scenario

The first benchmark scenario we propose is the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario. All SUSY particles are chosen to
be heavy. Consequently, all MSSM Higgs boson collider observables are only
mildly affected by SUSY particles and the phenomenology is very similar to
that of a type-II 2HDM. This scenario serves as a phenomenologically viable
extension of the $M_{h}^{\text{125}}$ scenario presented in Ref. [20] to low
$\tan\beta$ values777Low values of $\tan\beta$ in an effective 2HDM are also
well motivated from flavor and stability constraints [132].. Hence, we choose
the same Higgsino, bino and wino mass parameters,

$\displaystyle\mu=1~{}\text{TeV},\,\quad M_{1}=1~{}\text{TeV},\quad
M_{2}=1~{}\text{TeV},$ (3)

respectively. The other input parameters are fixed according to Eq. (2). With
this parameter choice, the scenario is similar to the old
“low-$\tan\beta$-high” scenario [18], where the electroweakinos were also
chosen to have masses around the TeV scale. The
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario is a concrete realization of an
MSSM scenario, which fulfills the assumptions used in the hMSSM approach [36,
38, 39]: It is defined in the region of interest, i.e. low $\tan\beta$ and low
$M_{A}$, where for low $\mu/M_{\text{{SUSY}}}{}$ the dominant corrections to
the Higgs-boson mass matrix stem from a single element in the $(2\times 2)$
$\mathcal{CP}$-even Higgs-boson mass matrix. Therefore it is a perfect
candidate for a more detailed comparison of remaining discrepancies in Higgs-
boson mass and mixing predictions as well as Higgs-boson self-couplings and
Higgs-to-Higgs decays, see e.g. Ref. [18]. Those discrepancies could reveal
potential limitations of the hMSSM approach. We present a comparison of the
heavy $\mathcal{CP}$-even Higgs-boson mass, $M_{H}$, and the Higgs-boson
mixing angle, $\alpha$, in the following subsection.

Figure 1: The $M_{h,\text{{EFT}{}}}^{\text{125}}$ benchmark scenario shown in
the $(M_{A}\,,\tan\beta)$ plane. The _green solid contour lines_ indicate the
required SUSY scale. The _black dotted line_ and _hatched area_ marks the
parameter space which is disfavored at the $2\sigma$ level by the measured
Higgs-boson signal rates. The _blue region_ with the _black dashed edge_ is
excluded at the $95\%~{}\mathrm{C.L.}$ by LHC searches for additional Higgs
bosons (the _dark blue band_ shows how the theoretical rate uncertainty
affects the exclusion). The _gray area_ is excluded because the mass of the
SM-like Higgs boson $h$ is below $122$ GeV.

In Fig. 1 we present the current constraints on the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario in the ($M_{A}$, $\tan\beta$)
parameter plane. As described above, the SUSY mass scale, $M_{\text{{SUSY}}}$,
is adjusted at every point in order to obtain $M_{h}\simeq 125$ GeV throughout
the parameter plane. In the _gray area_ , however, $M_{h}<122$ GeV, since
$M_{\text{{SUSY}}}$ would have to be raised above our imposed upper limit of
$10^{16}$ GeV in order to obtain large $M_{h}$ values.888Outside of the _gray
region_ , the prediction for $M_{h}$ quickly increases from $M_{h}=122$ GeV to
$M_{h}=125$ GeV. This part of the parameter space is therefore excluded.

Direct searches at the LHC for non-SM-like Higgs bosons exclude the _blue
region_ in Fig. 1, as determined with HiggsBounds. The _dark blue band_
indicates the theoretical uncertainty of the exclusion, obtained by varying
the cross section of $H$ and $A$ production in gluon fusion and in association
with a bottom-quark pair, as described in Section 2.2 and Section 3.1. For
$\tan\beta$ values larger than around $3$–$4$, the most important search
channel is $gg/b\bar{b}\to H/A\to\tau^{+}\tau^{-}$. The CMS analysis [22] is
slightly more sensitive than the ATLAS analysis [21] and excludes $M_{A}$
values of $\lesssim 400~{}(750)$ GeV for $\tan\beta\sim 5~{}(10)$, except for
a small parameter region at $M_{A}\sim 250$ GeV and $\tan\beta\sim 3-6$. In
this region, LHC searches for $pp\to H\to ZZ$ show similar or even higher
sensitivity. The applied ATLAS search limit [94], however, exhibits some
statistical fluctuations in this region, leading to the observed hole (and
tiny spike) in the exclusion.999Note that a proper combination of experimental
results by the LHC collaborations would presumably close the gap in the
exclusion. At lower $\tan\beta$ values direct searches for $pp\to H\to hh$
become important. Currently, the most sensitive final state of this process is
$\tau^{+}\tau^{-}b\bar{b}$, with the CMS search [100] being more sensitive for
lower masses, $M_{A}<420$ GeV, and the ATLAS search [97] for higher masses up
to $M_{A}\sim 500$ GeV.101010The transition between the two analyses results
in the spike observed in the exclusion region at ${M_{A}\sim 420}$ GeV and
${\tan\beta\sim 2.5}$. Beyond $M_{A}\sim 500$ GeV, at very low $\tan\beta$
values, the exclusion arises from the CMS combination of $H\to hh\to
b\bar{b}\gamma\gamma,~{}b\bar{b}\tau^{+}\tau^{-},~{}b\bar{b}b\bar{b},~{}b\bar{b}VV$
($V=W,Z$) search results [101]. Part of this region (at very small
$\tan\beta\sim 1$) is furthermore constrained by charged Higgs boson searches
in the $pp\to tbH^{\pm}\to tb(tb)$ channel [107].

The _hatched region_ of Fig. 1 is disfavored at the $2\sigma$ level by the SM-
like Higgs-boson rate measurements at the LHC, as evaluated by HiggsSignals.
Its boundary is located at around $M_{A}\simeq 650$ GeV and depends only
mildly on $\tan\beta$. Lower $M_{A}$ values are excluded as the coupling of
the light Higgs boson to bottom quarks is enhanced with respect to the SM
prediction. At larger $M_{A}$ values this coupling approaches the SM value, as
expected in the decoupling limit. At very small $\tan\beta$, the Higgs rate
measurements exclude values up to $M_{A}\simeq 700$ GeV due to a suppression
of the light Higgs-boson gluon-fusion cross section by a few percent. This
originates from a slight suppression of the light Higgs-boson coupling to top
quarks induced by higher-order corrections to the external Higgs leg
(accounted for by employing the $\mathbf{Z}$-matrix).

The _green contours_ in Fig. 1 indicate the $M_{\text{{SUSY}}}$ values
required to reach $M_{h}\simeq 125$ GeV. While only moderate
$M_{\text{{SUSY}}}$ values of up to $10^{4}$ GeV are required for
$\tan\beta\gtrsim 8$, much higher values up to around $10^{8}$ GeV are needed
for $\tan\beta\gtrsim 1.5$. Moreover, if $M_{A}$ is below 500 GeV,
$M_{\text{{SUSY}}}$ has to be raised to very large values of $10^{10}$ GeV and
higher. As mentioned above, for very low $M_{A}\lesssim 200$ GeV,
$M_{\text{{SUSY}}}$ would have to be raised above $10^{16}$ GeV to obtain
$M_{h}\geq 122$ GeV, a region that we disregard in our work.

Figure 2: Contour lines of $M_{h}\simeq 125$ GeV (_solid_) and $M_{h}\simeq
122,128$ GeV (_dashed_) as a function of $M_{\text{{SUSY}}}$ and
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$, for $\tan\beta=1$
(_blue_), $\tan\beta=2.5$ (_red_) and $\tan\beta=10$ (_green_). $M_{A}$ is
fixed to 1 TeV. All remaining parameters are as in the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario. The _orange star_ marks the
approximate position of the $M_{h}^{\text{125}}$ scenario [20].

We further explore the required SUSY scale in Fig. 2, which shows $M_{h}=125$
GeV contours (_solid_) as a function of $M_{\text{{SUSY}}}$ and
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$ (with
$X_{t}=A_{t}-\mu/\tan\beta$) for $\tan\beta=1$ (_blue_), $\tan\beta=2.5$
(_red_) and $\tan\beta=10$ (_green_) and $M_{A}=1\,$TeV. Note that in the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ benchmark scenario, as defined in Eqs. (2)
and (3), $X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$ is almost
zero. Clearly, the needed $M_{\text{{SUSY}}}$ value strongly depends on the
chosen $\tan\beta$ value. While for $\tan\beta=10$ values of
$\mathcal{O}(10^{3}\,{\rm GeV})$ are sufficient, for $\tan\beta=1$ values of
$\mathcal{O}(10^{8}\,{\rm GeV})$ are needed. We also observe that for high
SUSY scales there is only a mild dependence on
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$. This behavior
reflects the decrease of the strong gauge coupling and the top-quark Yukawa
coupling, which multiply the dominant threshold corrections between the full
MSSM and the EFT below the SUSY scale involving
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$, with rising
$M_{\text{{SUSY}}}$. Therefore, at low $\tan\beta$ values, choosing a high
value of $|X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}|$ does
not allow to significantly lower the required SUSY scale. The _dashed lines_
mark the contours of $M_{h}=122$ GeV and $M_{h}=128$ GeV, indicating the
allowed region when taking into account a simple global theoretical
uncertainty estimate of $3$ GeV on the Higgs mass calculation [43, 133]. The
broadening of the corresponding colored band with rising $M_{\text{{SUSY}}}$
corresponds to a growing uncertainty in the deduction of the required SUSY
scale.

For comparison, we also show in Fig. 2 the approximate position of the
$M_{h}^{\text{125}}$ scenario of Ref. [20] in the considered parameter plane
(_orange star_). In the $M_{h}^{\text{125}}$ scenario the masses of the third-
generation squarks is set to $1.5$ TeV. A large stop mixing parameter of
$X_{t}^{\text{OS}}=2.8$ GeV is needed to obtain $M_{h}\simeq 125$ GeV.111111In
the $M_{h}^{\text{125}}$ scenario, the OS scheme is used for the
renormalization of the stop parameters. We converted the OS parameters at the
one-loop level to the $\overline{\text{DR}}$ scheme to obtain the approximate
position in the
$(M_{\text{{SUSY}}},\,X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}})$
plane shown in Fig. 2.

Figure 3: _Left_ : Branching ratios of the heavy $\mathcal{CP}$-even Higgs
boson $H$ into a pair of the light $\mathcal{CP}$-even Higgs bosons $h$
(_blue_) and into a pair of top quarks (_green_) as a function of $M_{A}$ and
$\tan\beta$ in the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario.
_Right_ : Branching ratios of the $\mathcal{CP}$-odd Higgs boson $A$ into a
$Z$-boson and the light $\mathcal{CP}$-even Higgs boson $h$ (_blue_) and into
a pair of top quarks (_green_). In each plot, the gray exclusion region and
the boundaries of the blue and the hatched exclusion regions (shown as
_dashed_ and _dotted black lines_ , respectively) of Fig. 1 are also depicted.

We explore the decays of the $\mathcal{CP}$-even $H$ and $\mathcal{CP}$-odd
$A$ bosons in Fig. 3 in the parameter region of $M_{A}\leq 1\,{\rm TeV}$. The
_left panel_ shows the branching ratios of the $H$ boson decays into a pair of
light Higgs bosons, $H\to hh$ (_blue contours_), and into a pair of top
quarks, $H\to t\bar{t}$ (_green contours_). At low values $M_{H}\lesssim
2M_{t}$, the decay $H\to hh$ can reach a branching ratio of more than $50\%$
(at low $\tan\beta$). It mostly competes with the decays $H\to VV$ ($V=W,Z$)
in this mass regime. Once $M_{A}$ is raised above the kinematic threshold for
the $H\to t\bar{t}$ decay, $M_{H}\gtrsim 2M_{t}$, the decay $H\to t\bar{t}$
becomes the dominant mode and suppresses the $H\to hh$ and $H\to VV$ decays.
In the unexcluded region ($M_{A}\gtrsim 650$ GeV), the branching ratio for
$H\to hh$ drops below 10%, while the decay $H\to t\bar{t}$ can reach values
above $90\%$ for low $\tan\beta$. If $\tan\beta$ is increased the $H$ boson
coupling to top quarks becomes suppressed while its coupling to bottom quarks
and tau leptons becomes enhanced, such that the decay $H\to b\bar{b}$
eventually becomes dominant. The _right panel_ of Fig. 3 shows the branching
ratios of the $A$ boson decays into a $Z$ boson and a $h$ boson, $A\to Zh$
(_blue contours_), and into a top-quark pair, $A\to t\bar{t}$ (_green
contours_). We observe a qualitatively similar behavior as for the $H$ decays.
However, below the top-quark pair production threshold, the $A\to Zh$ decay
competes against the decay into a bottom-quark pair, $A\to b\bar{b}$, which is
dominant for $\tan\beta\gtrsim 3$. Beyond its kinematic threshold,
$M_{A}\simeq 2M_{t}$, the decay $A\to t\bar{t}$ quickly becomes dominant, and
the decay $A\to Zh$ is negligible. In this mass regime we therefore expect
that upcoming dedicated LHC searches for heavy Higgs bosons decaying to top-
quark pairs, see Ref. [134] for a Run-1 analysis by ATLAS, will be an
excellent probe. Thus, we encourage the experiments to perform such an
analysis. Interference effects between the signal $gg\to H/A\to t\bar{t}$ and
the background $gg\to t\bar{t}$ are known to be large, see Refs. [135, 136,
137, 138, 139, 140], and due to the heavy SUSY spectrum in our example can be
parametrized as a function of the Higgs masses and $\tan\beta$ for $M_{A}$
values in the decoupling limit ($M_{A}\gg M_{Z}$).

