Explanation of the Hints for a 95 GeV Higgs Boson within a 2-Higgs Doublet
Model
A<EMAIL_ADDRESS>R<EMAIL_ADDRESS>M<EMAIL_ADDRESS>M.
<EMAIL_ADDRESS>S.
<EMAIL_ADDRESS><EMAIL_ADDRESS>
S<EMAIL_ADDRESS>
1School of Physics and Astronomy, University of Southampton, Southampton, SO17
1BJ, United Kingdom.
\+ 2Particle Physics Department, Rutherford Appleton Laboratory, Chilton,
Didcot, Oxon OX11 0QX, United Kingdom.
3Polydisciplinary Faculty, Laboratory of Fundamental and Applied Physics, Cadi
Ayyad University, Sidi Bouzid, B.P. 4162, Safi, Morocco.
4Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20
Uppsala, Sweden.

###### Abstract

We suggest an explanation for and explore the consequences of the excess
around 95 GeV in the di-photon and di-tau invariant mass distributions
recently reported by the CMS collaboration at the Large Hadron Collider (LHC),
together with the discrepancy that has long been observed at the Large
Electron-Positron (LEP) collider in the $b\bar{b}$ invariant mass.
Interestingly, the most recent findings announced by the ATLAS collaboration
do not contradict, or even support, these intriguing observations. Their
search in the di-photon final state similarly reveals an excess of events
within the same mass range, albeit with a bit lower significance, thereby
corroborating and somewhat reinforcing the observations made by CMS. We
demonstrate that the lightest CP-even Higgs boson in the general 2-Higgs
Doublet Model (2HDM) Type-III can explain simultaneously the observed excesses
at approximately 1.3 $\sigma$ C.L. while satisfying up-to-date theoretical and
experimental constraints. Moreover, the 2HDM Type-III predicts an excess in
the $pp\to t\bar{t}H_{\rm SM}$ production channel of the 125 GeV Higgs boson,
$H_{\rm SM}$. This effect is caused by a up to 12% enhancement of the $H_{\rm
SM}tt$ Yukawa coupling in comparison to that predicted by the Standard Model.
Such an effect can be tested at the High Luminosity LHC (HL-LHC), which can
either discover or exclude the scenario we suggest. This unique characteristic
of the 2HDM Type-III makes this scenario with the 95 GeV resonance very
attractive for further theoretical and experimental investigations at the
(HL-)LHC and future colliders.

##  1 Introduction

In the last ten years, a great amount of effort has been put into the precise
determination of the properties of the Higgs boson, following its discovery at
the Large Hadron Collider (LHC) in 2012 [1, 2]. Many such properties are now
established with accuracies better than 10% and most of the experimental
observations made up to date are consistent with the Standard Model (SM)
expectations. Nevertheless, current precision Higgs physics at the LHC
provides room for the possibility to go Beyond the SM (BSM) in search of
additional Higgs states besides the SM-like one, with masses ranging from a
few GeV up to the TeV scale. Many well-motivated BSM scenarios with extended
Higgs sectors, either fundamental (e.g., various Supersymmetric models [3]) or
effective ones (e.g., 2-Higgs Doublet Models (2HDMs) [4, 5]), predict the
existence of extra light and heavy Higgs bosons, thus motivating searches for
these non-standard (pseudo)scalar states at various lepton and hadron
colliders.

The 2HDM is one of the most well-studied BSM scenarios where the SM Higgs
sector is extended by one additional Higgs doublet. In the most generic
version of the 2HDM, the Yukawa couplings are non-diagonal in flavour space
since each of the two Higgs doublets couple to all the SM fermions
simultaneously. As a consequence, unwanted tree-level Flavour Changing Neutral
Currents (FCNCs) may be induced, contradicting experimental observations. To
tackle this problem, usually a $Z_{2}$ symmetry is imposed on the model that
determines in turn the coupling structure of the two Higgs doublets to the SM
fermions, so that the 2HDM can be classified into the so-called Type-I, Type-
II, lepton-specific and flipped scenarios [5]. However, there is another
possibility, i.e., the 2HDM Type-III where, instead of introducing such a
$Z_{2}$ symmetry, one allows for simultaneous couplings of the two Higgs
doublets to all SM fermions. The generic Yukawa structure resulting from such
a configuration can be constrained using various theoretical requirements of
self-consistency of the model as well as a range of experimental measurements
of the Higgs masses and couplings present in the model.

In the ongoing search for a low-mass Higgs boson, the CMS collaboration
reported in 2018 an excess in the invariant mass of di-photon events near 95
GeV [6]. In March 2023, CMS has released their latest results, confirming the
excess by employing advanced analysis techniques and utilising data collected
during the first, second and third years of Run 2, corresponding to integrated
luminosities of 36.3 fb-1, 41.5 fb-1 and 54.4 fb-1, respectively, all at a
center-of-mass energy of 13 TeV [7]. The combined data exhibited an excess
with a local significance of 2.9$\sigma$ at a mass of $m_{\gamma\gamma}=95.4$
GeV.

The ATLAS collaboration recently released their findings in this channel
derived from the full Run 2 data set [8]. Notably, their latest analysis
showcases a significantly enhanced level of sensitivity compared to their
previous study, which relied on only 80 fb-1 of data [9]. In their updated
analysis, ATLAS reveals an excess with a local significance of 1.7$\sigma$ in
the $\gamma\gamma$ channel around an invariant mass of 95 GeV, remarkably
aligning with the reported CMS observation.

Furthermore, an additional excess has recently been reported by CMS in the
search for a light neutral (pseudo)scalar boson $\phi$ in the production and
decay process $gg,~{}b\bar{b}\to\phi\to\tau\tau$[10], with a local (global)
significance of $3.1\sigma(2.7\sigma)$ for $m_{\phi}\approx 100~{}\text{GeV}$.
Considering the poor resolution of $m_{\tau\tau}$ in comparison to
$m_{\gamma\gamma}$, the two excesses observed in the two final states actually
appear to be compatible. Previously, the Large Electron Positron (LEP)
collider collaborations [11] explored the low-mass domain extensively in the
$e^{+}e^{-}\to Z\phi$ production mode, with a generic Higgs boson state $\phi$
decaying via the $\tau\tau$ and $b\overline{b}$ channels. Interestingly, an
excess has been reported in 2006 in the $e^{+}e^{-}\to Z{\phi}(\to
b\overline{b})$ mode for $m_{b\bar{b}}$ around 98 GeV [12]. Given the limited
mass resolution of the di-jet invariant mass at LEP, this anomaly may well
coincide with the aforementioned excesses seen by CMS and/or ATLAS in the
$\gamma\gamma$ and $\tau\tau$ final state. Since the excesses appear in very
similar mass regions, several studies [13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27, 28, 29] have explored the possibility of simultaneously
explaining these anomalies within BSM frameworks featuring a non-standard
Higgs state lighter than 125 GeV, while being in agreement with current
measurements of the properties of the $\approx 125$ GeV SM-like Higgs state
observed at the LHC. In the attempt to explain the excesses in the
$\gamma\gamma$ and $b\overline{b}$ channels, it was found in Refs. [30, 31]
that the 2HDM Type-III with a particular Yukawa texture can successfully
accommodate both measurements simultaneously with the lightest CP-even Higgs
boson of the model, while being consistent with all relevant theoretical and
experimental constraints. Further recent studies have shown that actually all
three aforementioned signatures can be simultaneously explained in the 2HDM
plus a real (N2HDM) [26] and complex (S2HDM) [27, 29] singlet.

