Additional Higgs Bosons near 95 and 650 GeV in the NMSSM

Ulrich Ellwangera and Cyril Hugonieb
a IJCLab, CNRS/IN2P3, University Paris-Saclay, 91405 Orsay, France
<EMAIL_ADDRESS>
b LUPM, UMR 5299, CNRS/IN2P3, Université de Montpellier, 34095 Montpellier,
France
<EMAIL_ADDRESS>
Hints for an additional Higgs boson with a mass of about 95 GeV originate from
LEP and searches in the diphoton channel by CMS and ATLAS. A search for
resonant production of SM plus BSM Higgs bosons in the diphoton plus
$b\bar{b}$ channel by CMS showed some excess for a 650 GeV resonance decaying
into the SM Higgs plus a 95 GeV Higgs boson. We investigate whether these
phenomena can be interpreted simultaneously within the NMSSM subject to the
latest constraints on couplings of the SM Higgs boson, on extra Higgs bosons
from the LHC, and on dark matter direct detection cross sections.

##  1 Introduction

Various well-motivated extensions of the Standard Model (SM) predict
additional Higgs bosons, and the search for them is one of the tasks of
earlier, present and future experiments in particle physics. These have
provided some hints at where such additional Higgs bosons may exist.

The combination of searches for the SM Higgs boson at the ALEPH, DELPHI, L3
and OPAL experiments at LEP [1] showed some mild excess of events in the
$Z^{*}\to Z+b\bar{b}$ channel in the mass region of $95-100$ GeV.

Searches for Beyond-the-Standard Model (BSM) Higgs bosons at the LHC in the
diphoton channel were performed by CMS and ATLAS. A search at run 1 by CMS
showed a $\sim 2\,\sigma$ excess at 97 GeV [2], which was confirmed by CMS
later in [3] and in [4] for a mass hypothesis of 95.4 GeV. A somewhat less
sensitive search in the diphoton channel by ATLAS in [5] lead to an upper
limit on the fiducial cross section which did not contradict the possible
excess observed by CMS, a recent analysis by ATLAS in the diphoton channel in
[6] showed a mild excess of $1.5\,\sigma$ at 95 GeV. A search for BSM Higgs
bosons in the di-tau channel by CMS in [7] showed an excess of $2.6\,\sigma$
(local) for a mass of $95-100$ GeV. Finally a search for resonant production
via a heavy boson $X$ of a SM Higgs boson together with a BSM Higgs boson $Y$
in the diphoton plus $b\bar{b}$ channel by CMS in [8] showed an excess of
$3.5-3.8\,\sigma$ (local) for $M_{X}\sim 650$ GeV, $M_{Y}\sim 90-100$ GeV.

The hints for an additional Higgs boson in the mass range of $95-98$ GeV have
already lead to numerous explanations within Two-Higgs-Doublet models (2HDM),
2HDMs extended by singlets, radions, pseudo-Goldstone bosons, the Next-to-
Minimal supersymmetric extension of the SM (NMSSM) and the $\mu\nu$NMSSM [9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].

The $\sim 2\,\sigma$ excess at LEP was quantified in [10]. Let us denote the
extra (lighter) Higgs boson by $H_{1}$, with a reduced coupling to vector
bosons $W^{\pm},Z$ (relative to the coupling of a SM-like Higgs boson of
corresponding mass) given by $C_{V}(1)$. Then the authors in [10] define (see
also [31])

$\mu^{LEP}_{bb}\equiv C_{V}(1)^{2}\times BR(H_{1}\to
b\bar{b})/BR(H_{SM}^{95}\to b\bar{b})=0.117\pm 0.057$ (1.1)

where $H_{SM}^{95}$ denotes a SM-like Higgs boson with a mass of 95 GeV.

The possible values of $C_{V}(1)$ are strongly constrained by measurements of
CMS [46] and ATLAS [47] of the couplings of the SM Higgs boson to $W^{\pm},Z$
denoted by $\kappa_{W,Z}\equiv C_{V}(2)$ here. Combining the measurements of
CMS and ATLAS one finds $\kappa_{W,Z}>0.966$ at the $2\,\sigma$ level. In BSM
models with an arbitrary number of Higgs doublets and singlets one obtains the
sum rule $\sum_{i}C_{V}(i)^{2}=1$, hence

$C_{V}(1)^{2}<0.067$ (1.2)

at the $2\,\sigma$ level. The $BR(H_{1}\to b\bar{b})$ may be somewhat larger
than the corresponding branching fraction of the SM Higgs boson since the
kinematic suppression of decays of $H_{1}$ into vector bosons is somewhat
stronger; still it is impossible to obtain the central value for
$\mu^{LEP}_{bb}$ from (1.1), but $\mu^{LEP}_{bb}$ within the $2\,\sigma$ range
of (1.1) is well possible.

The best fits for a diphoton signal of $H_{1}$ in CMS and ATLAS were combined
in [41]. The authors in [41] obtain

$\mu_{\gamma\gamma}^{LHC}=\frac{\sigma(gg\to
H_{1}\to\gamma\gamma)}{\sigma(gg\to
H_{SM}^{95}\to\gamma\gamma)}=0.27^{+0.10}_{-0.09}\;.$ (1.3)

Again, $H_{SM}^{95}$ denotes a SM-like Higgs boson with a mass of 95 GeV.