###  4.3
$\boldsymbol{M}_{\boldsymbol{h},\text{{EFT}{}}}^{\text{125}}\boldsymbol{(\tilde{\chi})}$
scenario

The second benchmark scenario we propose is the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario. In contrast to the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario, this scenario features light
neutralinos and charginos whose presence significantly alters the Higgs
phenomenology. We choose for the Higgsino, bino and wino mass parameters

$\displaystyle\mu=180~{}\text{GeV},\,\quad M_{1}=160~{}\text{GeV},\quad
M_{2}=180~{}\text{GeV}\,,$ (4)

respectively, such that this scenario represents an extension of the
$M_{h}^{125}(\tilde{\chi})$ scenario [20] to low $\tan\beta$ values. The other
input parameters are fixed according to Eq. (2), and the SUSY scale is again
adjusted at every parameter point in order to obtain a light Higgs mass of
$M_{h}\simeq 125$ GeV.

Figure 4: The $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ benchmark scenario
shown in the $(M_{A}\,,\tan\beta)$ plane. The _green solid contour lines_ show
the required SUSY scale. The _black dotted line_ and _hatched area_ depict the
$2\sigma$ disfavored region arising from the Higgs boson signal rate
measurements. The _blue region_ with the _black dashed boundary_ is excluded
at the $95\%~{}\mathrm{C.L}$ by LHC searches for additional Higgs bosons (the
_dark blue band_ shows how the theoretical rate uncertainty affects the
exclusion). The _gray area_ is excluded because the mass of the SM-like Higgs
boson $h$ is below $122$ GeV.

In Fig. 4 we present the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario
in the ($M_{A}$, $\tan\beta$) parameter plane. The _green contour lines_ show
again the $M_{\text{{SUSY}}}$ values required to reach $M_{h}\simeq 125$ GeV.
The presence of light electroweakinos leads to an upwards shift of the SM-like
Higgs-boson mass of $\sim 1.5$ GeV, therefore, smaller $M_{\text{{SUSY}}}$
values are required as compared to the previous scenario. Again, we encounter
a parameter region (_gray area_) at very low $M_{A}\lesssim 200$ GeV, for
which $M_{\text{{SUSY}}}$ would have to be chosen above $10^{16}$ GeV to
obtain $M_{h}\geq 122$ GeV. However, in comparison to the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario, this region is slightly smaller
due to the aforementioned contribution of the light electroweakinos to the
light Higgs-boson mass.

We again show in Fig. 4 the direct constraints from LHC searches for non-SM-
like Higgs bosons (_dashed black line_ and _blue area_ , with the _dark blue
band_ indicating the theoretical uncertainty) and indirect constraints from
SM-like Higgs-boson signal-rate measurements (_dotted black line_ and _hatched
area_). The excluded area arising from direct searches for non-SM-like Higgs
bosons — the relevant search channels are the same as in the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario (see above) — is smaller than in
the previous case. In particular, $pp\to H/A\to\tau^{+}\tau^{-}$ searches only
exclude $M_{A}$ values up to $220~{}(400)$ GeV for moderately large
$\tan\beta$ values of $6$ ($10$). For $\tan\beta$ values between $2$ to $6$
the parameter space for $M_{A}\lesssim 250$ GeV is constrained mostly by
$pp\to H\to ZZ$ searches. The low $\tan\beta$ region is again constrained by
$pp\to H\to hh$ searches and charged Higgs-boson searches. The decrease in
sensitivity of all these search channels with respect to the previous scenario
arises from the fact that the heavy Higgs bosons $H$ and $A$ can decay to
pairs of light electroweakinos. If such decays have sizable rates, the
branching ratios for heavy Higgs-boson decays to SM particles are suppressed.
We will discuss the heavy Higgs-boson decays to electroweakinos in detail
below.

In Fig. 4 the parameter region at $M_{A}\lesssim 630$ GeV is excluded by the
SM-like Higgs-boson signal-strength measurements. In comparison to the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario, however, an additional exclusion
arises in the region of very small $\tan\beta$ values $\lesssim 1.5$
(depending on $M_{A}$). In this area the branching ratio of the light Higgs
decay to two photons, $h\to\gamma\gamma$, is significantly enhanced due to the
presence of light charginos. We will also explore this decay mode below.

Figure 5: Contour lines of $M_{h}\simeq 125$ GeV (_solid_) and $M_{h}\simeq
122,128$ GeV (_dashed_) as a function of $M_{\text{{SUSY}}}$ and
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}})$, for
$\tan\beta=1$ (_blue_), $\tan\beta=2.5$ (_red_) and $\tan\beta=10$ (_green_).
$M_{A}$ is fixed to $1$ TeV. All remaining parameters are as in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario. The _orange star_ marks
the approximate position of the $M_{h}^{125}(\tilde{\chi})$ scenario [20].

Fig. 5 shows the $M_{h}=125$ GeV contours (_solid_) around the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario as a function of
$M_{\text{{SUSY}}}$ and
$X_{t}^{\text{{$\overline{\text{DR}}$}}}/M_{\text{{SUSY}}}$ for $\tan\beta=1$
(_blue_), $\tan\beta=2.5$ (_red_) and $\tan\beta=10$ (_green_). In comparison
to the previous benchmark scenario, see Fig. 2, the Higgs-boson mass contours
are shifted by approximately half an order of magnitude to lower
$M_{\text{{SUSY}}}$ values. As mentioned before, this shift originates from
the presence of light electroweakinos in this scenario which lead to an
upwards shift of the light Higgs-boson mass. For comparison, we also show the
approximate position of the $M_{h}^{125}(\tilde{\chi})$ scenario of Ref. [20],
for which $M_{\text{{SUSY}}}=1.5$ TeV and $X_{t}^{\text{OS}}=2.5$ TeV. Keep in
mind the different renormalization schemes: Ref. [20] employs
$X_{t}^{\text{\text{OS}}}$, whereas this work is based on
$X_{t}^{\text{{$\overline{\text{DR}}$}}}$.

Figure 6: _Left_ : Decay width of the light $\mathcal{CP}$-even Higgs boson
$h$ into photons (_green contour lines_) in the ($M_{A}$, $\tan\beta$) plane
in the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario, normalized to the
corresponding SM prediction. _Right_ : Branching ratio of the decay
$h\to\gamma\gamma$, normalized to its SM prediction (_green contour lines_).
In each plot, the gray exclusion region and the boundaries of the blue and the
hatched exclusion regions (shown as _dashed_ and _dotted black lines_ ,
respectively) of Fig. 4 are also depicted.

We now discuss in detail the impact of the light electroweakinos on the decays
of the MSSM Higgs bosons. Such decays were already considered in early
discussions of discovery prospects of the CMS detector [141, 142, 143] and
were advocated by theorists in recent years [144, 145, 146, 147, 148, 149,
150, 151, 152, 46], see e.g. Ref. [153] for a thorough analysis on the
sensitivity in a class of benchmark scenarios. The electroweakino spectrum is
fixed at tree-level by the choice of $\mu$, $M_{1}$, $M_{2}$ and the value of
$\tan\beta$ and exhibits a strong wino-Higgsino mixing in both the neutralino
and chargino sector. This mixing, which pushes the wino and Higgsino mass
eigenstates away from each other, is enhanced for small values of $\tan\beta$,
such that at $\tan\beta=1$ the spectrum is slightly less compressed than at
$\tan\beta=10$. The lightest neutralino mass increases from $\sim 85$ GeV to
$\sim 112$ GeV between $\tan\beta=1$ and $\tan\beta=10$. In the _left panel_
of Fig. 6 we show the partial width of the decay $h\to\gamma\gamma$ normalized
to the SM prediction. The decay width is enhanced by $\gtrsim 20\%$ for low
$\tan\beta\lesssim 2$. This enhancement originates from loop corrections
involving light charginos. As discussed above, our choice of $M_{2}=\mu$ in
this scenario leads to a significant wino-Higgsino mixing in the chargino
sector, which, in turn, results in a large coupling of the charginos to the
MSSM Higgs bosons. Hence, we have a sizable contribution to $h\to\gamma\gamma$
from charginos in this scenario. The distortions for $M_{A}\lesssim 200$ GeV
are due to sizable mixing effects between the $h$ and $H$ bosons. In the
_right panel_ of Fig. 6 we show the branching ratio of the decay
$h\to\gamma\gamma$ normalized to its SM prediction. In comparison to the
partial width, the enhancement of the $h\to b\bar{b}$ decay width in the
low-$M_{A}$ regime leads to an additional suppression of the branching ratio
of the $h\to\gamma\gamma$ decay. For large $M_{A}$ values above around $800$
GeV and $\tan\beta\lesssim 2$, the branching ratio is enhanced by $\gtrsim
15\%$, which yields the exclusion from the $h\to\gamma\gamma$ signal rate
measurement at very low $\tan\beta$ values, which persists in the Higgs
decoupling regime ($M_{A}\gg M_{Z}$). Future precision measurements of this
Higgs-boson decay mode thus offer the possibility to indirectly probe for
light electroweakinos within this scenario, even if the remaining Higgs bosons
are very heavy. On the other hand, if the branching ratio $h\to\gamma\gamma$
remains to be consistent with the SM predictions in the future, the lower
bound on $\tan\beta$ will be increased. This will in turn lead to a more
stringent upper bound on the SUSY scale (see Fig. 5).

Figure 7: Branching ratios of the decays of the heavy $\mathcal{CP}$-even
Higgs boson $H$ (_left_) and the $\mathcal{CP}$-odd Higgs boson $A$ (_right_)
into electroweakino pairs, shown in the ($M_{A}$, $\tan\beta$) plane in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario. The contributions from
all kinematically allowed combinations of electroweakinos in the final state
are summed. In each plot, the gray exclusion region and the boundaries of the
blue and the hatched exclusion regions (shown as _dashed_ and _dotted black
lines_ , respectively) of Fig. 4 are also depicted.

Fig. 7 shows the branching ratios for the decays of the heavy Higgs bosons $H$
(_left panel_) and $A$ (_right panel_) into pairs of charginos and
neutralinos. The contributions from all kinematically accessible
electroweakino final states are summed. For both $H$ and $A$ the branching
ratio into electroweakinos exceeds $80\%$ for $\tan\beta\gtrsim 4$ and
$M_{A}\gtrsim 500$ GeV. When decreasing $M_{A}$ below $500$ GeV, we encounter
kinematic thresholds where some decay modes into electroweakinos become
inaccessible, leading to a gradual decrease with sharp transitions of the
inclusive Higgs-to-electroweakino branching ratio. The structures at
$M_{A}\sim 340$ GeV are caused by the kinematic threshold for the decays into
a pair of top quarks. The large branching ratios for the decays into
electroweakinos strongly motivates dedicated LHC searches for these
signatures. We will discuss the most promising signatures in detail below.

Figure 8: Charged Higgs-boson phenomenology in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario. _Left_ : Production cross
section (in fb) of a negatively charged Higgs boson $H^{-}$ in association
with a top quark (_green contour lines_) at the LHC with $13\,\mathrm{TeV}$
center-of-mass energy. _Right_ : Branching ratio of the charged Higgs boson
decaying into chargino–neutralino pairs (_green contour lines_). The
contributions from all kinematically allowed combinations of electroweakinos
in the final state are summed. In each plot, the gray exclusion region and the
boundaries of the blue and the hatched exclusion regions (shown as _dashed_
and _dotted black lines_ , respectively) of Fig. 4 are also depicted.

The presence of light electroweakinos also affects the decay rates of the
charged Higgs boson $H^{\pm}$. In the _right panel_ of Fig. 8 we show the
branching ratio of the charged Higgs boson decaying into neutralino-chargino
pairs. Again, the contributions from all kinematically accessible
electroweakino final states are summed. Similar as for the neutral Higgs
bosons, the branching ratio for charged Higgs-boson decays to electroweakinos
exceeds $80\%$ for large $M_{A}\gtrsim 700$ GeV and $\tan\beta\gtrsim 4$. We
furthermore provide in the _left panel_ of Fig. 8 the production cross section
(in fb) for top-quark associated production of a negatively charged Higgs
boson (the charge-conjugated process has identical production rate) at the LHC
with a center-of-mass energy of $13$ TeV. While most of the parameter region
with large cross section is already strongly constrained by the SM-like Higgs-
boson signal-rate measurements, the production cross section can still exceed
$10$ fb in the allowed parameter space at $\tan\beta\sim 3$ and $M_{A}\sim
700$ GeV. Together with a decay rate to electroweakinos of $60$–$70\%$, the
signal cross section for $pp\to tH^{\pm}\to t(\chi^{\pm}\chi)$ can still be
$\gtrsim 14~{}\mathrm{fb}$, corresponding to more than $2200$ expected signal
events in the currently recorded integrated luminosity of LHC Run-2 per
experiment, $\mathcal{L}_{\text{int}}\simeq 160~{}\mathrm{fb}^{-1}$. Thus,
searches for a charged Higgs boson decaying into electroweakinos could be a
promising way to further probe the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$
scenario.