In our study, we show that all three anomalies seen in the $\gamma\gamma$,
$\tau\tau$ and $b\bar{b}$ final states can also be explained within the 2HDM
Type-III of Refs. [30, 31], at approximately 1.3 $\sigma$ C.L. thereby making
the point that one does not need to go beyond the minimal 2HDM framework.
Moreover, in our study, we have found an important prediction. The parameter
space of 2HDM Type-III explaining the anomalous data, predicts an enhancement
of $H_{\rm SM}tt$ Yukawa coupling and the respective uplift of the
$gg,q\bar{q}\to t\bar{t}H_{\rm SM}$ production of the SM-like Higgs, which can
be tested in the near future to discover or exclude the scenario we suggest.

The paper is organised as follows. In section 2, we review the theoretical
framework we have chosen, i.e., the 2HDM Type-III. We describe the three
excesses observed at LEP and the LHC in section 3. In section 4, we outline
the relevant theoretical and experimental constraints considered in this
analysis. In section 5, we present our numerical set-up to scan the parameter
space of the 2HDM Type-III in order to find an explanation of the three
anomalies and how this can be achieved, including the consequences for other
Higgs processes. Finally, we conclude in section 6.

##  2 2HDM Type-III

The 2HDM includes two $SU(2)_{L}$ doublets with hypercharge $Y=1$. The most
general renormalisable $SU(2)_{L}\times U(1)_{Y}$ invariant scalar potential
is written as follows [5]:

$\displaystyle\mathcal{V}$
$\displaystyle=m_{11}^{2}\Phi_{1}^{\dagger}\Phi_{1}+m_{22}^{2}\Phi_{2}^{\dagger}\Phi_{2}-\left[m_{12}^{2}\Phi_{1}^{\dagger}\Phi_{2}+\rm{H.c.}\right]+\lambda_{1}(\Phi_{1}^{\dagger}\Phi_{1})^{2}+\lambda_{2}(\Phi_{2}^{\dagger}\Phi_{2})^{2}+\lambda_{3}(\Phi_{1}^{\dagger}\Phi_{1})(\Phi_{2}^{\dagger}\Phi_{2})~{}$
(1)
$\displaystyle+\lambda_{4}(\Phi_{1}^{\dagger}\Phi_{2})(\Phi_{2}^{\dagger}\Phi_{1})+\frac{1}{2}\left[\lambda_{5}(\Phi_{1}^{\dagger}\Phi_{2})^{2}+\rm{H.c.}\right]+\left\\{\left[\lambda_{6}(\Phi_{1}^{\dagger}\Phi_{1})+\lambda_{7}(\Phi_{2}^{\dagger}\Phi_{2})\right](\Phi_{1}^{\dagger}\Phi_{2})+\rm{H.c.}\right\\},$

where $m_{11}^{2}$, $m_{22}^{2}$, $m_{12}^{2}$ are mass squared terms and
$\lambda_{i}$ ($i=1,...,7$) are dimensionless quantities describing the
coupling of the order-4 interactions. Of all such parameters, 6 are real
($m_{11}^{2}$, $m_{22}^{2}$ and $\lambda_{i}$ with $i=1,...,4$) and 4 are a
priori complex ($m_{12}^{2}$ and $\lambda_{i}$ with $i=5,...,7$). Therefore,
in general, the model has 14 free parameters. Under appropriate manipulations,
this number can however be reduced. Following Ref. [32], to start with, one
can diagonalise the quadratic part of the potential in the
$({\Phi_{1},\Phi_{2}})$ space, removing the $m_{12}^{2}$ term, thus getting
rid of 2 parameters. Then, one can make a relative $U(1)$ transformation on
$\Phi_{1}$ or $\Phi_{2}$, making $\lambda_{5}$ real, hence down to 11
parameters. Next, by removing CP violation, the number of free parameters
reduces to 9 (this requires making one neutral Higgs state decouple from both
$VV$ ($VV=W^{+}W^{-}$ and $ZZ$) and $H^{+}H^{-}$ interactions). Furthermore,
the Yukawa matrices corresponding to the two doublets are not simultaneously
diagonalisable, which can pose a problem, as the off-diagonal elements lead to
tree-level Higgs mediated Flavour Changing Neutral Currents (FCNCs) on which
severe experimental bounds exist. The Glashow-Weinberg-Paschos (GWP) theorem
[33, 34] states that this type of FCNCs is absent if at most one Higgs
multiplet is responsible for providing mass to fermions of a given electric
charge. This GWP condition can be enforced by a discrete ${Z}_{2}$-symmetry
($\Phi_{1}\rightarrow+\Phi_{1}$ and $\Phi_{2}\rightarrow-\Phi_{2}$) on the
doublets, in which case the absence of FCNCs is natural. However, the need to
allow for a softly broken ${Z}_{2}$-symmetry (in turn re-introducing a small
$m^{2}_{12}$), as customarily done to enable Electro-Weak Symmetry Breaking
(EWSB) compliant with experimental measurements, relies on the existence of a
basis where $\lambda_{6}=\lambda_{7}$ = 0. As a consequence, altogether, one
loses 2 parameters ($\lambda_{6}$ and $\lambda_{7}$) but regains 1
($m^{2}_{12}$), thus reducing further their overall number down to 8.

Then, after EWSB has taken place, each scalar doublet acquires a Vacuum
Expectation Value (VEV) that can be parametrised as follows:

$\langle\Phi_{1}\rangle=\frac{v}{\sqrt{2}}\begin{pmatrix}0\\\
\cos\beta\end{pmatrix}\quad\quad\langle\Phi_{2}\rangle=\frac{v}{\sqrt{2}}\begin{pmatrix}0\\\
\sin\beta\end{pmatrix},$ (2)

where the angle $\beta$ determines the ratio of the two doublet VEVs, $v_{1}$
and $v_{2}$, as $\tan\beta=v_{2}/v_{1}$, and where $v=246$ GeV is a fixed
value, thereby giving a final count of 7 free parameters, which we choose to
be:

$\displaystyle
m_{h},~{}~{}m_{H},~{}~{}m_{A},~{}~{}m_{H^{\pm}},~{}~{}\sin(\beta-\alpha),~{}~{}\tan\beta,~{}~{}m^{2}_{12},$
(3)

where $\alpha$ is the mixing angle in the CP-even Higgs sector, $m_{H}$ and
$m_{h}$ denote the two CP-even Higgs masses (with $m_{h}<m_{H}$ and where
either of these can be the discovered SM-like Higgs state $H_{\rm SM}$111In
our numerical analysis, we will assume $H\equiv H_{\rm SM}$.) whereas
$m_{H^{\pm}}$ and $m_{A}$ are the masses of the charged and CP-odd Higgs
states, respectively. (In the remainder, we will use the short-hand notation
$s_{x}$ and $c_{x}$ in place of $\sin(x)$ and $\cos(x)$.)