The best fit for the excess in the di-tau channel at 95 GeV observed by CMS in
[7] corresponds to a cross section times branching fraction

$\sigma(gg\to H_{1}\to\tau\tau)=7.8^{+3.9}_{-3.1}\text{pb}\;.$ (1.4)

For $H_{SM}^{95}$ we obtain

$\mu_{\tau\tau}^{LHC}=\frac{\sigma(gg\to H_{1}\to\tau\tau)}{\sigma(gg\to
H_{SM}^{95}\to\tau\tau)}=1.38^{+0,69}_{-0.55}\;.$ (1.5)

Finally the best fit for the excess in the search for
$X\to(H_{SM}\to\gamma\gamma)+(H_{1}\to b\bar{b})$ for $M_{X}\simeq 650$ GeV
and $M_{H_{1}}=90-100$ GeV observed by CMS in [8] is a cross section times
branching fraction given by

$\sigma_{bb\gamma\gamma}=\sigma(gg\to X_{650}\to(H_{1}\to
b\bar{b})+(H_{SM}\to\gamma\gamma))=0.35^{+0.17}_{-0.13}\,\text{fb}\;.$ (1.6)

In fact, a search for $X\to(H_{SM}\to\tau\tau)+(H_{1}\to b\bar{b})$ has been
carried out by CMS in [48], without an excess for $M_{H_{1}}=90-100$ GeV and
$M_{X}=600$ GeV or $M_{X}=700$ GeV. Instead, an upper 95% CL limit of $\sim 3$
fb was obtained for this process for these choices of masses. For $H_{SM}$,
the $BR(H_{SM}\to\tau\tau)$ is about 30 times larger than the
$BR(H_{SM}\to\gamma\gamma)$. Accordingly, assuming $3$ fb as upper limit on
$X_{650}\to(H_{SM}\to\tau\tau)+(H_{1}\to b\bar{b})$ implies an upper 95% CL
limit of $\sim 0.1$ fb on $X_{650}\to(H_{SM}\to\gamma\gamma)+(H_{1}\to
b\bar{b})$ which is barely (but still) compatible with the lower $2\,\sigma$
boundary of $0.09$ fb of the fit in eq.(1.6). (The 650 GeV excess in [8] had
already been discussed in connection with the 95 GeV excesses in [37] and
[39].)

The aim of the present paper is to verify in how far the previous excesses can
be described simultaneously within the NMSSM [49, 50] subject to the most
recent constraints from the LHC, notably the recent measurements of Higgs
couplings by CMS [46] and ATLAS [47], the upper limit on the dark matter relic
density (allowing for additional contributions beyond the lightest
supersymmetric particle) and searches for direct detection of dark matter [51,
52, 53, 54, 55, 56]. To this end we employ the public codes NMSSMTools-6.0.1
[57, 58, 59] and MicrOMEGAs [60]. Similar studies of excesses within the NMSSM
have been performed before in [9, 10, 14, 16, 18, 24, 21, 26, 29, 35] without,
however, the most recent constraints from the LHC and, notably, without
considering the possible excess in
$X_{650}\to(H_{SM}\to\gamma\gamma)+(H_{1}\to b\bar{b})$.

In the next Section we summarize the relevant features of the NMSSM, and the
constraints which we apply to our scan of the parameter space of the NMSSM. In
Section 3 we show the results of scans of the NMSSM parameter space in the
form of figures showing correlations among masses and production cross
sections relevant for searches for additional heavy resonances in various
channels. We conclude in Section 4.

##  2 Applied constraints to the NMSSM

The Higgs sector of the NMSSM consists in two SU(2) doublets and a complex
SU(2) singlet. In the CP-conserving NMSSM, the physical scalars can be
decomposed into three neutral CP-even states, two neutral CP-odd states and
one complex charged state. One of the three neutral CP-even states has to
correspond to the SM-like Higgs boson. A priori the masses and couplings of
the remaining states can assume a large range of values, depending on the five
NMSSM-specific parameters $\lambda$, $\kappa$, $A_{\lambda}$, $A_{\kappa}$,
$\mu_{\rm eff}$ as well as on $\tan\beta$ [49, 50].

In general, the three neutral CP-even states as well as the two neutral CP-odd
states are mixtures of SU(2) doublets and a SU(2) singlet; thereby all scalars
obtain couplings to SM fermions and gauge bosons (originally reserved to the
SU(2) doublets). Still, in most of the parameter space one can denote each of
the three CP-even scalars $H_{1}$, $H_{2}$ and $H_{3}$ (ordered in mass) as
either mostly singlet-like, or mostly SM-like, or mostly MSSM-like. (Pure
singlet-like, SM-like or MSSM-like states represent the so-called Higgs
basis.)

The mostly singlet-like state is a candidate for an extra BSM Higgs boson
$H_{1}$ near 95 GeV [9, 10, 14, 16, 18, 24, 21, 26, 29, 35]. However, as
stated in the Introduction, the recent combinations of CMS [46] and ATLAS [47]
of the couplings of the SM Higgs boson in the $\kappa$ framework limit the
couplings of the singlet-like state. Consequently, its remaining allowed
production cross sections at LEP and the LHC contradict some of the scenarios
proposed earlier.

The notion MSSM-like refers to a nearly degenerate SU(2) doublet (if much
heavier than the SM-like Higgs boson) consisting in a neutral CP-even, a
neutral CP-odd and a charged complex state. The CP-even state $H_{3}$ is a
candidate for a heavy resonance $X$ near $650$ GeV generating the excess in
$X\to(H_{SM}\to\gamma\gamma)+(H_{1}\to b\bar{b})$ observed by CMS [8].
Expressions for triple Higgs couplings in the NMSSM have been given in [62];
for the triple Higgs coupling relevant here (recall that $H_{SM}=H_{2}$) one
finds at tree level

$-H_{1}H_{2}H_{3}\left(\sqrt{2}\kappa\mu_{\rm
eff}+\frac{\lambda}{\sqrt{2}}A_{\lambda}\right)+\dots\;,$ (2.1)

where the dots denote relatively small corrections originating from the
rotation from the Higgs basis to the physical basis. The production of
$X=H_{3}$ at the LHC can well take place via gluon fusion. We recall, however,
that the production cross section times branching fraction for
$X\to(H_{SM}\to\gamma\gamma)+(H_{1}\to b\bar{b})$ is limited to $\sim 0.1$ fb
by upper limits on $X\to(H_{SM}\to\tau\tau)+(H_{1}\to b\bar{b})$ from CMS in
[48].