Figure 9: Branching ratios for the decays of the heavy $\mathcal{CP}$-even
Higgs boson $H$ in the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario as
a function of $M_{A}$, for fixed $\tan\beta=2.5$ (_upper panels_) and $7.5$
(_lower panels_). The dominant decays into SM particles (_left panels_) and
electroweakinos (_right panels_) are displayed.

To disentangle in detail the different decay channels of the heavy Higgs
bosons, Fig. 9 shows the branching ratios for the dominant decay modes of the
$\mathcal{CP}$-even heavy Higgs boson $H$ into SM particles (including the
light Higgs boson $h$) (_left panels_) and SUSY particles (_right panels_) as
a function of $M_{A}$, focusing on the region $200\,{\rm GeV}\leq M_{A}\leq
1000$ GeV, for $\tan\beta=2.5$ (_upper panels_) and $\tan\beta=7.5$ (_lower
panels_). For $\tan\beta=2.5$ the decays into SM particles dominate for
$M_{A}\lesssim 350$ GeV with the strongest decays modes being $H\to
W^{\pm}W^{\mp},ZZ$ (for $M_{A}\lesssim 250$ GeV) and $H\to hh$ (for
$M_{A}\gtrsim 250$ GeV). In the $M_{A}$ range between $280$ GeV and $360$ GeV,
the dominant $H$ decay to electroweakinos is
$H\to\tilde{\chi}_{1}\tilde{\chi}_{3}$, featuring a decay rate of up to
$30\%$. For $M_{A}\gtrsim 350$ GeV, the decay into a pair of top quarks
becomes kinematically accessible, reaching around $30\%$ at high $M_{A}$
values, and leading to a suppression of the other decay modes. In this $M_{A}$
range, all other relevant decays contain electroweakinos in the final state,
with the dominant decay modes being
$H\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$ ($\sim 30\%$),
$H\to\tilde{\chi}_{1}\tilde{\chi}_{3}$ ($\sim 10\%$) and
$H\to\tilde{\chi}_{3}\tilde{\chi}_{4}$ ($\sim 10\%$).

For $\tan\beta=7.5$, the $H$ decay into a top-quark pair is suppressed, while
the decay into a bottom-quark pair and a $\tau$-lepton pair is enhanced. In
particular, the latter decays play a significant role for $M_{A}\lesssim 380$
GeV, whereas the $H$ decays to vector bosons or light Higgs bosons are
negligible. In this low $M_{A}$ range, the dominant Higgs-to-electroweakino
decays are to the lighter states,
$H\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$, the invisible decay
$H\to\tilde{\chi}_{1}\tilde{\chi}_{1}$ and
$H\to\tilde{\chi}_{1}\tilde{\chi}_{3}$, reaching decay rates of around $30\%$,
$20\%$ and $17\%$, respectively, at $M_{A}\simeq 380$ GeV. At larger $M_{A}$
values, the $H$ decays are strongly dominated by the electroweakino final
states, with $H\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$ ($\sim 30\%$),
$H\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$ ($\sim 20\%$),
$H\to\tilde{\chi}_{1}\tilde{\chi}_{4}$ ($\sim 12\%$) and
$H\to\tilde{\chi}_{1}\tilde{\chi}_{1}$ ($\sim 10\%$) being the dominant decay
modes. In general, for both $\tan\beta$ values, we observe that the branching
ratios are almost constant for $M_{A}\gtrsim 500$ GeV, i.e. as soon as all
decays of $H$ into pairs of electroweakinos are kinematically open.

Figure 10: Branching ratios for the decays of the $\mathcal{CP}$-odd Higgs
boson $A$ in the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario as a
function of $M_{A}$, for fixed $\tan\beta=2.5$ (_upper panels_) and $7.5$
(_lower panels_). The dominant decays into SM particles (_left panels_) and
electroweakinos (_right panels_) are displayed.

We now turn to the decays of the $\mathcal{CP}$-odd Higgs boson $A$ in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario, which are shown in Fig.
10 in analogy to Fig. 9. For $\tan\beta=2.5$, the decays into SM particles
only play a minor role below the threshold for decays into a top-quark pair.
In this region, the Higgs-to-electroweakino decays
$A\to\tilde{\chi}_{1}\tilde{\chi}_{1}$ and
$A\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$ are dominant. Above the
top-quark pair threshold, the $A$ boson dominantly decays into $t\bar{t}$ with
branching ratios of $\sim 40\%$ to $50\%$ and the decay modes into
electroweakino pairs $A\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$ and
$A\to\tilde{\chi}_{1}\tilde{\chi}_{1}$ drop to $\sim 20\%$ and $\sim 12\%$,
respectively. Other electroweakino final states become accessible at higher
$M_{A}$ values, however, they remain mostly subdominant.

For $\tan\beta=7.5$, the pattern of $A$ decays to SM particles changes
significantly. Below the $A\to t\bar{t}$ kinematic threshold, the decay $A\to
b\bar{b}$ dominates. Once the electroweakino final states become kinematically
accessible for $M_{A}\gtrsim 220$ GeV, the invisible decay
$A\to\tilde{\chi}_{1}\tilde{\chi}_{1}$ and the decay
$A\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$ reach values of up to
$40$–$50\%$, thus leading to a strong suppression of $A$ decays to SM final
states. Once the decay $A\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$ is
open, it remains the dominant decay mode with a rate of $\sim 30\%$ at high
$M_{A}$ values. Here, the next-to-highest decays rates are obtained for
$A\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$ and
$A\to\tilde{\chi}_{1}\tilde{\chi}_{1}$, amounting to around $10$–$20\%$ each.
The decays to SM particles, i.e. $A\to t\bar{t}$ and $A\to b\bar{b}$, have a
combined branching ratio of $\sim 11\%$ at large $M_{A}$.

Figure 11: Branching ratios for the decays of the charged Higgs boson $H^{+}$
in the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario as a function of
$M_{A}$, for fixed $\tan\beta=2.5$ (_upper panels_) and $7.5$ (_lower
panels_). The dominant decays into SM particles (_left panels_) and
electroweakinos (_right panels_) are displayed.

Lastly, we study in detail the decays of the charged Higgs boson in Fig. 11 in
analogy to Figs. 9 and 10. For $\tan\beta=2.5$, the dominant decay mode is
$H^{+}\to t\bar{b}$, which does not fall below $35\%$ in the considered
$M_{A}$ range. The decays into neutralino-chargino pairs, once they become
kinematically accessible, are all comparable in size, with the strongest modes
reaching branching ratios of $\sim 12\%$. For $\tan\beta=7.5$, the overall
behavior of the various decay modes is very similar to the case of
$\tan\beta=2.5$. For $M_{A}\lesssim 300$ GeV, however, the branching ratio
into $t\bar{b}$ is reduced by $\sim 20$–$30\%$, while the decay to
$\tau^{+}\nu_{\tau}$ is much more important, with decay rates of up to $30\%$.
Also the branching ratios for decays into neutralino-chargino pairs is
increased, with $\mathrm{BR}(H^{+}\to\tilde{\chi}_{2}\tilde{\chi}_{1}^{\pm})$
reaching values up to $30\%$ for $M_{A}\sim(280$–$360)$ GeV. The fact that the
rates of various $H^{+}$-to-electroweakino decays are very similar warrants a
combined experimental search for the various signatures arising from these
decays within this benchmark model.

The previous figures clearly show that decay rates of heavy neutral and
charged Higgs bosons to electroweakinos can be sizable in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario. This strongly motivates
dedicated searches for these type of decays. In the remaining part of this
section we will therefore discuss such decays in more detail, focusing on a
few representative parameter points.

Typically, LHC searches for electroweakino pairs that are produced via the
conventional processes, namely $s$-channel vector-boson exchange and
$t$-channel squark exchange, and decay to the lightest supersymmetric particle
(LSP) — the lightest neutralino, $\tilde{\chi}_{1}$ — by emitting a $W$\- or a
$Z$-boson, select events with $\geq 2$ leptons (i.e., electrons and muons) and
large missing transverse energy, $\cancel{E}_{T}$, see e.g. Refs. [154, 155,
156, 157, 158, 159] for recent LHC searches. However, their sensitivity is
significantly deteriorated when the mass difference between the decaying
electroweakino and the LSP is small. In this case, the emitted off-shell
vector boson can only yield a low-$p_{T}$ (“soft”) lepton that often does not
pass the lepton-reconstruction criteria. Dedicated searches for such
compressed electroweakino mass spectra have been designed [160, 161], which
require additional jet(s) from initial-state radiation (ISR) against which the
produced electroweakinos recoil, thus giving an additional boost to the final-
state leptons. However, these searches pay the price of a lower expected
signal-event yield due to the ISR jet(s) requirement, and can therefore only
cover the parameter space with very light electroweakinos.

The $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario features a heavily-
mixed electroweakino sector, such that the limits obtained by the direct LHC
searches mentioned above cannot be directly applied. These are obtained under
certain simplifying assumptions, e.g., for the stronger, “pure wino”
production scenario of Refs. [160, 161]: (i) the produced neutralinos and
charginos are pure winos, (ii) their masses are equal, and (iii) they decay to
$100\%$ into the lightest neutralino and a $Z$\- or a $W$-boson, respectively.
If these assumptions are fulfilled, current results with
$36\,\mathrm{fb}^{-1}$ of $13$ TeV data exclude “wino” masses of around
$180$–$230$ GeV for mass differences to the LSP between $5$ GeV and $25$ GeV.
We expect these searches to also exhibit some sensitivity to the
electroweakino spectrum of the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$
scenario, however, it is unclear whether they indeed exclude this scenario,
given the complexity of its mass and decay spectrum (see below for details).
We therefore strongly encourage dedicated analyses optimized for our and
similar scenarios by the experiments.