In the Yukawa sector, the general scalar to fermions couplings are given by:

$\displaystyle-{\cal L}_{Y}$ $\displaystyle=$
$\displaystyle\bar{Q}_{L}Y^{u}_{1}U_{R}\tilde{\Phi}_{1}+\bar{Q}_{L}Y^{u}_{2}U_{R}\tilde{\Phi}_{2}+\bar{Q}_{L}Y^{d}_{1}D_{R}\Phi_{1}+\bar{Q}_{L}Y^{d}_{2}D_{R}\Phi_{2}$
(4) $\displaystyle+$
$\displaystyle\bar{L}Y^{\ell}_{1}\ell_{R}\Phi_{1}+\bar{L}Y^{\ell}_{2}\ell_{R}\Phi_{2}+{\rm
H.c.},$

where $Y^{f}_{1,2}$ are $3\times 3$ Yukawa matrices in flavour space and
$\tilde{\Phi}_{1,2}=i\sigma_{1,2}\Phi_{1,2}^{*}$, with $\sigma_{1,2}$ being
the Pauli matrices. After EWSB has taken place, one can then derive the
fermion masses from Eq. (4).

Here, however, we investigate a modified version of the described 2HDM, the
so-called Type-III, where neither a global symmetry is implemented in the
Yukawa sector nor any alignment in flavour space is enforced. We adopt instead
the Cheng-Sher ansatz [35, 36], which assumes a flavour symmetry in turn
suggesting a specific texture of the Yukawa matrices, where FCNC effects are
proportional to the geometric mean of the two fermion masses and dimensionless
parameters222We refer the readers to Ref. [37] for more details.
$\chi_{ij}^{f}$ ($\propto\sqrt{m_{i}m_{j}}/v~{}\chi_{ij}^{f}$), where
$i,j=1-3$. After EWSB, the Yukawa sector can be expressed in terms of the mass
eigenstates of the Higgs bosons, as follows:

$\displaystyle-{\cal L}^{\rm III}_{Y}$
$\displaystyle=\sum_{f=u,d,\ell}\frac{m^{f}_{j}}{v}\times\left((\xi^{f}_{h})_{ij}\bar{f}_{Li}f_{Rj}h+(\xi^{f}_{H})_{ij}\bar{f}_{Li}f_{Rj}H-i(\xi^{f}_{A})_{ij}\bar{f}_{Li}f_{Rj}A\right)$
$\displaystyle+\frac{\sqrt{2}}{v}\sum_{k=1}^{3}\bar{u}_{i}\left[\left(m^{u}_{i}(\xi^{u*}_{A})_{ki}V_{kj}P_{L}+V_{ik}(\xi^{d}_{A})_{kj}m^{d}_{j}P_{R}\right)\right]d_{j}H^{+}$
$\displaystyle+\frac{\sqrt{2}}{v}\bar{\nu}_{i}(\xi^{\ell}_{A})_{ij}m^{\ell}_{j}P_{R}\ell_{j}H^{+}+{\rm
H.c.}\,,$ (5)

where the $(\xi^{f}_{\phi})_{ij}$ couplings are given in Tab. 1 in terms of
the free parameters $\chi_{ij}^{f}$, $\tan\beta$ and the mixing angle
$\alpha$. These expressions encompass the Higgs-fermion interactions of 2HDM
Type-II 333The 2HDM Type-II is restored when $\chi_{ij}=0$. together with a
contribution coming from the Yukawa texture444Here, $\xi_{f}^{\rm
III}=\xi_{f}^{II}+\Delta_{ij}$, with $\Delta_{ij}\sim\chi_{ij}$ [37, 38]..

$\phi$ | $(\xi^{u}_{\phi})_{ij}$ | $(\xi^{d}_{\phi})_{ij}$ | $(\xi^{\ell}_{\phi})_{ij}$
---|---|---|---
$h$ |  $\frac{c_{\alpha}}{s_{\beta}}\delta_{ij}-\frac{c_{\beta-\alpha}}{\sqrt{2}s_{\beta}}\sqrt{\frac{m^{u}_{i}}{m^{u}_{j}}}\chi^{u}_{ij}$ |  $-\frac{s_{\alpha}}{c_{\beta}}\delta_{ij}+\frac{c_{\beta-\alpha}}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{d}_{i}}{m^{d}_{j}}}\chi^{d}_{ij}$ |  $-\frac{s_{\alpha}}{c_{\beta}}\delta_{ij}+\frac{c_{\beta-\alpha}}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{\ell}_{i}}{m^{\ell}_{j}}}\chi^{\ell}_{ij}$
$H$ | $\frac{s_{\alpha}}{s_{\beta}}\delta_{ij}+\frac{s_{\beta-\alpha}}{\sqrt{2}s_{\beta}}\sqrt{\frac{m^{u}_{i}}{m^{u}_{j}}}\chi^{u}_{ij}$ | $\frac{c_{\alpha}}{c_{\beta}}\delta_{ij}-\frac{s_{\beta-\alpha}}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{d}_{i}}{m^{d}_{j}}}\chi^{d}_{ij}$ | $\frac{c_{\alpha}}{c_{\beta}}\delta_{ij}-\frac{s_{\beta-\alpha}}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{\ell}_{i}}{m^{\ell}_{j}}}\chi^{\ell}_{ij}$
$A$ | $\frac{1}{t_{\beta}}\delta_{ij}-\frac{1}{\sqrt{2}s_{\beta}}\sqrt{\frac{m^{u}_{i}}{m^{u}_{j}}}\chi^{u}_{ij}$ | $t_{\beta}\delta_{ij}-\frac{1}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{d}_{i}}{m^{d}_{j}}}\chi^{d}_{ij}$ | $t_{\beta}\delta_{ij}-\frac{1}{\sqrt{2}c_{\beta}}\sqrt{\frac{m^{\ell}_{i}}{m^{\ell}_{j}}}\chi^{\ell}_{ij}$
Table 1: Yukawa interactions in the 2HDM Type-III.

Based on the arguments presented above, the fundamental components of the
Yukawa sector can be obtained in terms of the $\chi_{ij}^{f}$ parameters.
These are additional free parameters of the model which describe masses and
mixings of the quarks and leptons. It is crucial to ensure that rare decays,
which are suppressed in the SM, do not exceed current bounds, though.
Specifically, it is important to investigate the contributions of Higgs bosons
to FCNC processes in $B$ mesons. Here, the non-diagonal terms are not
considered and the constraints from $\Delta B=2$ processes can be ignored due
to the suppression factor $\sqrt{m^{f}_{j}m^{f}_{i}}/v$. However, our analysis
takes into account transitions involving $\Delta B=1$ processes. The loop
transition $b\to s\gamma$ is also sensitive to BSM physics, as deviations from
the currently measured rate and SM predictions could indicate the presence of
a light charged Higgs boson with appropriate Yukawa couplings. Finally, since
$\rm{CP}$ violation is not observed in the lepton sector, it is reasonable to
assume that the $\chi_{ij}$’s are real numbers and the ensuing matrix is
symmetric. However, the presence of these terms could also modify FCNCs in the
Higgs sector, particularly $h\to f_{i}\bar{f_{j}}$ processes, which are
proportional to non-diagonal matrix terms [36, 39], so corresponding
constraints need to be enforced.