The scan of the general NMSSM parameter space is performed with help of the
codes NMSSMTools-6.0.1 [57, 58, 59] and MicrOMEGAs [60]. We impose constraints
from B-physics, from properties of the SM-like Higgs boson (a mass within
$125.2\pm 3$ GeV allowing for theoretical uncertainties), couplings in the
$\kappa$-framework satisfying combined limits of CMS [46] and ATLAS [47],
constraints from searches for BSM Higgs bosons by ATLAS and CMS as implemented
in NMSSMTools-6.0.1, and constraints from the absence of a Landau singularity
for the Yukawa couplings below the GUT scale. It confines values of the NMSSM-
specific coupling $\lambda$ to $\lambda\;\raise
1.29167pt\hbox{$<$\kern-7.5pt\raise-4.73611pt\hbox{$\sim$}}\;0.7$. Constraints
from the anomalous magnetic moment of the muon as in [61] are left aside as
these concern the smuon/gaugino sector which is irrelevant here. (Constraints
from the anomalous magnetic moment of the muon can always be satisfied by
choosing the soft supersymmetry breaking trilinear coupling $A_{\mu}$ large
enough.) The constraint on $M_{W}$ as applied in [61] is not used since it
relies on a single experimental result which differs significantly from many
others. All soft supersymmetry breaking terms are taken below 3 TeV.
Constraints on the sparticle spectrum are taken into account using the code
SModels-2.2.0 [63, 64, 65, 66].

We require that the lightest supersymmetric particle (LSP) is neutral (the
lightest neutralino), since it is stable and contributes necessarily to the
relic density of the universe. We do not require that it accounts for all of
the observed dark matter relic density as there may exist additional
contributions from physics far above the weak scale. However, the stable
lightest neutralino unavoidably contributes to dark matter direct detection
experiments, and must satisfy corresponding constraints which are imposed
since the properties of the lightest neutralino (its mass and its annihilation
rate typically via the CP-odd scalar $A_{1}$ in the s-channel) depend on
parameters which play also a role in the NMSSM Higgs sector. We find that the
LSP is a higgsino-singlino mixture, with a relic density $\Omega h^{2}\approx
10^{-3}$.

For the calculation of the cross sections $ggF\to H/A$ we start with the BSM
Higgs production cross sections at $\sqrt{s}=13$ TeV from the twiki web page
[67] (update in CERN Report 4 2016). These are multiplied by the reduced
couplings squared of $H/A$. Thereby we capture most of the radiative QCD
corrections in the form of K-factors; the remaining theoretical uncertainties
are at most of ${\cal O}(10\%)$.

Let us discuss in how far the excesses $\mu^{LEP}_{bb}$ in (1.1),
$\mu_{\gamma\gamma}^{LHC}$ in (1.3), $\mu_{\tau\tau}^{LHC}$ in (1.5) and
$\sigma_{bb\gamma\gamma}$ in (1.6) can be described simultaneously. First,
once the contribution of ATLAS to $\mu_{\gamma\gamma}^{LHC}$ is combined with
the corresponding contributions from CMS as in [41], a suppression of the
$BR(H_{1}\to b\bar{b})$ in order to enhance the $BR(H_{1}\to\gamma\gamma)$ (as
argued earlier in [31]) is no longer necessary; the excesses $\mu^{LEP}_{bb}$
and $\mu_{\gamma\gamma}^{LHC}$ can well be described simultaneously at the
$2\,\sigma$ level in the NMSSM with its type II Yukawa structure. Also the
excess in $\sigma_{bb\gamma\gamma}$ in (1.6) can be fitted simultaneously at
the $2\,\sigma$ level.

Hence, for the purpose of this paper we require that the singlet-like scalar
has a mass in the range $95.4\pm 3$ GeV (allowing for a theoretical
uncertainty of 3 GeV), $\mu^{LEP}_{bb}$ in the $2\,\sigma$ range of (1.1), and
$\mu_{\gamma\gamma}^{LHC}$ in the $2\,\sigma$ range of (1.3). In order to
describe the excess in $\sigma_{bb\gamma\gamma}$, we require that the MSSM-
like scalar $H_{3}$ has a mass in the range $650\pm 25$ GeV (given that the
mass $M_{X}$ in [8] is given in steps of $650\pm n\times 50$ GeV), and
$\sigma_{bb\gamma\gamma}$ in the $2\,\sigma$ range of (1.6).

However, a description of the di-tau excess $\mu_{\tau\tau}^{LHC}$ in (1.5)
would require a large $BR(H_{1}\to\tau^{+}\tau^{-})$ (or a large $H_{1}$
production cross section) which is incompatible with present constraints on
the $H_{1}-H_{SM}$ mixing angle from recent measurements of CMS [46] and ATLAS
[47] of the reduced couplings $\kappa_{W,Z}$ and $\kappa_{\tau}$ of $H_{SM}$;
a combination of ATLAS and CMS implies $\kappa_{W,Z}>0.966$ and
$\kappa_{\tau}>0.842$ at the $2\,\sigma$ level. (We found that a simultaneous
fit of the diphoton and di-tau excesses – actually including $\mu^{LEP}_{bb}$
– within the $2\,\sigma$ level would have been possible for
$\kappa_{W,Z}<0.913$.) The incompatibility of the $\mu_{\gamma\gamma}^{LHC}$
and $\mu_{\tau\tau}^{LHC}$ for a type II Yukawa structure was also underlined
in [41]. Thus we will not require a description of the di-tau excess
$\mu_{\tau\tau}^{LHC}$ in the following.