| scenario 1 | scenario 2 | scenario 3 | scenario 4
---|---|---|---|---
$\mu\;[{\rm GeV}]$ | 180 | 180 | 280 | 280
$M_{1}\;[{\rm GeV}]$ | 160 | 160 | 260 | 260
$M_{2}\;[{\rm GeV}]$ | 180 | 180 | 280 | 280
$\tan\beta$ | 2.5 | 7.5 | 2.5 | 7.5
Neutralino and chargino masses, production and decay rates
$m_{\tilde{\chi}_{1}}\;[{\rm GeV}]$ | 95.8 | 110.0 | 194.8 | 207.9
$m_{\tilde{\chi}_{2}}\;[{\rm GeV}]$ | 164.6 | 164.7 | 264.6 | 254.7
$m_{\tilde{\chi}_{3}}\;[{\rm GeV}]$ | 183.8 | 188.8 | 282.4 | 285.6
$m_{\tilde{\chi}_{4}}\;[{\rm GeV}]$ | 263.4 | 254.1 | 362.9 | 353.0
$m_{\tilde{\chi}^{\pm}_{1}}\;[{\rm GeV}]$ | 108.9 | 122.7 | 207.9 | 220.4
$m_{\tilde{\chi}^{\pm}_{2}}\;[{\rm GeV}]$ | 256.6 | 250.3 | 355.7 | 348.1
$\sigma(pp\to\tilde{\chi}_{1}\tilde{\chi}_{3})$ | [fb] | 407.0 | 329.0 | 58.7 | 52.3
$\sigma(pp\to\tilde{\chi}_{3}\tilde{\chi}_{4})$ | [fb] | 77.1 | 77.1 | 18.8 | 19.2
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1})$ | [fb] | 8661.0 | 5206.0 | 754.0 | 579.4
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2})$ | [fb] | 974.0 | 866.0 | 135.0 | 128.3
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{3})$ | [fb] | 660.0 | 547.0 | 102.0 | 91.9
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{4})$ | [fb] | 87.7 | 99.0 | 18.7 | 20.0
$\sigma(pp\to\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{2})$ | [fb] | 132.0 | 136.0 | 31.0 | 31.5
$\sigma(pp\to\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{3})$ | [fb] | 154.0 | 160.0 | 37.3 | 38.7
$\sigma(pp\to\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{4})$ | [fb] | 331.2 | 371.0 | 92.9 | 102.3
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp})$ | [fb] | 4613.0 | 2999.7 | 440.0 | 352.2
$\sigma(pp\to\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp})$ | [fb] | 71.4 | 65.6 | 15.2 | 14.3
$\sigma(pp\to\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{2}^{\mp})$ | [fb] | 199.0 | 217.2 | 54.5 | 58.9
$\mathrm{BR}(\tilde{\chi}_{2}\to\dots)$ |  100.0% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) |  99.0% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) |  100% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) |  100% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$)
| 54.8% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) | 55.5% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) | 52.2% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$) | 52.4% ($\tilde{\chi}_{1}^{\pm}W^{\mp\,*}$)
$\mathrm{BR}(\tilde{\chi}_{3}\to\dots)$ | 45.2% ($\tilde{\chi}_{1}^{0}Z^{*}$) | 44.5% ($\tilde{\chi}_{1}^{0}Z^{*}$) | 47.8% ($\tilde{\chi}_{1}^{0}Z^{*}$) | 47.6% ($\tilde{\chi}_{1}^{0}Z^{*}$)
$\mathrm{BR}(\tilde{\chi}_{4}^{0}\to\dots)$ |  99.5% ($\tilde{\chi}_{1}^{\pm}W^{\mp}$) |  99.1% ($\tilde{\chi}_{1}^{\pm}W^{\mp}$) |  99.8% ($\tilde{\chi}_{1}^{\pm}W^{\mp}$) |  99.5% ($\tilde{\chi}_{1}^{\pm}W^{\mp}$)
$\mathrm{BR}(\tilde{\chi}_{1}^{\pm}\to\dots)$ | 100% ($\tilde{\chi}_{1}^{0}W^{\pm\,*}$) | 100% ($\tilde{\chi}_{1}^{0}W^{\pm\,*}$) | 100% ($\tilde{\chi}_{1}^{0}W^{\pm\,*}$) | 100% ($\tilde{\chi}_{1}^{0}W^{\pm\,*}$)
$\mathrm{BR}(\tilde{\chi}_{2}^{\pm}\to\dots)$ |  53.4% ($\tilde{\chi}_{1}^{\pm}Z$) |  51.5% ($\tilde{\chi}_{1}^{\pm}Z$) |  53.7% ($\tilde{\chi}_{1}^{\pm}Z$) |  52.7% ($\tilde{\chi}_{1}^{\pm}Z$)
38.0% ($\tilde{\chi}_{1}^{0}W^{\pm}$) |  41.8% ($\tilde{\chi}_{1}^{0}W^{\pm}$) |  40.1% ($\tilde{\chi}_{1}^{0}W^{\pm}$) |  44.7% ($\tilde{\chi}_{1}^{0}W^{\pm}$)
Table 1: A detailed view on two parameter points from the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario (scenario 1 and 2), as well as two variations (scenario 3 and 4): relevant parameters for the electroweak sector (_top panel_); masses and rates for the dominant production modes (for the LHC at $13$ TeV) and decay modes of the neutralinos and charginos (_bottom panel_). | scenario 1 | scenario 2 | scenario 3 | scenario 4
---|---|---|---|---
$\mu\;[{\rm GeV}]$ | 180 | 180 | 280 | 280
$M_{1}\;[{\rm GeV}]$ | 160 | 160 | 260 | 260
$M_{2}\;[{\rm GeV}]$ | 180 | 180 | 280 | 280
$\tan\beta$ | 2.5 | 7.5 | 2.5 | 7.5
MSSM Higgs boson production and decay rates for $M_{A}=1$ TeV
$\sigma(gg\to H)$ | [fb] | 19.0 | 1.8 | 19.0 | 1.8
$\sigma(b\bar{b}\to H)$ | [fb] | 0.6 | 5.1 | 0.6 | 5.1
$\sigma(gg\to A)$ | [fb] | 24.6 | 3.6 | 24.6 | 3.6
$\sigma(b\bar{b}\to A)$ | [fb] | 0.6 | 5.1 | 0.6 | 5.1
$\sigma(pp\to tH^{-})$ | [fb] | 3.7 | 0.7 | 3.7 | 0.7
|  |  33.1% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$) |  32.6% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$) |  33.0% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$) |  36.0% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$)
$\mathrm{BR}(H\to\tilde{\chi}\tilde{\chi})$ |  11.1% ($\tilde{\chi}_{3}\tilde{\chi}_{4}$) |  18.4% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$) |  10.9% ($\tilde{\chi}_{1}\tilde{\chi}_{3}$) |  14.4% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$)
|  |  9.8% ($\tilde{\chi}_{1}\tilde{\chi}_{3}$) |  12.6% ($\tilde{\chi}_{3}\tilde{\chi}_{4}$) |  10.4% ($\tilde{\chi}_{3}\tilde{\chi}_{4}$) |  12.4% ($\tilde{\chi}_{3}\tilde{\chi}_{4}$)
|  | 20.2% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$) | 26.8% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$) | 19.6% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$) | 26.1% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}$)
$\mathrm{BR}(A\to\tilde{\chi}\tilde{\chi})$ | 13.2% ($\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{2}^{\mp}$) | 16.6% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$) | 12.5% ($\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{2}^{\mp}$) | 14.0% ($\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}$)
|  | 12.2% ($\tilde{\chi}_{1}\tilde{\chi}_{1}$) | 14.8% ($\tilde{\chi}_{1}\tilde{\chi}_{1}$) | 12.2% ($\tilde{\chi}_{1}\tilde{\chi}_{1}$) | 15.2% ($\tilde{\chi}_{1}\tilde{\chi}_{1}$)
|  |  12.7% ($\tilde{\chi}_{1}\tilde{\chi}_{2}^{+}$) |  19.9% ($\tilde{\chi}_{1}\tilde{\chi}_{2}^{+}$) |  12.3% ($\tilde{\chi}_{4}\tilde{\chi}_{1}^{+}$) |  17.4% ($\tilde{\chi}_{1}\tilde{\chi}_{2}^{+}$)
$\mathrm{BR}(H^{+}\to\tilde{\chi}\tilde{\chi}^{+})$ |  12.6% ($\tilde{\chi}_{4}\tilde{\chi}_{1}^{+}$) |  16.0% ($\tilde{\chi}_{4}\tilde{\chi}_{1}^{+}$) |  11.2% ($\tilde{\chi}_{1}\tilde{\chi}_{2}^{+}$) |  16.6% ($\tilde{\chi}_{4}\tilde{\chi}_{1}^{+}$)
|  |  9.4% ($\tilde{\chi}_{2}\tilde{\chi}_{2}^{+}$) |  13.1% ($\tilde{\chi}_{2}\tilde{\chi}_{1}^{+}$) |  9.5% ($\tilde{\chi}_{3}\tilde{\chi}_{1}^{+}$) |  13.1% ($\tilde{\chi}_{3}\tilde{\chi}_{1}^{+}$)
$\mathrm{BR}(h\to\gamma\gamma)_{\text{{MSSM}{}}/\text{{SM}{}}}$ | 1.12 | 1.02 | 1.02 | 0.98
Table 2: A detailed view on two parameter points from the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario (scenario 1 and 2), as
well as two variations (scenario 3 and 4): relevant parameters for the
electroweak sector (_top panel_); rates of the dominant production modes (for
the LHC at $13$ TeV) and decay modes to electroweakinos of the heavy Higgs
bosons $H$, $A$ and $H^{+}$, for fixed $M_{A}=1$ TeV (_bottom panel_).

In Tab. 1 we provide detailed information on the masses and dominant
production and decay modes of the neutralinos and charginos in the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ benchmark scenario, for $\tan\beta$
values of $2.5$ (scenario 1) and $7.5$ (scenario 2). We calculated the direct
neutralino/chargino production cross sections for the LHC at a center-of-mass
energy of $13$ TeVat the NLO+NLL level using Resummino (version 2.0.1) [162,
163, 164, 165, 166] with the CT14 PDF sets [167]. The value of $M_{A}$ does
not affect the electroweakino spectrum at tree-level, however, it obviously
affects the heavy Higgs-boson phenomenology. In Tab. 2 we provide for these
scenarios the $13$ TeV cross sections for the dominant heavy Higgs-boson
production modes, as well as the rates for the three dominant decays to
electroweakinos, for $M_{A}=1$ TeV.

For the heavy $\mathcal{CP}$-even Higgs boson $H$ we identify the cascade
decay

$\displaystyle
H\rightarrow\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}\rightarrow(\tilde{\chi}_{1}W^{\pm\,*})(\tilde{\chi}_{1}^{\mp}Z)\rightarrow\tilde{\chi}_{1}\tilde{\chi}_{1}W^{\pm\,*}W^{\mp\,*}Z$
(5)

as the most frequent process, with a total rate of around $17.7\%$ ($16.8\%$)
for $\tan\beta=2.5~{}(7.5)$. Despite their off-shellness, one can still expect
reasonably high-$p_{T}$ leptons from the $W$-bosons, provided that
$M_{H}\gg(m_{\tilde{\chi}_{1}^{\pm}}+m_{\tilde{\chi}_{2}^{\pm}})$, as is the
case in this example. This process can therefore lead to a spectacular
signature with up to $4$ reconstructable leptons, missing transverse energy,
and for larger $\tan\beta$ values possibly two additional $b$-jets, if the
heavy Higgs boson is produced in association with bottom quarks. Moreover,
many of the other possible cascade decays also lead to final states with
multiple $W$\- and or $Z$-bosons. In contrast, the direct (invisible) Higgs-
boson decay into two lightest neutralinos,
$H\to\tilde{\chi}_{1}\tilde{\chi}_{1}$, as well as decays leading to a
$Z+\cancel{E}_{T}$ final state (e.g., via
$H\to\tilde{\chi}_{1}\tilde{\chi}_{3}\to\tilde{\chi}_{1}\tilde{\chi}_{1}Z$)
occur with smaller rates, e.g. with branching ratios of $3.4\%$ and $4.4\%$,
respectively, in scenario 1.121212Our scenario(s) are therefore
phenomenologically very different to those considered in Ref. [153], where the
final state $Z+\cancel{E}_{T}$ is regarded as the most promising search
channel.

For the $\mathcal{CP}$-odd Higgs boson $A$, the most frequent process is

$\displaystyle
A\rightarrow\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{1}^{\mp}\rightarrow\tilde{\chi}_{1}\tilde{\chi}_{1}W^{\pm\,*}W^{\mp\,*}$
(6)

with a rate of $20.2\%$ ($26.5\%$) for $\tan\beta=2.5~{}(7.5)$. Experimentally
more promising, however, might be the cascade

$\displaystyle
A\rightarrow\tilde{\chi}_{2}^{\pm}\tilde{\chi}_{2}^{\mp}\to(\tilde{\chi}_{1}^{\pm}Z)(\tilde{\chi}_{1}^{\mp}Z)\to\tilde{\chi}_{1}\tilde{\chi}_{1}ZZW^{\pm\,*}W^{\mp\,*}$
(7)

occurring with a branching ratio of $3.8\%$ ($2.8\%$), or

$\displaystyle
A\rightarrow\tilde{\chi}_{1}^{\pm}\tilde{\chi}_{2}^{\mp}\to(\tilde{\chi}_{1}W^{\pm\,*})(\tilde{\chi}_{1}^{\mp}Z)\to\tilde{\chi}_{1}\tilde{\chi}_{1}ZW^{\pm\,*}W^{\mp\,*}$
(8)

with a decay rate of $2.7\%$ ($8.5\%$) for scenario 1 (scenario 2), i.e.
$\tan\beta=2.5~{}(7.5)$.

Finally, the most frequent charged Higgs-to-electroweakino decay cascade is

$\displaystyle
H^{\pm}\to\tilde{\chi}_{1}\tilde{\chi}_{2}^{\pm}\to\tilde{\chi}_{1}(\tilde{\chi}_{1}^{\pm}Z)\to\tilde{\chi}_{1}\tilde{\chi}_{1}ZW^{\pm\,*}$
(9)

with a rate of $6.8\%$ ($10.2\%$) in scenario 1 (scenario 2). Furthermore,
many other possible charged Higgs-boson cascade decays yield final states with
one or three $W$-bosons and missing transverse energy.

We stress again that searches for heavy Higgs-to-electroweakino processes are
highly complementary to direct electroweakino searches, in particular in the
case of a compressed electroweakino mass spectrum. While the final-state
leptons in events from direct electroweakino production tend to be soft and
difficult to reconstruct, this is not a problem in events where the
electroweakinos originate from a heavy Higgs boson, and therefore come with a
larger initial momentum. At the same time, the presence of a compressed
electroweakino spectrum implies that multiple light electroweakino states are
available, such that heavy Higgs-boson cascade decays via these states are
possible (and even sometimes preferred, as demonstrated above), thus yielding
multiple $W$\- and $Z$-bosons in the final state.