In the presence of the $\chi^{f}_{ij}$ texture parameters, alongside the
standard 2HDM inputs of Eq. (3), we will start our analysis by testing the
2HDM Type-III against theoretical and current experimental constraints, which
we do in the forthcoming section.

##  3 The Excesses in $h\to\gamma\gamma,~{}\tau\tau$ and $b\bar{b}$ Channels

In this section, we investigate whether the 2HDM Type-III can describe
consistently the excess observed by both LEP and the LHC at 94–100 GeV in the
$\gamma\gamma$, $\tau\tau$ and $b\overline{b}$ channels. The evaluation of the
so-called ‘signal strengths’ for these excesses was done in the Narrow Width
Approximation (NWA), in terms of the product of the relevant production cross
section ($\sigma$, which at the LHC is dominated by gluon-gluon fusion through
the top-quark loop555We have explicitly checked that in the region satisfying
the flavour physics constraints, the allowed values of $\sin(\beta-\alpha)$
and $\chi_{d}^{33}$ lead to a reduction of $|c_{\phi bb}|$ when compared to
$|c_{\phi tt}|$, so that the contribution from the bottom-quark loop is
negligible (nearly $2\%$). and at LEP by the Bjorken channel) as well as decay
Branching Ratios (${\cal BR}$s) as follows:

$\displaystyle\mu_{{b\bar{b}}}$ $\displaystyle=$
$\displaystyle\frac{\sigma_{\rm 2HDM}(e^{+}e^{-}\to Z\phi)}{\sigma_{\rm
SM}(e^{+}e^{-}\to Zh_{SM})}\times\frac{{\cal BR}_{\rm 2HDM}(\phi\to
b\bar{b})}{{\cal BR}_{\rm SM}(h_{\rm SM}\to b\bar{b})}=\left|c_{\phi
ZZ}\right|^{2}\times\frac{{\cal BR}_{\rm 2HDM}(\phi\to b\bar{b})}{{\cal
BR}_{\rm SM}(h_{\rm SM}\to b\bar{b})},$ (6)
$\displaystyle\mu_{\mathrm{\tau\tau}}$ $\displaystyle=$
$\displaystyle\frac{\sigma_{\rm 2HDM}(gg\to\phi)}{\sigma_{\rm SM}(gg\to h_{\rm
SM})}\times\frac{{\cal BR}_{\rm 2HDM}(\phi\to\tau\tau)}{{\cal BR}_{\rm
SM}(h_{\rm SM}\to\tau\tau)}=\left|c_{\phi tt}\right|^{2}\times\frac{{\cal
BR}_{\rm 2HDM}(\phi\to\tau\tau)}{{\cal BR}_{\rm SM}(h_{\rm SM}\to\tau\tau)},$
(7) $\displaystyle\mu_{\mathrm{\gamma\gamma}}$ $\displaystyle=$
$\displaystyle\frac{\sigma_{\rm 2HDM}(gg\to\phi)}{\sigma_{\rm SM}(gg\to h_{\rm
SM})}\times\frac{{\cal BR}_{\rm 2HDM}(\phi\to\gamma\gamma)}{{\cal BR}_{\rm
SM}(h_{\rm SM}\to\gamma\gamma)}=\left|c_{\phi tt}\right|^{2}\times\frac{{\cal
BR}_{\rm 2HDM}(\phi\to\gamma\gamma)}{{\cal BR}_{\rm SM}(h_{\rm
SM}\to\gamma\gamma)},$ (8)

where $c_{\phi ZZ}$ and $c_{\phi tt}$ are the $\phi$ couplings to $ZZ$ and
$t\bar{t}$ (entering the LEP and LHC production modes, respectively)
normalised to the corresponding SM values. In the present context, $\phi$
denotes the light CP-even Higgs scalar $h$ and our focus is exclusively on its
contributions to the signal. We do not consider the pseudoscalar state $A$ for
the explanation of these excesses in this analysis since for a CP-conserving
scenario such as ours, the $AZZ$ coupling is forbidden at tree level,
rendering the explanation of the LEP excess with a CP-odd state impossible.
The experimental measurements for the three signal strengths are expressed as
[29, 26, 27]666The value of $\mu_{\gamma\gamma}^{\mathrm{exp}}$ which we have
decided to take form the latest version of [29] approximately agrees with our
rough estimation which we have found to be about 0.3.:

$\displaystyle\mu_{\gamma\gamma}^{\mathrm{exp}}=\mu_{\gamma\gamma}^{\mathrm{ATLAS+CMS}}=0.24^{+0.09}_{-0.08},\quad\quad\quad\mu_{\tau\tau}^{\mathrm{exp}}=1.2\pm
0.5,\quad\quad\quad\mu_{b\bar{b}}^{\mathrm{exp}}=0.117\pm 0.057,$ (9)

where $h_{\rm SM}$ corresponds to a SM-like Higgs boson with a mass of $95$
GeV – the mass of the $h$ state of our interest from the 2HDM Type-III. In our
analysis, we have combined the di-photon measurements from the ATLAS and CMS
experiments, denoted as $\mu_{\gamma\gamma}^{\mathrm{ATLAS}}$ and
$\mu_{\gamma\gamma}^{\mathrm{CMS}}$, respectively. The ATLAS measurement
yields a central value of $0.18{\pm 0.1}$ [29] while the CMS measurement
yields a central value of $0.33^{+0.19}_{-0.12}$[27]. By doing so, we aimed at
leveraging the strengths of both experiments and improve the precision of our
analysis. The combined measurement, denoted as
$\mu_{\gamma\gamma}^{\mathrm{ATLAS+CMS}}$, is determined by taking the average
of the central values without assuming any correlation between them. To
evaluate the combined uncertainty we sum ATLAS and CMS uncertainties in
quadrature.

To determine whether a simultaneous fit to the observed excesses is possible,
a $\chi^{2}$ analysis is performed using measured central values
$\mu^{\mathrm{exp}}$ and the 1$\sigma$ uncertainties
$\Delta\mu^{\mathrm{exp}}$ of the signal rates related to the two excesses as
defined in Eqs. (6)–(8). The contribution to the $\chi^{2}$ value for each
channel ($\gamma\gamma$, $\tau\tau$, $b\bar{b}$) is calculated using the
formula

$\displaystyle\chi^{2}_{\gamma\gamma,\tau\tau,b\bar{b}}=\frac{\left(\mu_{\gamma\gamma,\tau\tau,b\bar{b}}-\mu_{\gamma\gamma,\tau\tau,b\bar{b}}^{\mathrm{exp}}\right)^{2}}{\left(\Delta\mu^{\mathrm{exp}}_{\gamma\gamma,\tau\tau,b\bar{b}}\right)^{2}}.$
(10)

So, the resulting $\chi^{2}$ which we will use to judge whether the points
from the model describe the excess in three channels, reads as:

$\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}=\chi^{2}_{\gamma\gamma}+\chi^{2}_{\tau\tau}+\chi^{2}_{b\bar{b}}.$
(11)

##  4 Theoretical and Experimental Constraints

In our study we use a comprehensive set of theoretical and experimental
constraints that must be satisfied to establish a viable model.