Actually we find that the desired cross section in the $2\,\sigma$ range of
(1.3) (together with all other constraints) can be achieved only for
$M_{H_{3}}\;\raise
1.29167pt\hbox{$<$\kern-7.5pt\raise-4.73611pt\hbox{$\sim$}}\;637$ GeV. This
becomes visible from Fig. 1 where we show $\mu^{LEP}_{bb}$ and
$\mu_{\gamma\gamma}^{LHC}$ for viable points as function of $M_{H_{3}}$, and
Fig. 2 where we show $\sigma_{bb\gamma\gamma}$ and $\sigma_{bb\tau\tau}$ as
function of $M_{H_{3}}$. As discussed in the Introduction, both
$\sigma_{bb\gamma\gamma}$ and $\sigma_{bb\tau\tau}$ are limited from above by
constraints from the search by CMS in [48]. Thus all constraints from
eqs.(1.1), (1.3) and (1.6) can be satisfied simultaneously, for input
parameters assuming values within the ranges shown in Table 1. The coloured
dots in all figures indicate six benchmark points (BPs) BP1 (red), BP2
(green), BP3 (blue), BP4 (yellow), BP5 (violet) and BP6 (orange), whose
properties are given in the Tables 2 and 3 in the next Section.

|
---|---
Figure 1: $\mu^{LEP}_{bb}$ as function of $M_{H_{3}}$ (left), $\mu_{\gamma\gamma}^{LHC}$ as function of $M_{H_{3}}$ (right). The coloured dots here and the subsequent figures denote six benchmark points whose properties are given in the Tables 2 and 3. |
---|---
Figure 2: $\sigma_{bb\gamma\gamma}$ as function of $M_{H_{3}}$ (left), $\sigma_{bb\tau\tau}$ as function of $M_{H_{3}}$ (right). $\sigma_{bb\gamma\gamma}$ and $\sigma_{bb\tau\tau}$ are limited from above by constraints from the search by CMS in [48]. $\lambda$ | $\kappa$ | $A_{\lambda}$ | $A_{\kappa}$ | $\mu_{\rm eff}$ | $\tan\beta$
---|---|---|---|---|---
$0.635-0.689$ | $0.302-0.376$ | $403-485$ | $-620-(-406)$ | $258-291$ | $1.97-2.29$
$M_{1}$ | $M_{2}$ | $M_{3}$ | $M_{Q_{3}},M_{T},M_{B}$ | $A_{t}$ | $M_{Q_{1}},M_{U},M_{D}$
$269-3000$ | $343-2371$ | $420-3000$ | $451-3000$ | $-1394-1201$ | $589-3000$
Table 1: Range of input parameters for our scan (dimensionful parameters in
GeV).

##  3 Benchmark Planes and Points

If the scenario with additional Higgs bosons near 95 GeV and 650 GeV is
realized within the NMSSM, several additional search channels can serve to
discover or to exclude it. In this section we present the prospects for such
additional searches in the form of benchmark planes of couplings and cross
sections.

A Higgs resonance $H_{3}$ near 650 GeV can be searched for by its decays into
heavy quarks. We find that the region in the NMSSM parameter space satisfying
the constraints corresponds to relatively small values of $\tan\beta\sim 2-3$.
Then the search for the $H_{3}$ decay into $b\bar{b}$ is not very promising,
in contrast to the search for its decay into $t\bar{t}$ as performed by CMS in
[68]. In Fig. 3 left we show its coupling strength modifier $g_{Htt}$ as a
function of the heavy scalar boson mass. The width of $H_{3}$ ($\sim 6$ GeV)
is always $\sim 1\%$ of its mass which is relevant for the search in this
channel. Nearly degenerate with $H_{3}$ (about 3 GeV lighter) is a
pseudoscalar $A_{2}$, with a width of $\sim 1.5\%$ of its mass and with a very
similar coupling strength modifier $g_{Att}$ shown in Fig. 3 right. The upper
limits from [68] are $\sim.735$ on $g_{H_{3}tt}$ and $\sim.675$ on
$g_{A_{2}tt}$. It should be noted that the branching fractions of these states
into $t\bar{t}$ could be somewhat reduced by up to $\approx 10\%$ due to
decays into neutralinos/charginos depending on the parameters of this sector.
Still, given that the limits from [68] are based on an integrated luminosity
at the LHC of $35.9$ fb-1, corresponding updates may well become sensitive to
the NMSSM scenarios presented here.

|
---|---
Figure 3: Left: Coupling strength modifier $g_{H_{3}tt}$ as a function of the
heavy scalar boson mass $M_{H_{3}}$. Right: Coupling strength modifier
$g_{A_{2}tt}$ as a function of the heavy pseudo-scalar boson mass $M_{A_{2}}$.
The upper limits from [68] are $\sim.735$ on $g_{H_{3}tt}$ and $\sim.675$ on
$g_{A_{2}tt}$.

The coupling $H_{2}H_{2}H_{3}$ contributes to resonant SM Higgs pair
production on which the most recent constraints originate from ATLAS in [69,
70] and CMS in [71, 72], the latter only for heavy resonances above 800 GeV.
From the combination of final states in [69] and for $M_{H_{3}}$ near $650$
GeV, the upper limit on $\sigma\times Br(ggF\to H_{3}\to H_{SM}+H_{SM})$ is
$\sim 11$ fb. However, one finds that the coupling $H_{2}H_{2}H_{3}$ is
suppressed by $M_{Z}$ and, for the allowed regions of the parameter space of
the NMSSM, much smaller than the $H_{1}H_{2}H_{3}$ coupling in (2.1) implying
a maximal cross section of $\sim 1$ fb for resonant SM Higgs pair production
for $M_{H_{3}}$ near $650$ GeV. Actually a mild $\sim 1\,\sigma$ excess is
visible in [70] for the $b\bar{b}\gamma\gamma$ channel for $M_{H_{3}}$ near
$650$ GeV, but the required cross section for a visible excess in this channel
would be impossible to achieve within the allowed regions of the parameter
space of the NMSSM.