For the current choice of electroweakino masses, and the example value of
$M_{A}=1\;{\rm TeV}$ in Tab. 2, the production cross sections for direct
electroweakino-pair production exceed the heavy Higgs-boson production cross
sections by roughly two orders of magnitude. The leading direct
electroweakino-production channels are the chargino-pair production processes
$pp\to\tilde{\chi}^{\pm}_{1}\tilde{\chi}^{\mp}_{1}$ and
$pp\to\tilde{\chi}^{\pm}_{2}\tilde{\chi}^{\mp}_{2}$. Due to the large
difference in the rates, a dedicated search analysis of direct electroweakino
production might turn out to be more sensitive than a dedicated search for the
heavy Higgs-to-electroweakino channels for this specific parameter choice,
despite the more experimentally challenging kinematics in the first case.
However, lifting the electroweakino-mass spectrum (see below) and/or
decreasing the heavy Higgs-boson masses, while still maintaining the
possibility of sizable heavy Higgs-to-electroweakino decay rates, leads to
scenarios where both search strategies are sensitive and complementary.131313A
detailed analysis and comparison of the LHC sensitivity to direct
electroweakino production and to heavy Higgs-to-electroweakino decays within
these (and other) scenarios is left for future work.

In the light of the fact that the choice of the electroweakino-mass parameters
of the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario may already be in
conflict with present LHC data (if a dedicated analyses was performed), we
want to close this section with some remarks on alternative scenarios with
slightly heavier electroweakinos. In Tabs. 1 and 2 we also include detailed
information on two alternative parameter points, scenario 3 and scenario 4, in
which $M_{1}$, $M_{2}$ and $\mu$ are increased from their
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario values by $100$ GeV.
Again, the scenarios are distinct in the choice of $\tan\beta$ values, $2.5$
and $7.5$, respectively. With respect to the original
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ parameter points, scenario 1 and
scenario 2, all electroweakino masses are simply increased by around $100$
GeV. However, interestingly, there are no significant changes in the
electroweakino and heavy Higgs-boson decay spectra, and our above discussion
of collider signatures still holds. Also the effect of raising the
electroweakino spectrum on the Higgs-boson production cross sections is below
the quoted precision. On the other hand, current constraints from direct
electroweakino searches are safely avoided for this alternative choice of
$M_{1}$, $M_{2}$ and $\mu$, as the production rates for direct neutralino and
chargino production are significantly smaller than for the original parameter
choice, see Tab. 1. Lastly, note that due to the increased chargino masses,
the enhancement of the $h\to\gamma\gamma$ rate is less pronounced in this
case, as shown in the last row of Tab. 2.

###  4.4 Comparison with the hMSSM approach

We already emphasized that the $M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario is
the perfect candidate to assess the region of validity of the hMSSM approach
[36, 38, 39], as it covers the same region in the ($M_{A},\tan\beta$)
parameter plane, and for low values of $\mu/M_{\text{{SUSY}}}{}$ fulfills the
hMSSM assumptions. As a first step, we present a comparison of the predicted
heavy $\mathcal{CP}$-even Higgs-boson mass, $M_{H}$, and the (effective)
$\mathcal{CP}$-even Higgs-boson mixing angle, $\alpha$, in Fig. 12.141414We
leave a discussion of more elaborate quantities such as the Higgs-boson self-
couplings and Higgs-to-Higgs decays to future work. We only depict the range
$M_{A}\in[150,1000]$ GeV, since at values of $M_{A}\lesssim 150$ GeV the hMSSM
approach is ill-defined — the light-Higgs boson is not SM-like — and for
values of $M_{A}>1$ TeV the observed differences are negligible.

Figure 12: _Left_ : Relative difference in the prediction of the (effective)
$\mathcal{CP}$-even Higgs-boson mixing angle $\alpha$ between the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario and the hMSSM approach in $\%$.
_Right_ : Relative difference in the prediction of the heavy
$\mathcal{CP}$-even Higgs-boson mass $M_{H}$ between the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario and the hMSSM approach in $\%$.

According to Fig. 12 the hMSSM approach provides a very good approximation to
both the $\mathcal{CP}$-even Higgs-boson mixing angle and the heavy Higgs-
boson mass at sufficiently large values of $M_{A}$ and $\tan\beta$, where
differences are at the permille level. On the other hand, at low values of
$M_{A}\lesssim 600$ GeV and $\tan\beta\lesssim 4$, the discrepancies can reach
a few percent and at very low values, i.e. in the lower-left corner, even
exceed $10$%, in particular for the (effective) $\mathcal{CP}$-even Higgs-
boson mixing angle. Such discrepancies are slightly larger than the
differences observed between the “low-$\tan\beta$-high” scenario and the hMSSM
[18, 33], where however lower values of $M_{\text{{SUSY}}}{}$ were used in the
low $M_{A}$ and low $\tan\beta$ region. In the experimentally allowed region
with $M_{A}\gtrsim 700$ GeV, however, the differences are well below the
percent level and thus the hMSSM approach provides a decent description of the
MSSM Higgs-boson sector, at least within its region of validity, i.e. for not
too large values of $\tan\beta$.

The hMSSM approach assumes that the ratio $\mu/M_{\text{{SUSY}}}{}$ is small.
It therefore also makes sense to compare the hMSSM approach against the
$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$ scenario, which by definition has
an even smaller value of $\mu$ than the $M_{h,\text{{EFT}{}}}^{\text{125}}$
scenario. On the other hand, the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$
scenario clearly violates one assumption of the hMSSM approach, namely it
comes with light electroweakinos, which alter Higgs-boson phenomenology
substantially, as discussed in detail in the previous section. Indeed, we find
slightly larger differences in the prediction of the $\mathcal{CP}$-even
Higgs-boson mixing angle and the heavy Higgs-boson mass than those depicted in
Fig. 12, which are due to the Feynman-diagrammatic corrections induced by
light electroweakinos on the Higgs-boson self energies. However again the
differences are well below the permille level in the experimentally still
allowed region.

##  5 Summary

In this paper we have proposed two new benchmark scenarios for MSSM Higgs-
boson searches at the LHC, supplementing the scenarios suggested in Ref. [20].
In the scenarios proposed in Ref. [20] all SUSY particles are below or close
to the TeV scale. Consequently, the parameter region of $\tan\beta\lesssim 8$
is incompatible with observations due to a too-low prediction of the SM-like
Higgs-boson mass. In this work we re-opened this parameter region by allowing
for squark masses of up to $10^{16}$ GeV, thus making it possible to reach a
SM-like Higgs-boson mass of $\sim 125$ GeV even for low values of $\tan\beta$
and $M_{A}$ (except for a region of very low values of $M_{A}<200$ GeV). The
presented scenarios are designed to provide guidance for experimental efforts
to probe the low $\tan\beta$ region of the MSSM Higgs sector and also to
motivate new LHC searches for additional heavy Higgs bosons.

Our first scenario, the “$M_{h,\text{{EFT}{}}}^{\text{125}}$” benchmark
scenario, can be considered as extension of the $M_{h}^{\text{125}}$ scenario
[20] to low $\tan\beta$ values. In this scenario all supersymmetric particles
have masses around or above the TeV scale. Consequently, the phenomenology
resembles the one of a type-II 2HDM with the Higgs-boson couplings constrained
to be as in the MSSM. The strongest constraint in this scenario originates
from the signal-strength measurements of the SM-like Higgs boson, excluding
the region of $M_{A}\lesssim 650$ GeV. Since the
$M_{h,\text{{EFT}{}}}^{\text{125}}$ scenario fulfills the assumptions of the
hMSSM approach, it is a candidate for more detailed comparisons between a
complete MSSM scenario and the hMSSM approach. We presented a comparison for
the predictions of the $\mathcal{CP}$-even Higgs-boson mixing angle and the
heavy Higgs-boson mass and in the experimentally allowed region find
discrepancies only at the permille level. On the other hand, in particular the
Higgs-boson self-couplings and Higgs-to-Higgs decays need further
investigations. Since they are however hardly of relevance for our work,
except from small corners of the parameter space that are already ruled out by
Higgs-boson signal-strength measurements, we leave them to future work.

In our second scenario, the “$M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$”
benchmark scenario, neutralinos and charginos are chosen to be light. This
scenario represents an extension of the $M_{h}^{125}(\tilde{\chi})$ scenario
[20] to low $\tan\beta$ values. The effect of low-mass charginos enhances the
decay rate of the SM-like Higgs boson into photons, in particular in
compressed scenarios with large gaugino-Higgsino mixing. Future precision
measurements of this rate will therefore indirectly probe a significant part
of the parameter space with light electroweakinos. We furthermore studied in
detail the possible decays of the heavy Higgs bosons into electroweakinos.
While the presence of these decay modes weakens the sensitivity of LHC
searches for heavy Higgs bosons decaying into SM particles, they also provide
an interesting and promising new avenue for new physics searches. In fact, a
signal in these channels would simultaneously reveal the presence of BSM Higgs
bosons _and_ supersymmetric particles. In particular, in scenarios with a
compressed electroweakino mass spectrum (as chosen here), these signatures
often feature multiple $W$\- and/or $Z$-bosons, giving rise to multi-lepton
final states, plus missing transverse energy. Moreover, as these
electroweakinos originate from the decay of a heavy resonance, they can have
sizable initial momentum, leading to better prospects for the reconstruction
of leptons, as opposed to direct electroweakino production. LHC searches for
heavy Higgs bosons decaying to electroweakinos are therefore highly
complementary to existing searches for direct electroweakino production. One
of the main purposes of the $M_{h,\text{{EFT}{}}}^{125}(\tilde{\chi})$
benchmark scenario (as well as the $M_{h}^{125}(\tilde{\chi})$ scenario [20])
is to motivate and initiate the design of dedicated searches for heavy Higgs-
to-electroweakino decay signatures.

## Acknowledgments

We thank Emanuele Bagnaschi, Sven Heinemeyer, Gabriel Lee, Pietro Slavich,
Alexander Voigt, Georg Weiglein and Carlos Wagner for helpful discussions.
This work was initiated in the context of the activities of the LHC Higgs
Cross Section Working Group (LHC-HXSWG).