###  4.1 Theoretical Constraints

In our study we impose the following set of the theoretical constraints on the
scalar potential.

  * •

Unitarity: The scattering processes involving (pseudo)scalar-(pseudo)scalar,
gauge-gauge and/or (pseudo)scalar-gauge initial and/or final states must
satisfy unitarity constraints. The eigenvalues $e_{i}$ of the tree-level
2-to-2 body scattering matrix should meet the following criteria:
$|e_{i}|<8\pi$ [40, 41].

  * •

Perturbativity: Adherence to perturbativity constraints imposes an upper limit
on the quartic couplings of the Higgs potential: $|\lambda_{i}|<8\pi$ [5].

  * •

Vacuum Stability: The scalar potential must be positive and bounded from below
in any direction of the fields $\Phi_{i}$ to ensure vacuum stability. This
requires that $\lambda_{1}>0$, $\lambda_{2}>0$,
$\lambda_{3}>-\sqrt{\lambda_{1}\lambda_{2}}$, and
$\lambda_{3}+\lambda_{4}-|\lambda_{5}|>-\sqrt{\lambda_{1}\lambda_{2}}$ [42,
43].

###  4.2 Experimental Constraints

We also apply a variety of experimental constraints from EW Precision
Observables (EWPOs), measurements of the observed Higgs boson properties at
the LHC, lack of signals from non-SM-like Higgs bosons at LEP, Tevatrron and
LHC as well as flavour observables, which include the following.

  * •

EWPOs: We require a $95\%$ C.L. in matching the global fit results of the EW
oblique parameters $S,T$ and $U$ [44, 45] with the following values [46]:

$\displaystyle S=0.05\pm 0.08,\quad T=0.09\pm
0.07,\quad\rho_{ST}=0.92~{}~{}(\mathrm{for}~{}U=0).\hskip 42.67912pt$

  * •

SM-like Higgs Boson Discovery:

We made sure that the points from our parameter space agree with the
experimental measurement of the properties of the discovered SM-like Higgs
boson with mass of $\approx 125$ GeV red at 95% C.L. To do this we have used
the public code HiggsSignals-3 [47, 48] via HiggsTools [49] to perform a
$\chi^{2}$ test in order to check how the Higgs signal strengths from Tevatron
and LHC are compatible with the model predictions.

  * •

Non-SM-like Higgs Boson Exclusions: To further scrutinise the parameter space
of our 2HDM Type-III, we subject the selected parameter space points to
rigorous examinations against exclusion limits derived from additional Higgs
boson searches. We utilise the code HiggsBounds-6 [50, 51, 52, 53] via
HiggsTools to incorporate the exclusion constraints from various experiments,
including LEP, Tevatron and the LHC.

  * •

$B$-Physics Observables: We test various $B$-physics observables against
experimental data using the public code SuperIso_v4.1 [54]. The following
experimental measurements are used in our analysis:

Observable Value Reference ${\cal BR}(\overline{B}\to
X_{s}\gamma)|_{E_{\gamma}<1.6\mathrm{~{}GeV}}$ $\left(3.32\pm
0.15\right)\times 10^{-4}$ [55] ${\cal BR}(B^{+}\to\tau^{+}\nu_{\tau})$
$\left(1.06\pm 0.19\right)\times 10^{-4}$ [55] ${\cal
BR}(D_{s}\to\tau\nu_{\tau})$ $\left(5.51\pm 0.18\right)\times 10^{-2}$ [55]
${\cal BR}(B_{s}\to\mu^{+}\mu^{-})$ (LHCb)
$\left(3.09^{+0.46}_{-0.43}\right)\times 10^{-9}$ [56, 57] ${\cal
BR}(B_{s}\to\mu^{+}\mu^{-})$ (CMS) $\left(3.83^{+0.38}_{-0.36}\right)\times
10^{-9}$ [58] ${\cal BR}(B^{0}\to\mu^{+}\mu^{-})$ (LHCb)
$\left(1.2^{+0.8}_{-0.7}\right)\times 10^{-10}$ [56, 57] ${\cal
BR}(B^{0}\to\mu^{+}\mu^{-})$ (CMS) $\left(0.37^{+0.75}_{-0.67}\right)\times
10^{-10}$ [58] ${\cal BR}(K\to\mu\nu_{\mu})/{\cal BR}(\pi\to\mu\nu_{\mu})$
$0.6357\pm 0.0011$ [59]

Table 2: Flavour physics observables and corresponding values employed in our
analysis.

By rigorously examining these $B$-physics observables against experimental
constraints, we can validate the compatibility of our 2HDM Type-III with
existing data and potentially uncover any deviations that could indicate new
physics phenomena.

##  5 Explanation of the Excesses

In this section, we present our numerical analysis of the 2HDM Type-III
parameter space. For the 2HDM Type-III spectrum generation, we have employed
2HDMC 1.8.0[60], which considers the theoretical constraints discussed in the
previous section, along with the electroweak precision observables (EWPOs).
Subsequently, we validate our results by comparing them to Higgs data,
utilizing HiggsTools [49], which includes the most recent versions of both
HiggsBounds and HiggsSignals. In accordance with the above discussions, we
consider the scenario where the heavier CP-even Higgs boson $H$ is the SM-like
Higgs particle $H_{\rm SM}$ discovered at the LHC with $m_{H_{\rm SM}}\approx$
125 GeV. In this scenario the lighter CP-even Higgs, $h$, is the source of the
observed excess in $\gamma\gamma$, $\tau\tau$ and $b\bar{b}$ channels around
95 GeV, which we previously labelled as $h_{\rm SM}$. To explore this
scenario, we conducted a systematic random scan across the parameter ranges
specified in Tab. 3777In this work, we do not include the contributions to the
signal from the CP-odd state..

$m_{h}$ $m_{H}$ $m_{A}$ $m_{H^{\pm}}$ $s_{\beta-\alpha}$ $\tan\beta$
$m_{12}^{2}$ $\chi_{ij}^{f,\ell}$ $[94;\,97]$ $125.09$ $[80;\,300]$
$[160;\,200]$ $[-0.5;\,0]$ $[1;\,30]$ $m_{h}^{2}\tan\beta/(1+{\tan^{2}\beta})$
$[-3;\,3]$

Table 3: Scan ranges of the 2HDM Type-III input parameters. Masses are given
in GeV.