Relatively large cross sections of $\approx 10$ fb are found within the
allowed regions of the parameter space of the NMSSM for the process $ggF\to
H_{3}\to H_{1}+H_{1}$, with branching ratios of $H_{1}$ into $b\bar{b}$,
$\tau^{+}\tau^{-}$ and $\gamma\gamma$ $\sim 20\%$ larger than for $H_{SM}$. We
find it worthwhile to perform corresponding searches in channels with low
enough SM backgrounds; they may lead to hints for or the discovery of two BSM
Higgs bosons at a time. Corresponding cross sections times branching fractions
are shown in Figs. 4. (No upper limits exist on this process at present.)

|
---|---
|
Figure 4: Upper left: $\sigma(ggF\to H_{3}\to H_{1}H_{1}\to
b\bar{b}b\bar{b}$), upper right: $\sigma(ggF\to H_{3}\to H_{1}H_{1}\to
b\bar{b}\tau^{+}\tau^{-}$), lower left: $\sigma(ggF\to H_{3}\to H_{1}H_{1}\to
b\bar{b}\gamma\gamma$), lower right: $\sigma(ggF\to H_{3}\to
H_{1}H_{1}\to\gamma\gamma\tau^{+}\tau^{-}$), all cross sections as a function
of the heavy scalar boson mass $M_{H_{3}}$

Also the heavy pseudoscalar $A_{2}$ with its mass close to $M_{H_{3}}$ gives
rise to interesting signatures. Searches for $ggF\to A_{2}\to Z+H_{SM}$ and
for $ggF\to A_{2}\to Z+H_{1}$ have been performed by CMS in [73, 74] and by
ATLAS in [75]. For $A_{2}$ masses relevant here, upper limits on the cross
sections for $ggF\to A_{2}\to Z+(H_{SM}\to b\bar{b})$ from CMS [73] and from
ATLAS [75] are $\sim 30$ fb, upper limits on cross sections for $ggF\to
A_{2}\to(Z\to\ell\ell)+(H_{1}\to b\bar{b})$ from CMS [74] are $\sim 20$ fb. In
Figs. 5 we show, both as function of $M_{A_{2}}$, $\sigma(ggF\to A_{2}\to
Z+(H_{SM}\to b\bar{b}))$ on the left, and $\sigma(ggF\to
A_{2}\to(Z\to\ell\ell)+(H_{1}\to b\bar{b}))$ on the right. Both cross sections
are factors of 20 (for $Z+H_{SM}$) or 5 (for $Z+H_{1}$) below the limits from
ATLAS/CMS, but since the limits from CMS are based on $35.9$ fb-1 of
integrated luminosity the cross section from Fig. 5 are not out of reach in
the future. Note that once one multiplies the cross sections into $H_{1}$ on
the right hand side by $1/0.0673$ in order to compensate the
BR$(Z\to\ell\ell)$, one finds that these are by a factor $\sim 30-40$ larger
than the cross sections into $H_{SM}$ on the left and side.

|
---|---
Figure 5: Left: $\sigma(ggF\to A_{2}\to Z+(H_{SM}\to b\bar{b}))$, right:
$\sigma(ggF\to A_{2}\to(Z\to\ell\ell)+(H_{1}\to b\bar{b}))$, both as function
of $M_{A_{2}}$.

We end this Section with Tables giving the details of some benchmark points
satisfying all of the imposed constraints. The benchmark points are chosen
such that they cover various regions visible in Figs.$\ 1-5$. NMSSM specific
input parameters and $M_{H_{3}}$ are given in Table 2.

| $\lambda$ | $\kappa$ | $A_{\lambda}$ | $A_{\kappa}$ | $\mu_{\rm eff}$ | $\tan\beta$ | $M_{H_{3}}$ | colour
---|---|---|---|---|---|---|---|---
BP1 | 0.678 | 0.333 | 466 | $-449$ | 262 | 2.27 | 628 | red
BP2 | 0.658 | 0.359 | 438 | $-539$ | 273 | 2.20 | 636 | green
BP3 | 0.648 | 0.363 | 419 | $-590$ | 285 | 2.04 | 630 | blue
BP4 | 0.663 | 0.348 | 448 | $-514$ | 273 | 2.18 | 632 | yellow
BP5 | 0.656 | 0.349 | 432 | $-531$ | 272 | 2.15 | 628 | violet
BP8 | 0.665 | 0.343 | 443 | $-515$ | 276 | 2.11 | 626 | orange
Table 2: NMSSM specific input parameters and $M_{H_{3}}$ for six benchmark
points.

In Table 3 we show the corresponding (reduced) cross sections as defined in
(1.1), (1.3) and (1.6), reduced couplings of $H_{3}$ and $A_{2}$ to top
quarks, as well as cross sections times branching fractions for additional
processes involving $H_{3}$ or $A_{2}$. The ratio of the cross sections
$\sigma^{A_{2}}_{ZH_{1}}$ to $\sigma^{A_{2}}_{ZH_{SM}}$ shows more clearly the
factor $\sim 30-40$ in favour of $\sigma^{A_{2}}_{ZH_{1}}$.

| BP1 | BP2 | BP3 | BP4 | BP5 | BP6
---|---|---|---|---|---|---
( $\mu^{LEP}_{bb}$: | $1.86\times 10^{-2}$ | $1.63\times 10^{-2}$ | $1.27\times 10^{-2}$ | $1.59\times 10^{-2}$ | $1.69\times 10^{-2}$ | $1.43\times 10^{-2}$
$\mu^{LHC}_{\gamma\gamma}$: | $9.37\times 10^{-2}$ | $9.17\times 10^{-2}$ | $9.04\times 10^{-2}$ | $9.04\times 10^{-2}$ | $1.17\times 10^{-1}$ | $9.08\times 10^{-2}$
$\sigma_{bb\gamma\gamma}$: | $9.01\times 10^{-2}$ | $9.01\times 10^{-2}$ | $9.01\times 10^{-2}$ | $9.01\times 10^{-2}$ | $9.01\times 10^{-2}$ | $9.56\times 10^{-2}$
$g_{H_{3}tt}$: | $-0.442$ | $-0.458$ | $-0.497$ | $-0.462$ | $-0.469$ | $-0.480$
$g_{A_{2}tt}$: | $0.439$ | $0.453$ | $0.487$ | $0.457$ | $0.462$ | $0.472$
[ $\sigma^{H_{1}H_{SM}}_{bb\tau\tau}$: | $2.76$ | $2.64$ | $2.55$ | $2.75$ | $2.70$ | $2.73$
[ $\sigma^{H_{1}H_{1}}_{bbbb}$: | $7.82$ | $6.56$ | $6.11$ | 6.88 | 7.08 | 7.44
[ $\sigma^{A_{2}}_{ZH_{SM}}$: | $1.37$ | $1.42$ | $1.70$ | $1.45$ | $1.67$ | $1.56$
[ $\sigma^{A_{2}}_{ZH_{1}}$: | $56.2$ | $52.6$ | $50.1$ | 53.5 | 53.1 | 54.4
Table 3: $\mu^{LEP}_{bb}$, $\mu^{LHC}_{\gamma\gamma}$ and
$\sigma_{bb\gamma\gamma}$ from Section 1, reduced couplings to $tt$ and
additional cross sections times branching fractions for processes for the six
benchmark points.
$\sigma^{H_{1}H_{SM}}_{bb\tau\tau}$ denotes the cross section for $ggF\to
H_{3}\to(H_{1}\to b\bar{b})+(H_{SM}\to\tau\tau)$,
$\sigma^{H_{1}H_{1}}_{bbbb}$ the cross section for $ggF\to H_{3}\to(H_{1}\to
b\bar{b})+(H_{1}\to b\bar{b})$,
$\sigma^{A_{2}}_{ZH_{SM}}$ the cross section for $ggF\to A_{2}\to Z+(H_{SM}\to
b\bar{b})$, and
$\sigma^{A_{2}}_{ZH_{1}}$ the cross section for $ggF\to A_{2}\to Z+(H_{1}\to
b\bar{b})$. All cross sections are given in fb.