## References

  * [1] ATLAS Collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B716 (2012) 1–29, arXiv:1207.7214 [hep-ex].
  * [2] CMS Collaboration, S. Chatrchyan et al., Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B716 (2012) 30–61, arXiv:1207.7235 [hep-ex].
  * [3] ATLAS, CMS Collaboration, G. Aad et al., Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments. Phys. Rev. Lett. 114 (2015) 191803, arXiv:1503.07589 [hep-ex].
  * [4] ATLAS, CMS Collaboration, G. Aad et al., Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at $\sqrt{s}=7$ and 8 TeV. JHEP 08 (2016) 045, arXiv:1606.02266 [hep-ex].
  * [5] H. P. Nilles, Supersymmetry, Supergravity and Particle Physics. Phys. Rept. 110 (1984) 1–162.
  * [6] H. E. Haber and G. L. Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model. Phys. Rept. 117 (1985) 75–263.
  * [7] J. F. Gunion and H. E. Haber, Higgs Bosons in Supersymmetric Models. 1. Nucl. Phys. B272 (1986) 1. [Erratum: Nucl. Phys.B402,567(1993)].
  * [8] S. Heinemeyer, O. Stål, and G. Weiglein, Interpreting the LHC Higgs Search Results in the MSSM. Phys. Lett. B710 (2012) 201–206, arXiv:1112.3026 [hep-ph].
  * [9] M. Drees, A Supersymmetric Explanation of the Excess of Higgs–Like Events at the LHC and at LEP. Phys. Rev. D86 (2012) 115018, arXiv:1210.6507 [hep-ph].
  * [10] P. Bechtle, S. Heinemeyer, O. Stål, T. Stefaniak, G. Weiglein, and L. Zeune, MSSM Interpretations of the LHC Discovery: Light or Heavy Higgs? Eur. Phys. J. C73 (2013) no. 4, 2354, arXiv:1211.1955 [hep-ph].
  * [11] P. Bechtle, H. E. Haber, S. Heinemeyer, O. Stål, T. Stefaniak, G. Weiglein, and L. Zeune, The Light and Heavy Higgs Interpretation of the MSSM. Eur. Phys. J. C77 (2017) no. 2, 67, arXiv:1608.00638 [hep-ph].
  * [12] H. E. Haber, S. Heinemeyer, and T. Stefaniak, The Impact of Two-Loop Effects on the Scenario of MSSM Higgs Alignment without Decoupling. Eur. Phys. J. C77 (2017) no. 11, 742, arXiv:1708.04416 [hep-ph].
  * [13] P. Draper and H. Rzehak, A Review of Higgs Mass Calculations in Supersymmetric Models. Phys. Rept. 619 (2016) 1–24, arXiv:1601.01890 [hep-ph].
  * [14] M. Carena, S. Heinemeyer, C. E. M. Wagner, and G. Weiglein, “Suggestions for improved benchmark scenarios for Higgs boson searches at LEP-2,” in Workshop on New Theoretical Developments for Higgs Physics at LEP-2 Geneva, Switzerland, October 27, 1999.  1999\.  arXiv:hep-ph/9912223 [hep-ph].
  * [15] M. Carena, S. Heinemeyer, C. E. M. Wagner, and G. Weiglein, Suggestions for benchmark scenarios for MSSM Higgs boson searches at hadron colliders. Eur. Phys. J. C26 (2003) 601–607, arXiv:hep-ph/0202167 [hep-ph].
  * [16] M. Carena, S. Heinemeyer, O. Stål, C. E. M. Wagner, and G. Weiglein, MSSM Higgs Boson Searches at the LHC: Benchmark Scenarios after the Discovery of a Higgs-like Particle. Eur. Phys. J. C73 (2013) no. 9, 2552, arXiv:1302.7033 [hep-ph].
  * [17] M. Carena, J. R. Ellis, A. Pilaftsis, and C. E. M. Wagner, CP violating MSSM Higgs bosons in the light of LEP-2. Phys. Lett. B495 (2000) 155–163, arXiv:hep-ph/0009212 [hep-ph].
  * [18] E. Bagnaschi, F. Frensch, S. Heinemeyer, G. Lee, S. R. Liebler, M. Mühlleitner, A. R. Mc Carn, J. Quevillon, N. Rompotis, P. Slavich, M. Spira, C. Wagner, and R. Wolf, Benchmark scenarios for low $\tan\beta$ in the MSSM Tech. Rep. LHCHXSWG-2015-002, CERN, Geneva, Aug, 2015.  https://cds.cern.ch/record/2039911.
  * [19] M. Carena, J. Ellis, J. S. Lee, A. Pilaftsis, and C. E. M. Wagner, CP Violation in Heavy MSSM Higgs Scenarios. JHEP 02 (2016) 123, arXiv:1512.00437 [hep-ph].
  * [20] H. Bahl, E. Fuchs, T. Hahn, S. Heinemeyer, S. Liebler, S. Patel, P. Slavich, T. Stefaniak, C. E. M. Wagner, and G. Weiglein, MSSM Higgs Boson Searches at the LHC: Benchmark Scenarios for Run 2 and Beyond. arXiv:1808.07542 [hep-ph].
  * [21] ATLAS Collaboration, M. Aaboud et al., Search for additional heavy neutral Higgs and gauge bosons in the ditau final state produced in 36 fb-1 of pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector. JHEP 01 (2018) 055, arXiv:1709.07242 [hep-ex].
  * [22] CMS Collaboration, A. M. Sirunyan et al., Search for additional neutral MSSM Higgs bosons in the $\tau\tau$ final state in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 09 (2018) 007, arXiv:1803.06553 [hep-ex].
  * [23] G. F. Giudice and A. Strumia, Probing High-Scale and Split Supersymmetry with Higgs Mass Measurements. Nucl. Phys. B858 (2012) 63–83, arXiv:1108.6077 [hep-ph].
  * [24] T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak, and G. Weiglein, High-Precision Predictions for the Light CP -Even Higgs Boson Mass of the Minimal Supersymmetric Standard Model. Phys. Rev. Lett. 112 (2014) no. 14, 141801, arXiv:1312.4937 [hep-ph].
  * [25] P. Draper, G. Lee, and C. E. M. Wagner, Precise estimates of the Higgs mass in heavy supersymmetry. Phys. Rev. D89 (2014) no. 5, 055023, arXiv:1312.5743 [hep-ph].
  * [26] E. Bagnaschi, G. F. Giudice, P. Slavich, and A. Strumia, Higgs Mass and Unnatural Supersymmetry. JHEP 09 (2014) 092, arXiv:1407.4081 [hep-ph].
  * [27] J. Pardo Vega and G. Villadoro, SusyHD: Higgs mass Determination in Supersymmetry. JHEP 07 (2015) 159, arXiv:1504.05200 [hep-ph].
  * [28] H. Bahl and W. Hollik, Precise prediction for the light MSSM Higgs boson mass combining effective field theory and fixed-order calculations. Eur. Phys. J. C76 (2016) no. 9, 499, arXiv:1608.01880 [hep-ph].
  * [29] E. Bagnaschi, J. Pardo Vega, and P. Slavich, Improved determination of the Higgs mass in the MSSM with heavy superpartners. Eur. Phys. J. C77 (2017) no. 5, 334, arXiv:1703.08166 [hep-ph].
  * [30] H. Bahl, S. Heinemeyer, W. Hollik, and G. Weiglein, Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass. Eur. Phys. J. C78 (2018) no. 1, 57, arXiv:1706.00346 [hep-ph].
  * [31] R. V. Harlander, J. Klappert, A. D. Ochoa Franco, and A. Voigt, The light CP-even MSSM Higgs mass resummed to fourth logarithmic order. Eur. Phys. J. C78 (2018) no. 10, 874, arXiv:1807.03509 [hep-ph].
  * [32] H. E. Haber and R. Hempfling, The Renormalization group improved Higgs sector of the minimal supersymmetric model. Phys. Rev. D48 (1993) 4280–4309, arXiv:hep-ph/9307201 [hep-ph].
  * [33] G. Lee and C. E. M. Wagner, Higgs bosons in heavy supersymmetry with an intermediate mA. Phys. Rev. D92 (2015) no. 7, 075032, arXiv:1508.00576 [hep-ph].
  * [34] P. Athron, M. Bach, D. Harries, T. Kwasnitza, J.-h. Park, D. Stöckinger, A. Voigt, and J. Ziebell, FlexibleSUSY 2.0: Extensions to investigate the phenomenology of SUSY and non-SUSY models. Comput. Phys. Commun. 230 (2018) 145–217, arXiv:1710.03760 [hep-ph].
  * [35] M. Gabelmann, M. Mühlleitner, and F. Staub, Automatised matching between two scalar sectors at the one-loop level. Eur. Phys. J. C79 (2019) no. 2, 163, arXiv:1810.12326 [hep-ph].
  * [36] A. Djouadi and J. Quevillon, The MSSM Higgs sector at a high $M_{SUSY}$: reopening the low tan$\beta$ regime and heavy Higgs searches. JHEP 10 (2013) 028, arXiv:1304.1787 [hep-ph].
  * [37] L. Maiani, A. D. Polosa, and V. Riquer, Bounds to the Higgs Sector Masses in Minimal Supersymmetry from LHC Data. Phys. Lett. B724 (2013) 274–277, arXiv:1305.2172 [hep-ph].
  * [38] A. Djouadi, L. Maiani, G. Moreau, A. Polosa, J. Quevillon, and V. Riquer, The post-Higgs MSSM scenario: Habemus MSSM? Eur. Phys. J. C73 (2013) 2650, arXiv:1307.5205 [hep-ph].
  * [39] A. Djouadi, L. Maiani, A. Polosa, J. Quevillon, and V. Riquer, Fully covering the MSSM Higgs sector at the LHC. JHEP 06 (2015) 168, arXiv:1502.05653 [hep-ph].
  * [40] S. Liebler, M. Mühlleitner, M. Spira, and M. Stadelmaier, The hMSSM approach for Higgs self-couplings revisited. Eur. Phys. J. C79 (2019) no. 1, 65, arXiv:1810.10979 [hep-ph].
  * [41] S. Heinemeyer, W. Hollik, and G. Weiglein, FeynHiggs: A Program for the calculation of the masses of the neutral CP even Higgs bosons in the MSSM. Comput. Phys. Commun. 124 (2000) 76–89, arXiv:hep-ph/9812320 [hep-ph].
  * [42] S. Heinemeyer, W. Hollik, and G. Weiglein, The Masses of the neutral CP - even Higgs bosons in the MSSM: Accurate analysis at the two loop level. Eur. Phys. J. C9 (1999) 343–366, arXiv:hep-ph/9812472 [hep-ph].
  * [43] G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, and G. Weiglein, Towards high precision predictions for the MSSM Higgs sector. Eur. Phys. J. C28 (2003) 133–143, arXiv:hep-ph/0212020 [hep-ph].
  * [44] M. Frank, T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak, and G. Weiglein, The Higgs Boson Masses and Mixings of the Complex MSSM in the Feynman-Diagrammatic Approach. JHEP 02 (2007) 047, arXiv:hep-ph/0611326 [hep-ph].
  * [45] H. Bahl, T. Hahn, S. Heinemeyer, W. Hollik, S. Paßehr, H. Rzehak, and G. Weiglein, Precision calculations in the MSSM Higgs-boson sector with FeynHiggs 2.14. arXiv:1811.09073 [hep-ph].
  * [46] H. Bahl and W. Hollik, Precise prediction of the MSSM Higgs boson masses for low MA. JHEP 07 (2018) 182, arXiv:1805.00867 [hep-ph].
  * [47] R. V. Harlander, S. Liebler, and H. Mantler, SusHi: A program for the calculation of Higgs production in gluon fusion and bottom-quark annihilation in the Standard Model and the MSSM. Comput. Phys. Commun. 184 (2013) 1605–1617, arXiv:1212.3249 [hep-ph].
  * [48] R. V. Harlander, S. Liebler, and H. Mantler, SusHi Bento: Beyond NNLO and the heavy-top limit. Comput. Phys. Commun. 212 (2017) 239–257, arXiv:1605.03190 [hep-ph].
  * [49] S. Forte, D. Napoletano, and M. Ubiali, Higgs production in bottom-quark fusion: matching beyond leading order. Phys. Lett. B763 (2016) 190–196, arXiv:1607.00389 [hep-ph].
  * [50] S. Forte, D. Napoletano, and M. Ubiali, Higgs production in bottom-quark fusion in a matched scheme. Phys. Lett. B751 (2015) 331–337, arXiv:1508.01529 [hep-ph].
  * [51] M. Bonvini, A. S. Papanastasiou, and F. J. Tackmann, Matched predictions for the $b\overline{b}H$ cross section at the 13 TeV LHC. JHEP 10 (2016) 053, arXiv:1605.01733 [hep-ph].
  * [52] M. Bonvini, A. S. Papanastasiou, and F. J. Tackmann, Resummation and matching of b-quark mass effects in $b\overline{b}H$ production. JHEP 11 (2015) 196, arXiv:1508.03288 [hep-ph].
  * [53] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, and K. E. Williams, HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron. Comput. Phys. Commun. 181 (2010) 138–167, arXiv:0811.4169 [hep-ph].
  * [54] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, and K. E. Williams, HiggsBounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron. Comput. Phys. Commun. 182 (2011) 2605–2631, arXiv:1102.1898 [hep-ph].
  * [55] P. Bechtle, O. Brein, S. Heinemeyer, O. Stål, T. Stefaniak, G. Weiglein, and K. E. Williams, $\mathsf{HiggsBounds}-4$: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC. Eur. Phys. J. C74 (2014) no. 3, 2693, arXiv:1311.0055 [hep-ph].
  * [56] P. Bechtle, S. Heinemeyer, O. Stål, T. Stefaniak, and G. Weiglein, Applying Exclusion Likelihoods from LHC Searches to Extended Higgs Sectors. Eur. Phys. J. C75 (2015) no. 9, 421, arXiv:1507.06706 [hep-ph].
  * [57] P. Bechtle, S. Heinemeyer, O. Stål, T. Stefaniak, and G. Weiglein, $HiggsSignals$: Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC. Eur. Phys. J. C74 (2014) no. 2, 2711, arXiv:1305.1933 [hep-ph].
  * [58] A. V. Bednyakov, On three-loop RGE for the Higgs sector of 2HDM. arXiv:1809.04527 [hep-ph]. [JHEP11,154(2018)].