We then investigate parameter spaces that satisfy the condition
$\chi^{2}_{125}\leq 189.4$, corresponding to a 95% Confidence Level (C.L.) for
159 degrees of freedom, where $\chi^{2}_{125}$ corresponds to the $\chi^{2}$
evaluated by HiggsSignals for the 125 GeV Higgs signal strength measurements.
Subsequently, we examine 2-dimensional (2D) planes of the signal strength
parameters: $(\mu_{\gamma\gamma}-\mu_{\tau\tau})$,
($\mu_{\gamma\gamma}-\mu_{b\bar{b}}$) and ($\mu_{b\bar{b}}-\mu_{\tau\tau}$).

Figure 1: The colour map of $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$ in the
($\mu_{\gamma\gamma}-\mu_{\tau\tau})$, ($\mu_{\gamma\gamma}-\mu_{b\bar{b}}$)
and ($\mu_{b\bar{b}}-\mu_{\tau\tau}$) planes of the signal strength parameters
for 2HDM Type-III parameter space under study. The ellipses define the regions
consistent with the excess at 1$\sigma$ C.L. The contribution from
$\mu_{\gamma\gamma}$ to $\chi^{2}$ for black, gray and red contours comes from
CMS, ATLAS and combined CMS+ATLAS data respectively. As detailed in the text,
the contribution to $\chi^{2}$ from $\mu_{\tau\tau}$ (left frame) comes from
CMS data while the contribution from $\mu_{b\bar{b}}$ (middle frame) comes
from LEP data. Grey points are excluded by
$\sigma(tt\phi)\times\mathcal{BR}(\phi\to\tau\tau)$ [61]. The position of
$\chi^{2}_{95\mathrm{min}}$ is marked by a green star.

In the following we will refer to the $h$ and $H$ states of the 2HDM Type-III
by using the labels ‘$h_{95}$’ and ‘$h_{125}$’, respectively. In Fig. 1, we
present the results for $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$ in the
form of its colour map projected into the
($\mu_{\tau\tau}$-$\mu_{\gamma\gamma}$) (left),
($\mu_{b\bar{b}}$-$\mu_{\gamma\gamma}$) (middle) and
($\mu_{\tau\tau}$-$\mu_{b\bar{b}}$) (right) planes of the signal strength
parameters. The dashed ellipses define the regions consistent with the excess
at 1$\sigma$ described by the $\chi^{2}_{x}+\chi^{2}_{y}=2.30$ equation, where
the subscripts $x$ and $y$ label each possible pairing out of three signal
channels ($\gamma\gamma$, $\tau\tau$ and $b\bar{b}$), depending on the frame
of Fig. 1. The black, gray and red contours are for the $\chi^{2}$ constructed
using the $\mu_{\gamma\gamma}^{\mathrm{CMS}}$,
$\mu_{\gamma\gamma}^{\mathrm{ATLAS}}$ and
$\mu_{\gamma\gamma}^{\mathrm{CMS+ATLAS}}$ signal strengths, respectively. The
value of $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$ is indicated by the
vertical colourmap. The grey points represent exclusions based on recent CMS
searches888This limit has not yet been integrated into HiggsBounds-6. [61] for
the production of a Higgs boson in association with either a top-quark pair or
a $Z$ boson, with the subsequent decay into a tau pair. The green star,
indicating the position of $\chi^{2}_{95,\mathrm{min}}$ which is the minimum
of $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$, has a value of 4.55,
corresponds to a 1.26 $\sigma$ C.L. for three degrees of freedom even though
this minimum lies solely within the 1$\sigma$ C.L. contour for the
$\mu_{\tau\tau}$-$\mu_{\gamma\gamma}$ pair of signal strengths and not for the
other pairs. Furthermore, numerous points surrounding
$\chi^{2}_{95,\mathrm{min}}$ depicted by the dark blue colour indicating the
capability of the 2HDM Type-III to explain the observed excess across all
three channels simultaneously at $1.5\sigma$ C.L or better reaching up to
about 1.3$\sigma$.

One can also note from the middle and the right frames of Fig. 1 that all
points are situated outside of the 1$\sigma$ ellipses because it is difficult
to achieve large enough values of $\mu_{b\bar{b}}$ satisfying the three
constraints simultaneously. This happens because the $\gamma\gamma$ excess is
achieved via enhancement of ${\cal BR}(h_{95}\to\gamma\gamma)$ due to the
decrease of $\Gamma_{b\bar{b}}$ (the main channel of $h_{95}$ decay) and the
respective decrease of ${\cal BR}(h_{95}\to b\bar{b})$.

Figure 2: The $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$ dependence upon
$s_{\beta-\alpha}$. The colour bar indicates the value of $|c_{h_{125}VV}|$
(left) and $|c_{h_{125}\gamma\gamma}|$ (right). The horizontal dashed(dash-
dot) line represents the 1.5$\sigma$(2$\sigma$) region.

In Fig. 2, we show $\chi^{2}_{\gamma\gamma+\tau\tau+b\bar{b}}$ in our
parameter scans as a function of $s_{\beta-\alpha}$. We also indicate the
value of the Higgs couplings to SM gauge bosons, $|c_{h_{125}VV}|$ (left) and
$|c_{h_{125}\gamma\gamma}|$999The normalised coupling for the loop-induced
channel ${h\to\gamma\gamma}$ is defined by
$|c_{h\to\gamma\gamma}|^{2}\equiv\frac{\Gamma(h\to\gamma\gamma)^{\mathrm{2HDM}}}{\Gamma(h\to\gamma\gamma)^{\mathrm{SM}}}$.
(right) in the colour bar. The horizontal dashed(dash-dot) line represents the
1$\sigma$(2$\sigma$) region corresponding to the three excesses
($\gamma\gamma,~{}\tau\tau,~{}b\bar{b}$). Clearly one can read from the left
panel that, when simultaneously describing the three excesses at 1.3$\sigma$
C.L., the SM-like Higgs coupling to vector bosons $|c_{h_{125}VV}|$ which is
proportional to $c_{\beta-\alpha}$ lie close to $\sim 1$, In contract the
coupling to $\gamma\gamma$ exhibits a slight deviation from the predicted SM
value, reaching a minimum of 0.91 and a maximum of 0.96.

Figure 3: As in Fig. 2, but the colour coding indicates the value of
$|c_{h_{125}t\bar{t}}|$ (left) and $|c_{h_{125}b\bar{b}}|$ (right).

Fig. 3 presents analogous plots to those displayed in Fig. 2. However, in this
case, the colour bar represents the values of the couplings of the $\approx
125$ GeV Higgs state to $t\bar{t}$ (left) and to $b\bar{b}$ (right). The
explanation of the three excesses simultaneously requires an enhancement of up
to 12% and 8% in $c_{h_{125}t\bar{t}}$ and $c_{h_{125}b\bar{b}}$,
respectively. The reason for the enhancement in $c_{h_{125}t\bar{t}}$ can be
understood as follows. The requirement of fitting the three excesses at
1.3$\sigma$ C.L. restricts $\sin(\beta-\alpha)$ in the range $\approx$
[-0.18,-0.13]. This makes the ${s_{\alpha}}/{s_{\beta}}$ term in the
$c_{h_{125}t\bar{t}}$ coupling (see second row, Tab. 1) slightly larger than
one. The $\chi_{33}^{u}$ parameter in the second term is constrained by
flavour physics to be both small and negative, making the contribution from
the second term minimal. In contrast, the enhancement in $c_{h_{125}b\bar{b}}$
originates from both terms, as $\chi_{33}^{d}$ is larger, contributing
substantially to the coupling. A typical set of values for the $\chi_{ij}^{f}$
parameters can be found in Tab. 4 where we describe the features of our best
fit point. The implications of the enhancements, in particular in the
$c_{h_{125}t\bar{t}}$ coupling, will be discussed subsequently.