##  4 Summary and Conclusions

In the present paper we have shown which sparticle spectra in the NMSSM can
simultaneously describe an extra Higgs boson near 95 GeV, and an excess in the
resonant production of SM plus BSM Higgs bosons in the diphoton plus
$b\bar{b}$ channel by CMS in [8] for a heavy resonance of a mass near $\sim
650$ GeV. This region of the parameter space of the NMSSM is limited, amongst
others, by a search for $X\to(H_{SM}\to\tau\tau)+(H_{1}\to b\bar{b})$ by CMS
in [48] for $M_{X}=600,700$ GeV. Still, we find viable regions in the
parameter space at the $2\,\sigma$ level. Admittedly this is perhaps not the
strongest hint for new physics at present, but we find it worthwhile to
underline that this region exists even in the light of the latest results from
the LHC, notably in light of the measurements of CMS [46] and ATLAS [47] of
the couplings of the SM Higgs boson.

One interesting feature is that relatively light higgsino-like charginos with
masses below $\sim 400$ GeV can help to enhance the $BR(H_{1}\to\gamma\gamma)$
via loops to the level required by eq.(1.3), at least within the $2\,\sigma$
level. This also implies relatively light neutralinos, which is visible in the
form of $\mu_{\text{eff}}$ for the benchmark points shown.

In the NMSSM, the spectrum of additional Higgs bosons near 650 GeV is
necessarily MSSM-like, i.e. consists in nearly degenerate scalars, pseudo-
scalars and charged scalars. However, their branching fractions into standard
search channels are reduced by their decays into light Higgs bosons, higgsinos
and charginos. Searches for the $b\bar{b}$ final state are disfavoured by the
low value of $\tan\beta$, searches for the $t\bar{t}$ channel are more
promising.

Cross sections times branching fractions for the production of the MSSM-like
sector are shown in Figs.$\ 2-4$, which should help to verify or exclude the
NMSSM scenarios presented here in the future. Some of the available searches
by ATLAS and CMS already touch the parameter space of the NMSSM, and our
tables allow to estimate which future searches can be promising not only using
available data, but also after the upgrade of the LHC to High Luminosity after
a suitable rescaling. The parameters shown in Tab.$\ 1$ help to clarify which
range of NMSSM parameters correspond to these scenarios. It is remarkable that
the relevant ranges of large $\lambda$ and small $\tan\beta$ coincide with the
ones where a NMSSM-specific uplift of the SM Higgs mass at tree level helps to
explain its value well above $M_{Z}$ [49, 50].

## Acknowledgements

U.E. acknowledges motivating and helpful discussions with members of the LHC-
HXSWG3-NMSSM working group.