  * [59] I. Schienbein, F. Staub, T. Steudtner, and K. Svirina, Revisiting RGEs for general gauge theories. Nucl. Phys. B939 (2019) 1–48, arXiv:1809.06797 [hep-ph].
  * [60] P. H. Chankowski, S. Pokorski, and J. Rosiek, Complete on-shell renormalization scheme for the minimal supersymmetric Higgs sector. Nucl. Phys. B423 (1994) 437–496, arXiv:hep-ph/9303309 [hep-ph].
  * [61] A. Dabelstein, Fermionic decays of neutral MSSM Higgs bosons at the one loop level. Nucl. Phys. B456 (1995) 25–56, arXiv:hep-ph/9503443 [hep-ph].
  * [62] D. M. Pierce, J. A. Bagger, K. T. Matchev, and R.-j. Zhang, Precision corrections in the minimal supersymmetric standard model. Nucl. Phys. B491 (1997) 3–67, arXiv:hep-ph/9606211 [hep-ph].
  * [63] E. Bagnaschi, F. Brümmer, W. Buchmüller, A. Voigt, and G. Weiglein, Vacuum stability and supersymmetry at high scales with two Higgs doublets. JHEP 03 (2016) 158, arXiv:1512.07761 [hep-ph].
  * [64] S. Liebler, S. Patel, and G. Weiglein, Phenomenology of on-shell Higgs production in the MSSM with complex parameters. Eur. Phys. J. C77 (2017) no. 5, 305, arXiv:1611.09308 [hep-ph].
  * [65] E. Fuchs and G. Weiglein, Breit-Wigner approximation for propagators of mixed unstable states. JHEP 09 (2017) 079, arXiv:1610.06193 [hep-ph].
  * [66] H. Bahl, Pole mass determination in presence of heavy particles. JHEP 02 (2019) 121, arXiv:1812.06452 [hep-ph].
  * [67] M. Spira, A. Djouadi, D. Graudenz, and P. M. Zerwas, Higgs boson production at the LHC. Nucl. Phys. B453 (1995) 17–82, arXiv:hep-ph/9504378 [hep-ph].
  * [68] R. Harlander and P. Kant, Higgs production and decay: Analytic results at next-to-leading order QCD. JHEP 12 (2005) 015, arXiv:hep-ph/0509189 [hep-ph].
  * [69] R. V. Harlander and W. B. Kilgore, Next-to-next-to-leading order Higgs production at hadron colliders. Phys. Rev. Lett. 88 (2002) 201801, arXiv:hep-ph/0201206 [hep-ph].
  * [70] C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD. Nucl. Phys. B646 (2002) 220–256, arXiv:hep-ph/0207004 [hep-ph].
  * [71] V. Ravindran, J. Smith, and W. L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions. Nucl. Phys. B665 (2003) 325–366, arXiv:hep-ph/0302135 [hep-ph].
  * [72] R. V. Harlander and W. B. Kilgore, Production of a pseudoscalar Higgs boson at hadron colliders at next-to-next-to leading order. JHEP 10 (2002) 017, arXiv:hep-ph/0208096 [hep-ph].
  * [73] C. Anastasiou and K. Melnikov, Pseudoscalar Higgs boson production at hadron colliders in NNLO QCD. Phys. Rev. D67 (2003) 037501, arXiv:hep-ph/0208115 [hep-ph].
  * [74] C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog, and B. Mistlberger, Higgs Boson Gluon Fusion Production Beyond Threshold in N${}^{3}LO$ QCD. JHEP 03 (2015) 091, arXiv:1411.3584 [hep-ph].
  * [75] C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, F. Herzog, and B. Mistlberger, Soft expansion of double-real-virtual corrections to Higgs production at N3LO. JHEP 08 (2015) 051, arXiv:1505.04110 [hep-ph].
  * [76] C. Anastasiou, C. Duhr, F. Dulat, E. Furlan, T. Gehrmann, F. Herzog, A. Lazopoulos, and B. Mistlberger, High precision determination of the gluon fusion Higgs boson cross-section at the LHC. JHEP 05 (2016) 058, arXiv:1602.00695 [hep-ph].
  * [77] LHC Higgs Cross Section Working Group Collaboration, D. de Florian et al., Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector. arXiv:1610.07922 [hep-ph].
  * [78] B. Mistlberger, Higgs Boson Production at Hadron Colliders at N3LO in QCD. JHEP 05 (2018) 028, arXiv:1802.00833 [hep-ph].
  * [79] U. Aglietti, R. Bonciani, G. Degrassi, and A. Vicini, Two loop light fermion contribution to Higgs production and decays. Phys. Lett. B595 (2004) 432–441, arXiv:hep-ph/0404071 [hep-ph].
  * [80] R. Bonciani, G. Degrassi, and A. Vicini, On the Generalized Harmonic Polylogarithms of One Complex Variable. Comput. Phys. Commun. 182 (2011) 1253–1264, arXiv:1007.1891 [hep-ph].
  * [81] J. Butterworth et al., PDF4LHC recommendations for LHC Run II. J. Phys. G43 (2016) 023001, arXiv:1510.03865 [hep-ph].
  * [82] R. Harlander, M. Krämer, and M. Schumacher, Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach. arXiv:1112.3478 [hep-ph].
  * [83] R. V. Harlander and W. B. Kilgore, Higgs boson production in bottom quark fusion at next-to-next-to leading order. Phys. Rev. D68 (2003) 013001, arXiv:hep-ph/0304035 [hep-ph].
  * [84] S. Dittmaier, M. Krämer, and M. Spira, Higgs radiation off bottom quarks at the Tevatron and the CERN LHC. Phys. Rev. D70 (2004) 074010, arXiv:hep-ph/0309204 [hep-ph].
  * [85] S. Dawson, C. B. Jackson, L. Reina, and D. Wackeroth, Exclusive Higgs boson production with bottom quarks at hadron colliders. Phys. Rev. D69 (2004) 074027, arXiv:hep-ph/0311067 [hep-ph].
  * [86] E. Bagnaschi, R. V. Harlander, S. Liebler, H. Mantler, P. Slavich, and A. Vicini, Towards precise predictions for Higgs-boson production in the MSSM. JHEP 06 (2014) 167, arXiv:1404.0327 [hep-ph].
  * [87] E. L. Berger, T. Han, J. Jiang, and T. Plehn, Associated production of a top quark and a charged Higgs boson. Phys. Rev. D71 (2005) 115012, arXiv:hep-ph/0312286 [hep-ph].
  * [88] S. Dittmaier, M. Krämer, M. Spira, and M. Walser, Charged-Higgs-boson production at the LHC: NLO supersymmetric QCD corrections. Phys. Rev. D83 (2011) 055005, arXiv:0906.2648 [hep-ph].
  * [89] M. Flechl, R. Klees, M. Krämer, M. Spira, and M. Ubiali, Improved cross-section predictions for heavy charged Higgs boson production at the LHC. Phys. Rev. D91 (2015) no. 7, 075015, arXiv:1409.5615 [hep-ph].
  * [90] C. Degrande, M. Ubiali, M. Wiesemann, and M. Zaro, Heavy charged Higgs boson production at the LHC. JHEP 10 (2015) 145, arXiv:1507.02549 [hep-ph].
  * [91] C. Degrande, R. Frederix, V. Hirschi, M. Ubiali, M. Wiesemann, and M. Zaro, Accurate predictions for charged Higgs production: Closing the $m_{H^{\pm}}\sim m_{t}$ window. Phys. Lett. B772 (2017) 87–92, arXiv:1607.05291 [hep-ph].
  * [92] CMS Collaboration, Search for additional neutral Higgs bosons decaying to a pair of tau leptons in $pp$ collisions at $\sqrt{s}$ = 7 and 8 TeV. CMS-PAS-HIG-14-029 (2015) .
  * [93] ATLAS Collaboration, G. Aad et al., Search for an additional, heavy Higgs boson in the $H\rightarrow ZZ$ decay channel at $\sqrt{s}=8\;\text{ TeV }$ in $pp$ collision data with the ATLAS detector. Eur. Phys. J. C76 (2016) no. 1, 45, arXiv:1507.05930 [hep-ex].
  * [94] ATLAS Collaboration, M. Aaboud et al., Search for heavy ZZ resonances in the $\ell^{+}\ell^{-}\ell^{+}\ell^{-}$ and $\ell^{+}\ell^{-}\nu\bar{\nu}$ final states using proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector. Eur. Phys. J. C78 (2018) no. 4, 293, arXiv:1712.06386 [hep-ex].
  * [95] CMS Collaboration, V. Khachatryan et al., Search for a Higgs boson in the mass range from 145 to 1000 GeV decaying to a pair of W or Z bosons. JHEP 10 (2015) 144, arXiv:1504.00936 [hep-ex].
  * [96] CMS Collaboration, A. M. Sirunyan et al., Search for a new scalar resonance decaying to a pair of Z bosons in proton-proton collisions at $\sqrt{s}=13$ TeV. JHEP 06 (2018) 127, arXiv:1804.01939 [hep-ex].
  * [97] ATLAS Collaboration, M. Aaboud et al., Search for Resonant and Nonresonant Higgs Boson Pair Production in the ${b\bar{b}\tau^{+}\tau^{-}}$ Decay Channel in $pp$ Collisions at $\sqrt{s}=13$ TeV with the ATLAS Detector. Phys. Rev. Lett. 121 (2018) no. 19, 191801, arXiv:1808.00336 [hep-ex].
  * [98] CMS Collaboration, A. M. Sirunyan et al., Search for Higgs boson pair production in events with two bottom quarks and two tau leptons in proton-proton collisions at $\sqrt{s}$ =13TeV. Phys. Lett. B778 (2018) 101–127, arXiv:1707.02909 [hep-ex].
  * [99] CMS Collaboration, A. M. Sirunyan et al., Search for resonant and nonresonant Higgs boson pair production in the $\mathrm{b}\overline{\mathrm{b}}\mathit{\ell\nu\ell\nu}$ final state in proton-proton collisions at $\sqrt{s}=13$ TeV. JHEP 01 (2018) 054, arXiv:1708.04188 [hep-ex].
  * [100] CMS Collaboration, Search for pair production of Higgs bosons in the two tau leptons and two bottom quarks final state using proton-proton collisions at $\sqrt{s}=13~{}\mathrm{TeV}$. CMS-PAS-HIG-17-002 (2017) .
  * [101] CMS Collaboration, A. M. Sirunyan et al., Combination of searches for Higgs boson pair production in proton-proton collisions at $\sqrt{s}=$ 13 TeV. arXiv:1811.09689 [hep-ex].
  * [102] CMS Collaboration, V. Khachatryan et al., Search for a charged Higgs boson in pp collisions at $\sqrt{s}=8$ TeV. JHEP 11 (2015) 018, arXiv:1508.07774 [hep-ex].
  * [103] CMS Collaboration, Search for charged Higgs bosons with the $\mathrm{H}^{\scriptscriptstyle\pm}\rightarrow\tau^{\scriptscriptstyle\pm}\nu_{\tau}$ decay channel in the fully hadronic final state at $\sqrt{s}=13~{}\mathrm{TeV}$. CMS-PAS-HIG-16-031 (2016) .
  * [104] ATLAS Collaboration, G. Aad et al., Search for charged Higgs bosons decaying via $H^{\pm}\rightarrow\tau^{\pm}\nu$ in fully hadronic final states using $pp$ collision data at $\sqrt{s}=8$ TeV with the ATLAS detector. JHEP 03 (2015) 088, arXiv:1412.6663 [hep-ex].
  * [105] ATLAS Collaboration, M. Aaboud et al., Search for charged Higgs bosons decaying via $H^{\pm}\to\tau^{\pm}\nu_{\tau}$ in the $\tau$+jets and $\tau$+lepton final states with 36 fb-1 of $pp$ collision data recorded at $\sqrt{s}=13$ TeV with the ATLAS experiment. JHEP 09 (2018) 139, arXiv:1807.07915 [hep-ex].
  * [106] ATLAS Collaboration, G. Aad et al., Search for charged Higgs bosons in the $H^{\pm}\rightarrow tb$ decay channel in $pp$ collisions at $\sqrt{s}=8$ TeV using the ATLAS detector. JHEP 03 (2016) 127, arXiv:1512.03704 [hep-ex].
  * [107] ATLAS Collaboration, M. Aaboud et al., Search for charged Higgs bosons decaying into top and bottom quarks at $\sqrt{s}$ = 13 TeV with the ATLAS detector. JHEP 11 (2018) 085, arXiv:1808.03599 [hep-ex].
  * [108] ATLAS Collaboration, Measurements of the Higgs boson production cross section via Vector Boson Fusion and associated $WH$ production in the $WW^{\ast}\to\ell\nu\ell\nu$ decay mode with the ATLAS detector at $\sqrt{s}$ = 13 TeV. ATLAS-CONF-2016-112 (2016) .
  * [109] ATLAS Collaboration, Measurement of gluon fusion and vector boson fusion Higgs boson production cross-sections in the $H\to WW^{*}\to e\nu\mu\nu$ decay channel in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector. ATLAS-CONF-2018-004 (2018) .
  * [110] ATLAS Collaboration, M. Aaboud et al., Evidence for the $H\to b\overline{b}$ decay with the ATLAS detector. JHEP 12 (2017) 024, arXiv:1708.03299 [hep-ex].
  * [111] ATLAS Collaboration, M. Aaboud et al., Measurement of the Higgs boson coupling properties in the $H\rightarrow ZZ^{*}\rightarrow 4\ell$ decay channel at $\sqrt{s}$ = 13 TeV with the ATLAS detector. JHEP 03 (2018) 095, arXiv:1712.02304 [hep-ex].
  * [112] ATLAS Collaboration, M. Aaboud et al., Evidence for the associated production of the Higgs boson and a top quark pair with the ATLAS detector. Phys. Rev. D97 (2018) no. 7, 072003, arXiv:1712.08891 [hep-ex].
  * [113] ATLAS Collaboration, M. Aaboud et al., Search for the standard model Higgs boson produced in association with top quarks and decaying into a $b\bar{b}$ pair in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector. Phys. Rev. D97 (2018) no. 7, 072016, arXiv:1712.08895 [hep-ex].
  * [114] ATLAS Collaboration, M. Aaboud et al., Measurements of Higgs boson properties in the diphoton decay channel with 36 fb-1 of $pp$ collision data at $\sqrt{s}=13$ TeV with the ATLAS detector. Phys. Rev. D98 (2018) 052005, arXiv:1802.04146 [hep-ex].