In Fig. 4, we directly compare our allowed parameter points to the
experimental data by superimposing these onto the CMS 13 TeV low-mass
$\gamma\gamma$ [7] analysis data. The light green colour represents the
parameter points that fit the excesses within a three-dimensional C.L. from
$1.5\sigma$ up to $1.3\sigma$, whereas the points that fit the excesses at
2$\sigma$ or more are shown in red. It can be clearly observed from the plots
that our parameter points are exactly suited to satisfy the excesses.

Figure 4: Allowed points, following the discussed theoretical and experimental
constraints, superimposed onto the results of the CMS 13 TeV low-mass
$\gamma\gamma$ [7] analysis. (Notably, the plot further includes the depiction
of the ATLAS expected and observed limits from [8], showcased in blue.) The
light green colour represents the parameter points that fit the excesses
within a three-dimensional C.L. of 1.5$\sigma$ ($\chi^{2}_{95}\leq 5.59$) or
better, reaching up to $1.3\sigma$, whereas the points that fit the excesses
at 2$\sigma$ or more are shown in red.

Fig. 5 depicts the correlation between the normalised couplings of the
$\approx 125$ GeV Higgs using the same color scheme detailed in Fig. 4. One
can see from the plots that the explanation of the three excesses in
$b\overline{b}$, $\tau\tau$ and $\gamma\gamma$ channels requires an
enhancement of the $h_{125}t\overline{t}$ and $h_{125}b\overline{b}$ couplings
deviating by $\sim 11.5\%$ from the SM for $t\bar{t}$ and by $\sim 8\%$ for
$b\bar{b}$. In contrast, a decrease can be seen in the Higgs coupling to
$\tau\tau$ ($c_{h_{125}\tau\tau}$), deviating from the SM value by about 11%.
Furthermore, the plot includes green dashed lines representing the current
$1\sigma$ uncertainties of the normalised couplings $c_{h_{125}i\bar{j}}$, as
measured by CMS [62]. Additionally, orange and blue ellipses are depicted,
illustrating the projected experimental precision for the normalised couplings
at the HL-LHC [63] with an integrated luminosity of 3000 fb-1 and the
projected precision from a combination of data from the HL-LHC and ILC 500,
respectively. One should bear in mind that the center of these experimental
projections, for HL-LHC and ILC 500, corresponds to the SM value represented
by black diamonds. Clearly, each point that simultaneously describes the three
excesses is situated outside the ellipses corresponding to the HL-LHC and ILC
500. Since the points deviate significantly from the SM predictions, the
expected precision of the HL-LHC and ILC 500 experiments would allow us to
distinguish between the SM-like properties of $h_{125}$ and the $H$ from the
2HDM Type-III model within the parameter range that aligns with the observed
excesses. Moreover, one can see that already at the HL-LHC one will be able
either to discover or rule out the scenario which describes the current excess
in three channels under study.

Figure 5: Correlations between the normalized couplings
$|c_{h_{125}\tau\tau}|$, $|c_{h_{125}VV}|$, $|c_{h_{125}t\bar{t}}|$, and
$|c_{b_{125}t\bar{b}}|$, with colours corresponding to those in Fig. 4, are
illustrated. Also presented are the current 1$\sigma$ uncertainties of the
coupling coefficients’ measurements from CMS [62], depicted by green dashed
lines. The orange and blue ellipses indicate the projected uncertainties at
the HL-LHC [63], and following a combination of data from both the HL-LHC and
the ILC at a center-of-mass energy of 500 GeV [64], respectively.

Fig. 6 illustrates the allowed parameter space in the 2HDM Type-III satisfying
theoretical and experimental constraints in the
$(m_{h},\sigma_{tth_{125}}/\sigma_{tth}^{\mathrm{SM}})$ plane. The black
dashed line corresponds to the observed value from CMS [62] and the lime green
(yellow) band represents instead the $1\sigma$ ($2\sigma$) range. The hatched
area denotes the 95% C.L. probability sensitivity of the HL-LHC [63] to the
normalised cross section $\sigma_{tth_{125}}/\sigma_{tth}^{\mathrm{SM}}$,
centered on the SM value (solid red line). It is evident from the figure that
all the points that simultaneously explain the three excesses at $1.5\sigma$
C.L or better. represented by the light green colour, fall within the
2$\sigma$ measurement range of CMS. Additionally, as seen in Fig. 5, these
points exhibit an enhancement in the $h_{125}{t\bar{t}}$ coupling. In fact,
due to such an enhancement, these points deviate significantly from the
$2\sigma$ level of the HL-LHC projection. Note, however, that the central
value used for the HL-LHC measurement corresponds to the SM prediction, i.e.,
1. Thus, for points that are notably away from the SM prediction, the
projected precision of the HL-LHC experiment would be sufficient to
distinguish between the SM-like properties of the $h_{125}$ and the
predictions of the 2HDM Type-III within the parameter space consistent with
the observed enhancement in the $h_{125}{t\bar{t}}$ coupling.

Figure 6: Predicted signal strength
$\sigma_{tth_{125}}/\sigma_{tth}^{\mathrm{SM}}$ in relation to the three
observed excesses. The black dashed line represents the observed value from
CMS [62] while the lime green (yellow) band denotes the $1.5\sigma$
($2\sigma$) range around the observed value. The hatched area illustrates the
95% probability sensitivity of the HL-LHC [63] to the normalised cross section
$\sigma_{tth_{125}}/\sigma_{tth}^{\mathrm{SM}}$, centred on the value of the
SM (depicted as a solid red line). The colours correspond to those in Fig. 4.

In summary, there is a smoking-gun prediction stemming from our 2HDM Type-III
scenario, which simultaneously explains $\gamma\gamma,\tau\tau$ and $b\bar{b}$
anomalies at 1.3 $\sigma$ C.L. and can be tested at the LHC. On the one hand,
$c_{h_{125}t\bar{t}}$ and $c_{h_{125}b\bar{b}}$ are consistently larger than
1, while $c_{h_{125}\tau\tau}$ is consistently smaller than 1. Among these
couplings, $c_{h_{125}t\bar{t}}$ can be precisely measured in various
production modes, not only in gluon-gluon fusion where, however, there is
contamination from $b$-quark loops, but also in associated production with
$t\bar{t}$ pairs, which could then be tested at the (HL-)LHC, via $pp\to
t\bar{t}h_{125}$, and an ILC 500, via $e^{+}e^{-}\to t\bar{t}h_{125}$.