## References

  * [1] R. Barate et al. [LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3 and OPAL], Phys. Lett. B 565 (2003), 61-75 [arXiv:hep-ex/0306033 [hep-ex]].
  * [2] CMS Collaboration, “Search for new resonances in the diphoton final state in the mass range between 80 and 115 GeV in pp collisions at $\sqrt{s}$=8 TeV”, CMS-PAS-HIG-14-037
  * [3] A. M. Sirunyan et al. [CMS], Phys. Lett. B 793 (2019), 320-347 [arXiv:1811.08459 [hep-ex]].
  * [4] CMS Collaboration, “Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at $\sqrt{s}$=13 TeV”, CMS-PAS-HIG-20-002
  * [5] ATLAS Collaboration, “Search for resonances in the 65 to 110 GeV diphoton invariant mass range using 80 fb-1 of pp collisions collected at $\sqrt{s}$=13 TeV with the ATLAS detector”, ATLAS-CONF-2018-025
  * [6] ATLAS Collaboration, “Search for diphoton resonances in the 66 to 110 GeV mass range using 140 fb-1 of 13 TeV pp collisions collected with the ATLAS detector”, ATLAS-CONF-2023-035
  * [7] A. Tumasyan et al. [CMS], JHEP 07 (2023), 073 [arXiv:2208.02717 [hep-ex]].
  * [8] CMS Collaboration, “Search for a new resonance decaying to two scalars in the final state with two bottom quarks and two photons in proton-proton collisions at $\sqrt{s}$= 13 TeV”, CMS-PAS-HIG-21-011
  * [9] G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml and J. H. Schwarz, JHEP 01 (2013), 069 [arXiv:1210.1976 [hep-ph]].
  * [10] J. Cao, X. Guo, Y. He, P. Wu and Y. Zhang, Phys. Rev. D 95 (2017) no.11, 116001 [arXiv:1612.08522 [hep-ph]].
  * [11] P. J. Fox and N. Weiner, JHEP 08 (2018), 025 [arXiv:1710.07649 [hep-ph]].
  * [12] F. Richard, [arXiv:1712.06410 [hep-ex]].
  * [13] U. Haisch and A. Malinauskas, JHEP 03 (2018), 135 [arXiv:1712.06599 [hep-ph]].
  * [14] T. Biekötter, S. Heinemeyer and C. Muñoz, Eur. Phys. J. C 78 (2018) no.6, 504 [arXiv:1712.07475 [hep-ph]].
  * [15] D. Liu, J. Liu, C. E. M. Wagner and X. P. Wang, JHEP 06 (2018), 150 [arXiv:1805.01476 [hep-ph]].
  * [16] F. Domingo, S. Heinemeyer, S. Paßehr and G. Weiglein, Eur. Phys. J. C 78 (2018) no.11, 942 [arXiv:1807.06322 [hep-ph]].
  * [17] W. G. Hollik, S. Liebler, G. Moortgat-Pick, S. Paßehr and G. Weiglein, Eur. Phys. J. C 79 (2019) no.1, 75 [arXiv:1809.07371 [hep-ph]].
  * [18] K. Wang, F. Wang, J. Zhu and Q. Jie, Chin. Phys. C 42 (2018) no.10, 103109-103109 [arXiv:1811.04435 [hep-ph]].
  * [19] T. Biekötter, M. Chakraborti and S. Heinemeyer, Eur. Phys. J. C 80 (2020) no.1, 2 [arXiv:1903.11661 [hep-ph]].
  * [20] J. M. Cline and T. Toma, Phys. Rev. D 100 (2019) no.3, 035023 [arXiv:1906.02175 [hep-ph]].
  * [21] K. Choi, S. H. Im, K. S. Jeong and C. B. Park, Eur. Phys. J. C 79 (2019) no.11, 956 [arXiv:1906.03389 [hep-ph]].
  * [22] A. Kundu, S. Maharana and P. Mondal, Nucl. Phys. B 955 (2020), 115057
[arXiv:1907.12808 [hep-ph]].

  * [23] D. Sachdeva and S. Sadhukhan, Phys. Rev. D 101 (2020) no.5, 055045 [arXiv:1908.01668 [hep-ph]].
  * [24] J. Cao, X. Jia, Y. Yue, H. Zhou and P. Zhu, Phys. Rev. D 101 (2020) no.5, 055008 [arXiv:1908.07206 [hep-ph]].
  * [25] J. A. Aguilar-Saavedra and F. R. Joaquim, Eur. Phys. J. C 80 (2020) no.5, 403 [arXiv:2002.07697 [hep-ph]].
  * [26] W. G. Hollik, C. Li, G. Moortgat-Pick and S. Paasch, Eur. Phys. J. C 81 (2021) no.2, 141 [arXiv:2004.14852 [hep-ph]].
  * [27] A. A. Abdelalim, B. Das, S. Khalil and S. Moretti, Nucl. Phys. B 985 (2022), 116013 [arXiv:2012.04952 [hep-ph]].
  * [28] T. Biekötter and M. O. Olea-Romacho, JHEP 10 (2021), 215 [arXiv:2108.10864 [hep-ph]].
  * [29] T. Biekötter, A. Grohsjean, S. Heinemeyer, C. Schwanenberger and G. Weiglein, Eur. Phys. J. C 82 (2022) no.2, 178 [arXiv:2109.01128 [hep-ph]].
  * [30] S. Heinemeyer, C. Li, F. Lika, G. Moortgat-Pick and S. Paasch, Phys. Rev. D 106 (2022) no.7, 075003 [arXiv:2112.11958 [hep-ph]].
  * [31] T. Biekötter, S. Heinemeyer and G. Weiglein, JHEP 08 (2022), 201 [arXiv:2203.13180 [hep-ph]].
  * [32] T. Biekötter, S. Heinemeyer and G. Weiglein, Eur. Phys. J. C 83 (2023) no.5, 450 [arXiv:2204.05975 [hep-ph]].
  * [33] R. Benbrik, M. Boukidi, S. Moretti and S. Semlali, Phys. Lett. B 832 (2022), 137245 [arXiv:2204.07470 [hep-ph]].
  * [34] R. Benbrik, M. Boukidi and B. Manaut, “$W$-mass and 96 GeV excess in type-III 2HDM,” [arXiv:2204.11755 [hep-ph]].
  * [35] W. Li, J. Zhu, K. Wang, S. Ma, P. Tian and H. Qiao, “A light Higgs boson in the NMSSM confronted with the CMS di-photon and di-tau excesses,” [arXiv:2212.11739 [hep-ph]].
  * [36] G. Coloretti, A. Crivellin, S. Bhattacharya and B. Mellado, “Searching for Low-Mass Resonances Decaying into $W$ Bosons,” [arXiv:2302.07276 [hep-ph]].
  * [37] S. Banik, A. Crivellin, S. Iguro and T. Kitahara, “Asymmetric Di-Higgs Signals of the N2HDM-$U(1)$,” [arXiv:2303.11351 [hep-ph]].
  * [38] T. Biekötter, S. Heinemeyer and G. Weiglein, “The CMS di-photon excess at 95 GeV in view of the LHC Run 2 results,” [arXiv:2303.12018 [hep-ph]].
  * [39] D. Azevedo, T. Biekötter and P. M. Ferreira, “2HDM interpretations of the CMS diphoton excess at 95 GeV,” [arXiv:2305.19716 [hep-ph]].
  * [40] P. Escribano, V. M. Lozano and A. Vicente, “A Scotogenic explanation for the 95 GeV excesses,” [arXiv:2306.03735 [hep-ph]].
  * [41] T. Biekötter, S. Heinemeyer and G. Weiglein, “The 95.4 GeV di-photon excess at ATLAS and CMS,” [arXiv:2306.03889 [hep-ph]].
  * [42] A. Belyaev, R. Benbrik, M. Boukidi, M. Chakraborti, S. Moretti and S. Semlali, “Explanation of the Hints for a 95 GeV Higgs Boson within a 2-Higgs Doublet Model,” [arXiv:2306.09029 [hep-ph]].
  * [43] J. A. Aguilar-Saavedra, H. B. Câmara, F. R. Joaquim and J. F. Seabra, “Confronting the 95 GeV excesses within the UN2HDM,” [arXiv:2307.03768 [hep-ph]].
  * [44] J. Dutta, J. Lahiri, C. Li, G. Moortgat-Pick, S. F. Tabira and J. A. Ziegler, “Dark Matter Phenomenology in 2HDMS in light of the 95 GeV excess,” [arXiv:2308.05653 [hep-ph]].
  * [45] M. Maniatis and O. Nachtmann, [arXiv:2309.04869 [hep-ph]].
  * [46] A. Tumasyan et al. [CMS], Nature 607 (2022) no.7917, 60-68 [arXiv:2207.00043 [hep-ex]].
  * [47] [ATLAS], Nature 607 (2022) no.7917, 52-59 [erratum: Nature 612 (2022) no.7941, E24] [arXiv:2207.00092 [hep-ex]].
  * [48] A. Tumasyan et al. [CMS], JHEP 11 (2021), 057 [arXiv:2106.10361 [hep-ex]].
  * [49] M. Maniatis, Int. J. Mod. Phys. A 25 (2010), 3505-3602 [arXiv:0906.0777 [hep-ph]].
  * [50] U. Ellwanger, C. Hugonie and A. M. Teixeira, Phys. Rept. 496 (2010) 1
[arXiv:0910.1785 [hep-ph]].