  * [115] CMS Collaboration, Measurements of properties of the Higgs boson in the diphoton decay channel with the full 2016 data set. CMS-PAS-HIG-16-040 (2017) .
  * [116] CMS Collaboration, A. M. Sirunyan et al., Measurements of properties of the Higgs boson decaying into the four-lepton final state in pp collisions at $\sqrt{s}=13$ TeV. JHEP 11 (2017) 047, arXiv:1706.09936 [hep-ex].
  * [117] CMS Collaboration, A. M. Sirunyan et al., Observation of the Higgs boson decay to a pair of $\tau$ leptons with the CMS detector. Phys. Lett. B779 (2018) 283–316, arXiv:1708.00373 [hep-ex].
  * [118] CMS Collaboration, A. M. Sirunyan et al., Inclusive search for a highly boosted Higgs boson decaying to a bottom quark-antiquark pair. Phys. Rev. Lett. 120 (2018) no. 7, 071802, arXiv:1709.05543 [hep-ex].
  * [119] CMS Collaboration, A. M. Sirunyan et al., Evidence for the Higgs boson decay to a bottom quark-antiquark pair. Phys. Lett. B780 (2018) 501–532, arXiv:1709.07497 [hep-ex].
  * [120] CMS Collaboration, A. M. Sirunyan et al., Evidence for associated production of a Higgs boson with a top quark pair in final states with electrons, muons, and hadronically decaying $\tau$ leptons at $\sqrt{s}=$ 13 TeV. JHEP 08 (2018) 066, arXiv:1803.05485 [hep-ex].
  * [121] CMS Collaboration, A. M. Sirunyan et al., Search for $\mathrm{t}\overline{\mathrm{t}}$H production in the all-jet final state in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 06 (2018) 101, arXiv:1803.06986 [hep-ex].
  * [122] CMS Collaboration, A. M. Sirunyan et al., Search for $\mathrm{t\overline{t}}$H production in the H $\rightarrow$ $\mathrm{b\overline{b}}$ decay channel with leptonic $\mathrm{t\overline{t}}$ decays in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 03 (2019) 026, arXiv:1804.03682 [hep-ex].
  * [123] CMS Collaboration, A. M. Sirunyan et al., Measurements of properties of the Higgs boson decaying to a W boson pair in pp collisions at $\sqrt{s}=$ 13 TeV. Phys. Lett. B791 (2019) 96, arXiv:1806.05246 [hep-ex].
  * [124] CMS Collaboration, A. M. Sirunyan et al., Search for the Higgs boson decaying to two muons in proton-proton collisions at $\sqrt{s}=$ 13 TeV. Phys. Rev. Lett. 122 (2019) no. 2, 021801, arXiv:1807.06325 [hep-ex].
  * [125] Particle Data Group Collaboration, C. Patrignani et al., Review of Particle Physics. Chin. Phys. C40 (2016) no. 10, 100001.
  * [126] ATLAS Collaboration, M. Aaboud et al., Search for squarks and gluinos in events with an isolated lepton, jets, and missing transverse momentum at $\sqrt{s}=13$ TeV with the ATLAS detector. Phys. Rev. D96 (2017) no. 11, 112010, arXiv:1708.08232 [hep-ex].
  * [127] ATLAS Collaboration, M. Aaboud et al., Search for squarks and gluinos in final states with jets and missing transverse momentum using 36 fb-1 of $\sqrt{s}=13$ TeV pp collision data with the ATLAS detector. Phys. Rev. D97 (2018) no. 11, 112001, arXiv:1712.02332 [hep-ex].
  * [128] CMS Collaboration, A. M. Sirunyan et al., Search for supersymmetry in multijet events with missing transverse momentum in proton-proton collisions at 13 TeV. Phys. Rev. D96 (2017) no. 3, 032003, arXiv:1704.07781 [hep-ex].
  * [129] CMS Collaboration, A. M. Sirunyan et al., Search for new phenomena with the $M_{\mathrm{T2}}$ variable in the all-hadronic final state produced in proton–proton collisions at $\sqrt{s}=13$ TeV. Eur. Phys. J. C77 (2017) no. 10, 710, arXiv:1705.04650 [hep-ex].
  * [130] CMS Collaboration, A. M. Sirunyan et al., Search for natural and split supersymmetry in proton-proton collisions at $\sqrt{s}=13$ TeV in final states with jets and missing transverse momentum. JHEP 05 (2018) 025, arXiv:1802.02110 [hep-ex].
  * [131] ATLAS Collaboration, M. Aaboud et al., Search for supersymmetry in final states with two same-sign or three leptons and jets using 36 fb-1 of $\sqrt{s}=13$ TeV $pp$ collision data with the ATLAS detector. JHEP 09 (2017) 084, arXiv:1706.03731 [hep-ex].
  * [132] G. Bhattacharyya, D. Das, M. J. Pérez, I. Saha, A. Santamaria, and O. Vives, Can measurements of 2HDM parameters provide hints for high scale supersymmetry? Phys. Rev. D97 (2018) no. 9, 095018, arXiv:1712.00791 [hep-ph].
  * [133] B. C. Allanach, A. Djouadi, J. L. Kneur, W. Porod, and P. Slavich, Precise determination of the neutral Higgs boson masses in the MSSM. JHEP 09 (2004) 044, arXiv:hep-ph/0406166 [hep-ph].
  * [134] ATLAS Collaboration, M. Aaboud et al., Search for Heavy Higgs Bosons $A/H$ Decaying to a Top Quark Pair in $pp$ Collisions at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ with the ATLAS Detector. Phys. Rev. Lett. 119 (2017) no. 19, 191803, arXiv:1707.06025 [hep-ex].
  * [135] K. J. F. Gaemers and F. Hoogeveen, Higgs Production and Decay Into Heavy Flavors With the Gluon Fusion Mechanism. Phys. Lett. 146B (1984) 347–349.
  * [136] D. Dicus, A. Stange, and S. Willenbrock, Higgs decay to top quarks at hadron colliders. Phys. Lett. B333 (1994) 126–131, arXiv:hep-ph/9404359 [hep-ph].
  * [137] S. Moretti and D. A. Ross, On the top-antitop invariant mass spectrum at the LHC from a Higgs boson signal perspective. Phys. Lett. B712 (2012) 245–249, arXiv:1203.3746 [hep-ph].
  * [138] R. Frederix and F. Maltoni, Top pair invariant mass distribution: A Window on new physics. JHEP 01 (2009) 047, arXiv:0712.2355 [hep-ph].
  * [139] B. Hespel, F. Maltoni, and E. Vryonidou, Signal background interference effects in heavy scalar production and decay to a top-anti-top pair. JHEP 10 (2016) 016, arXiv:1606.04149 [hep-ph].
  * [140] A. Djouadi, J. Ellis, A. Popov, and J. Quevillon, Interference Effects in $t{\bar{t}}$ Production at the LHC as a Window on New Physics. arXiv:1901.03417 [hep-ph].
  * [141] D. Denegri, V. Drollinger, R. Kinnunen, K. Lassila-Perini, S. Lehti, F. Moortgat, A. Nikitenko, S. Slabospitsky, and N. Stepanov, Summary of the CMS discovery potential for the MSSM SUSY Higgses. arXiv:hep-ph/0112045 [hep-ph].
  * [142] F. Moortgat, S. Abdullin, and D. Denegri, Observability of MSSM Higgs bosons via sparticle decay modes in CMS. arXiv:hep-ph/0112046 [hep-ph].
  * [143] S. Abdullin et al., Summary of the CMS potential for the Higgs boson discovery. Eur. Phys. J. C39S2 (2005) 41–61.
  * [144] E. Arganda, J. L. Diaz-Cruz, and A. Szynkman, Decays of $H^{0}/A^{0}$ in supersymmetric scenarios with heavy sfermions. Eur. Phys. J. C73 (2013) no. 4, 2384, arXiv:1211.0163 [hep-ph].
  * [145] E. Arganda, J. Lorenzo Diaz-Cruz, and A. Szynkman, Slim SUSY. Phys. Lett. B722 (2013) 100–106, arXiv:1301.0708 [hep-ph].
  * [146] N. Craig, F. D’Eramo, P. Draper, S. Thomas, and H. Zhang, The Hunt for the Rest of the Higgs Bosons. JHEP 06 (2015) 137, arXiv:1504.04630 [hep-ph].
  * [147] B. Ananthanarayan, J. Lahiri, and P. N. Pandita, Invisible decays of the heavier Higgs boson in the minimal supersymmetric standard model. Phys. Rev. D91 (2015) 115025, arXiv:1507.01747 [hep-ph].
  * [148] R. K. Barman, B. Bhattacherjee, A. Chakraborty, and A. Choudhury, Study of MSSM heavy Higgs bosons decaying into charginos and neutralinos. Phys. Rev. D94 (2016) no. 7, 075013, arXiv:1607.00676 [hep-ph].
  * [149] R. K. Barman, B. Bhattacherjee, A. Choudhury, D. Chowdhury, J. Lahiri, and S. Ray, Current status of MSSM Higgs sector with LHC 13 TeV data. arXiv:1608.02573 [hep-ph].
  * [150] E. Arganda, J. L. Díaz-Cruz, N. Mileo, R. A. Morales, and A. Szynkman, Search strategies for pair production of heavy Higgs bosons decaying invisibly at the LHC. Nucl. Phys. B929 (2018) 171–192, arXiv:1710.07254 [hep-ph].
  * [151] S. Profumo, T. Stefaniak, and L. Stephenson Haskins, The Not-So-Well Tempered Neutralino. Phys. Rev. D96 (2017) no. 5, 055018, arXiv:1706.08537 [hep-ph].
  * [152] A. Aboubrahim and P. Nath, Naturalness, the hyperbolic branch, and prospects for the observation of charged Higgs bosons at high luminosity LHC and 27 TeV LHC. Phys. Rev. D98 (2018) no. 9, 095024, arXiv:1810.12868 [hep-ph].
  * [153] S. Gori, Z. Liu, and B. Shakya, Heavy Higgs as a Portal to the Supersymmetric Electroweak Sector. arXiv:1811.11918 [hep-ph].
  * [154] CMS Collaboration, A. M. Sirunyan et al., Search for electroweak production of charginos and neutralinos in multilepton final states in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 03 (2018) 166, arXiv:1709.05406 [hep-ex].
  * [155] CMS Collaboration, A. M. Sirunyan et al., Searches for pair production of charginos and top squarks in final states with two oppositely charged leptons in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 11 (2018) 079, arXiv:1807.07799 [hep-ex].
  * [156] CMS Collaboration, A. M. Sirunyan et al., Combined search for electroweak production of charginos and neutralinos in proton-proton collisions at $\sqrt{s}=$ 13 TeV. JHEP 03 (2018) 160, arXiv:1801.03957 [hep-ex].
  * [157] ATLAS Collaboration, M. Aaboud et al., Search for chargino-neutralino production using recursive jigsaw reconstruction in final states with two or three charged leptons in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector. Phys. Rev. D98 (2018) no. 9, 092012, arXiv:1806.02293 [hep-ex].
  * [158] ATLAS Collaboration, M. Aaboud et al., Search for supersymmetry in events with four or more leptons in $\sqrt{s}=13$ TeV $pp$ collisions with ATLAS. Phys. Rev. D98 (2018) no. 3, 032009, arXiv:1804.03602 [hep-ex].
  * [159] ATLAS Collaboration, M. Aaboud et al., Search for electroweak production of supersymmetric particles in final states with two or three leptons at $\sqrt{s}=13\,$TeV with the ATLAS detector. Eur. Phys. J. C78 (2018) no. 12, 995, arXiv:1803.02762 [hep-ex].
  * [160] CMS Collaboration, A. M. Sirunyan et al., Search for new physics in events with two soft oppositely charged leptons and missing transverse momentum in proton-proton collisions at $\sqrt{s}=$ 13 TeV. Phys. Lett. B782 (2018) 440–467, arXiv:1801.01846 [hep-ex].
  * [161] ATLAS Collaboration, M. Aaboud et al., Search for electroweak production of supersymmetric states in scenarios with compressed mass spectra at $\sqrt{s}=13$ TeV with the ATLAS detector. Phys. Rev. D97 (2018) no. 5, 052010, arXiv:1712.08119 [hep-ex].
  * [162] J. Debove, B. Fuks, and M. Klasen, Transverse-momentum resummation for gaugino-pair production at hadron colliders. Phys. Lett. B688 (2010) 208–211, arXiv:0907.1105 [hep-ph].
  * [163] J. Debove, B. Fuks, and M. Klasen, Threshold resummation for gaugino pair production at hadron colliders. Nucl. Phys. B842 (2011) 51–85, arXiv:1005.2909 [hep-ph].
  * [164] J. Debove, B. Fuks, and M. Klasen, Joint Resummation for Gaugino Pair Production at Hadron Colliders. Nucl. Phys. B849 (2011) 64–79, arXiv:1102.4422 [hep-ph].
  * [165] B. Fuks, M. Klasen, D. R. Lamprea, and M. Rothering, Gaugino production in proton-proton collisions at a center-of-mass energy of 8 TeV. JHEP 10 (2012) 081, arXiv:1207.2159 [hep-ph].
  * [166] B. Fuks, M. Klasen, D. R. Lamprea, and M. Rothering, Precision predictions for electroweak superpartner production at hadron colliders with Resummino. Eur. Phys. J. C73 (2013) 2480, arXiv:1304.0790 [hep-ph].
  * [167] S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C. P. Yuan, New parton distribution functions from a global analysis of quantum chromodynamics. Phys. Rev. D93 (2016) no. 3, 033006, arXiv:1506.07443 [hep-ph].