Finally, we conclude this section by providing a detailed overview of our best
fit point in Tab. 4. One can observe from Tab. 4 that the best fit point
features a small negative value for the $\chi^{u}_{33}$ parameter. This, in
combination with the small negative $\sin(\beta-\alpha)$ values preferred in
our parameter scan gives rise to the observed enhancement in the
$h_{125}{t\bar{t}}$ couplings (see Tab. 1).

##  6 Conclusions

To date, large data samples have been accumulated by the LHC experiments and
many analyses have been performed to examine the discussed 95 GeV excesses,
following initial observations. In order to better explain the nature of these
potential anomalies, a careful examination of the data, in-depth simulations
and advanced computational approaches have been carried out in the literature.
Along these lines, we have in this article proposed a theoretical framework,
the 2HDM Type-III with a specific Yukawa texture, as a possible solution to
the $\gamma\gamma$, $\tau\tau$ and $b\bar{b}$ anomalies. Specifically, we
concentrated on a Higgs boson with a mass of about 95 GeV produced by gluon-
gluon fusion at the 13 TeV LHC and decaying into $\tau\tau$ and $\gamma\gamma$
as well as produced by Higgs-strahlung at LEP and decaying into $b\bar{b}$.

By assuming that the heaviest CP-even Higgs state, $H$, is the one discovered
at the LHC with mass $\approx 125$ GeV, we have identified parameter space
regions where the lightest CP-even state, $h$, with a mass of $\approx 95$
GeV, can explain simultaneously the observed excesses through a $\chi^{2}$
analysis at approximately 1.3 $\sigma$ C.L. while accommodating both standard
theoretical requirements of self-consistency and up-to-date experimental
constraints.

Throughout this paper, we have analysed correlations amongst the signal
strengths $\mu_{\gamma\gamma}$, $\mu_{\tau\tau}$ and $\mu_{b\bar{b}}$ at
1$\sigma$ level, arguing that the results presented are compelling and support
a more extensive investigation of the proposed 2HDM Type-III scenario, by
looking at processes predicted therein, which would constitute an hallmark
signature of it, like $pp\to t\bar{t}H$ production, at both Run 3 of the LHC
and the HL-LHC, which would be significantly enhanced with respect to the SM
yield.

In fact, also the study of $e^{+}e^{-}\to t\bar{t}H$ at the ILC 500, which
would probe the coupling of $H$ to top (anti)quarks at the percent level, will
play a crucial role in confirming the BSM construct pursued in our
investigation. Thus, by incorporating the insights gained from these
complementary measurements, a more comprehensive understanding of the nature
of the studied excesses and the underlying theoretical framework can be
achieved (assuming their persistence in future data samples at these
machines).

Moreover, the anticipated precision of the HL-LHC and ILC 500 allows for
effective differentiation between the SM-like characteristics of the $H$ state
and the predictions of the 2HDM Type-III. This distinction is achievable for
data points that display notable deviations from the SM predictions, while
remaining within the parameter space that corresponds to the observed
enhancement in the ${t\bar{t}}H$ coupling. Finally, one should stress that the
precise measurement of the ${t\bar{t}}H$ coupling would be also very
instrumental for discovery or dismissal of the proposed scenario already in
the near future at the HL-LHC.

To aid such investigations, we have presented the details of our best fit
point for further phenomenological studies in these directions.

## Acknowledgments

AB and SM are supported in part through the NExT Institute and STFC CG
ST/L000296/1. AB would like to thank Prof. Glen Cowan for discussions around
the statistical aspects of our study. The work of RB and MB is supported by
the Moroccan Ministry of Higher Education and Scientific Research MESRSFC and
CNRST Project PPR/2015/6. MB acknowledges the use of CNRST/HPC-MARWAN in
completing this work. SS is supported in full by the NExT Institute.

Parameters ★☆ (Masses are in GeV) $m_{h}$ 95.03 $m_{H}$ 125.09 $m_{A}$ 94.77
$m_{H^{\pm}}$ 162.95 $\tan\beta$ 1.74 $\sin(\beta-\alpha)$ -0.17
$\chi_{11}^{u}$ 0.02 $\chi_{22}^{u}$ 0.54 $\chi_{33}^{u}$ -0.08
$\chi_{11}^{d}$ -0.41 $\chi_{22}^{d}$ 0.24 $\chi_{33}^{d}$ 1.55
$\chi_{11}^{\ell}$ -0.06 $\chi_{22}^{\ell}$ 0.33 $\chi_{33}^{\ell}$ 0.97
Effective coupling $c_{h_{125}i\bar{i}}$ $c_{h_{125}t\bar{t}}$ 1.10
$c_{h_{125}b\bar{b}}$ 1.06 $c_{h_{125}\tau\tau}$ 0.92 Collider signal strength
$\mu_{\gamma\gamma}$ 0.25 $\mu_{\tau\tau}$ 0.51 $\mu_{b\bar{b}}$ 0.02 Total
decay width in MeV $\Gamma(h)$ 0.27 $\Gamma(H)$ 4.73 $\Gamma(A)$ 0.66
$\Gamma(H^{\pm})$ 4.77 ${\cal BR}(h\to XY)$ in % ${\cal BR}(h\to\gamma\gamma)$
0.15 ${\cal BR}(h\to gg)$ 13.82 ${\cal BR}(h\to b\bar{b})$ 65.37 ${\cal
BR}(h\to c\bar{c})$ $-$ ${\cal BR}(h\to s\bar{s})$ 0.50 ${\cal
BR}(h\to\mu^{+}\mu^{-})$ 0.67 ${\cal BR}(h\to\tau\tau)$ 19.33 ${\cal BR}(h\to
ZZ)$ $-$ ${\cal BR}(h\to W^{+}W^{-})$ 0.12 ${\cal BR}(H\to XY)$ in % ${\cal
BR}(H\to\gamma\gamma)$ 0.16 ${\cal BR}(H\to gg)$ 8.16 ${\cal BR}(H\to
b\bar{b})$ 64.08 ${\cal BR}(H\to c\bar{c})$ 3.07 ${\cal BR}(H\to\tau\tau)$
4.70 ${\cal BR}(H\to ZZ)$ 2.19 ${\cal BR}(H\to W^{+}W^{-})$ 17.48 ${\cal
BR}(A\to XY)$ in % ${\cal BR}(A\to\gamma\gamma)$ 0.046 ${\cal BR}(A\to gg)$
28.70 ${\cal BR}(A\to b\bar{b})$ 66.95 ${\cal BR}(A\to c\bar{c})$ 0.40 ${\cal
BR}(A\to\mu\mu)$ 0.16 ${\cal BR}(A\to\tau\tau)$ 3.53 ${\cal BR}(H^{\pm}\to
XY)$ in % ${\cal BR}(H^{\pm}\to cs)$ 0.11 ${\cal BR}(H^{\pm}\to W^{+}h)$ 33.79
${\cal BR}(H^{\pm}\to W^{+}A)$ 35.62 ${\cal BR}(H^{\pm}\to\tau\nu)$ 0.84
${\cal BR}(H^{\pm}\to tb)$ 29.47

Table 4: The full description of the best fit point
$\chi^{2}_{95,\mathrm{min}}$ (green star).

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