  * [51] G. Angloher et al. [CRESST], Eur. Phys. J. C 76 (2016) no.1, 25 [arXiv:1509.01515 [astro-ph.CO]].
  * [52] P. Agnes et al. [DarkSide], Phys. Rev. Lett. 121 (2018) no.8, 081307 [arXiv:1802.06994 [astro-ph.HE]].
  * [53] E. Aprile et al. [XENON], Phys. Rev. Lett. 121 (2018) no.11, 111302 [arXiv:1805.12562 [astro-ph.CO]].
  * [54] E. Aprile et al. [XENON], Phys. Rev. Lett. 122 (2019) no.14, 141301 [arXiv:1902.03234 [astro-ph.CO]].
  * [55] C. Amole et al. [PICO], Phys. Rev. D 100 (2019) no.2, 022001 [arXiv:1902.04031 [astro-ph.CO]].
  * [56] Y. Meng et al. [PandaX-4T], Phys. Rev. Lett. 127 (2021) no.26, 261802 [arXiv:2107.13438 [hep-ex]].
  * [57] U. Ellwanger, J. F. Gunion and C. Hugonie, JHEP 02 (2005), 066 [arXiv:hep-ph/0406215 [hep-ph]].
  * [58] U. Ellwanger and C. Hugonie, Comput. Phys. Commun. 175 (2006), 290-303 [arXiv:hep-ph/0508022 [hep-ph]].
  * [59] https://www.lupm.in2p3.fr/users/nmssm/index.html
  * [60] G. Belanger, F. Boudjema, A. Pukhov and A. Semenov, Comput. Phys. Commun. 185 (2014), 960-985 [arXiv:1305.0237 [hep-ph]].
  * [61] F. Domingo, U. Ellwanger and C. Hugonie, Eur. Phys. J. C 82 (2022) no.11, 1074 [arXiv:2209.03863 [hep-ph]].
  * [62] U. Ellwanger and C. Hugonie, Eur. Phys. J. C 82 (2022) no.5, 406 [arXiv:2203.05049 [hep-ph]].
  * [63] S. Kraml, S. Kulkarni, U. Laa, A. Lessa, W. Magerl, D. Proschofsky-Spindler and W. Waltenberger, Eur. Phys. J. C 74 (2014), 2868 [arXiv:1312.4175 [hep-ph]].
  * [64] J. Dutta, S. Kraml, A. Lessa and W. Waltenberger, LHEP 1 (2018) no.1, 5-12 [arXiv:1803.02204 [hep-ph]].
  * [65] C. K. Khosa, S. Kraml, A. Lessa, P. Neuhuber and W. Waltenberger, LHEP 2020 (2020), 158 [arXiv:2005.00555 [hep-ph]].
  * [66] G. Alguero, J. Heisig, C. Khosa, S. Kraml, S. Kulkarni, A. Lessa, H. Reyes-González, W. Waltenberger and A. Wongel, “Constraining new physics with SModelS version 2,” [arXiv:2112.00769 [hep-ph]].
  * [67] https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageBSMAt13TeV
  * [68] A. M. Sirunyan et al. [CMS], JHEP 04 (2020), 171 [erratum: JHEP 03 (2022), 187] [arXiv:1908.01115 [hep-ex]].
  * [69] ATLAS Collaboration, “Combination of searches for non-resonant and resonant Higgs boson pair production in the $b\bar{b}\gamma\gamma$, $b\bar{b}\tau^{+}\tau^{-}$ and $b\bar{b}b\bar{b}$ decay channels using $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector”, ATLAS-CONF-2021-052
  * [70] G. Aad et al. [ATLAS], Phys. Rev. D 106 (2022) no.5, 052001 [arXiv:2112.11876 [hep-ex]].
  * [71] CMS Collaboration, “Search for a massive scalar resonance decaying to a ligh scalar and a Higgs boson in the four $b$ quark final state with boosted topology”, CMS-PAS-B2G-20-007
  * [72] A. Tumasyan et al. [CMS], JHEP 05 (2022), 005 [arXiv:2112.03161 [hep-ex]].
  * [73] A. M. Sirunyan et al. [CMS], Eur. Phys. J. C 79 (2019) no.7, 564 [arXiv:1903.00941 [hep-ex]].
  * [74] A. M. Sirunyan et al. [CMS], JHEP 03 (2020), 055 [arXiv:1911.03781 [hep-ex]].
  * [75] G. Aad et al. [ATLAS], JHEP 06 (2023), 016 [arXiv:2207.00230 [hep-ex]].