Explanation of the Hints for a 95 GeV Higgs Boson within a 2-Higgs Doublet Model

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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 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 σ C.L. while satisfying up-to-date theoretical and experimental constraints.Moreover, the 2HDM Type-III predicts an excess in the pp → t tH SM production channel of the 125 GeV Higgs boson, H SM .This effect is caused by a up to 12% enhancement of the H 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.

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 2.9σ at a mass of m γγ = 95.4GeV.
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 1.7σ in the γγ 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 ϕ in the production and decay process gg, b b → ϕ → τ τ [10], with a local (global) significance of 3.1σ(2.7σ)for m ϕ ≈ 100 GeV.Considering the poor resolution of m τ τ in comparison to m γγ , 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 − → Zϕ production mode, with a generic Higgs boson state ϕ decaying via the τ τ and bb channels.Interestingly, an excess has been reported in 2006 in the e + e − → Zϕ(→ bb) mode for m b 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 γγ and τ τ 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 ≈ 125 GeV SM-like Higgs state observed at the LHC.In the attempt to explain the excesses in the γγ and bb 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 γγ, τ τ and b b final states can also be explained within the 2HDM Type-III of Refs.[30,31], at approximately 1.3 σ 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 SM tt Yukawa coupling and the respective uplift of the gg, q q → t tH 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.

2HDM Type-III
The 2HDM includes two SU (2) L doublets with hypercharge Y = 1.The most general renormalisable SU (2) L × U (1) Y invariant scalar potential is written as follows [5]: where m 2 11 , m 2 22 , m 2 12 are mass squared terms and λ i (i = 1, ..., 7) are dimensionless quantities describing the coupling of the order-4 interactions.Of all such parameters, 6 are real (m 2  11 , m 2  22 and λ i with i = 1, ..., 4) and 4 are a priori complex (m 2 12 and λ 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 (Φ 1 , Φ 2 ) space, removing the m 2  12 term, thus getting rid of 2 parameters.Then, one can make a relative U (1) transformation on Φ 1 or Φ 2 , making λ 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 V V (V V = 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 (Φ 1 → +Φ 1 and Φ 2 → −Φ 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 m2 12 ), as customarily done to enable Electro-Weak Symmetry Breaking (EWSB) compliant with experimental measurements, relies on the existence of a basis where λ 6 = λ 7 = 0.As a consequence, altogether, one loses 2 parameters (λ 6 and λ 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: where the angle β determines the ratio of the two doublet VEVs, v 1 and v 2 , as tan β = 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: where α 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 SM1 ) whereas m H ± 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: where Y f 1,2 are 3 × 3 Yukawa matrices in flavour space and Φ1,2 = iσ 1,2 Φ * 1,2 , with σ 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 , 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: where the (ξ f ϕ ) ij couplings are given in Tab. 1 in terms of the free parameters χ f ij , tan β and the mixing angle α.These expressions encompass the Higgs-fermion interactions of 2HDM Type-II3 together with a contribution coming from the Yukawa texture 4 .
Based on the arguments presented above, the fundamental components of the Yukawa sector can be obtained in terms of the χ f ij 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 ∆B = 2 processes can be ignored due to the suppression factor √ m f j m f i /v.However, our analysis takes into account transitions involving ∆B = 1 processes.The loop transition b → sγ 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 CP violation is not observed in the lepton sector, it is reasonable to assume that the χ 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 → f i fj processes, which are proportional to non-diagonal matrix terms [36,39], so corresponding constraints need to be enforced.
In the presence of the χ 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 → γγ, τ τ and b 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 γγ, τ τ and bb 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 (σ, which at the LHC is dominated by gluon-gluon fusion through the top-quark loop 5 and at LEP by the Bjorken channel) as well as decay Branching Ratios (BRs) as follows: where c ϕZZ and c ϕtt are the ϕ couplings to ZZ and t t (entering the LEP and LHC production modes, respectively) normalised to the corresponding SM values.In the present context, ϕ 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 [26,27,29] 6 : where h 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 diphoton measurements from the ATLAS and CMS experiments, denoted as µ ATLAS γγ and µ CMS γγ , respectively.The ATLAS measurement yields a central value of 0.18±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 µ ATLAS+CMS γγ , 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 χ 2 analysis is performed using measured central values µ exp and the 1σ uncertainties ∆µ exp of the signal rates related to the two excesses as defined in Eqs. ( 6)- (8).The contribution to the χ 2 value for each channel (γγ, τ τ , b b) is calculated using the formula So, the resulting χ 2 which we will use to judge whether the points from the model describe the excess in three channels, reads as: (11)

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.

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, gaugegauge 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 | < 8π [40,41].
• Vacuum Stability: The scalar potential must be positive and bounded from below in any direction of the fields Φ i to ensure vacuum stability.This requires that λ 1 > 0, λ 2 > 0, [42,43].

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.
• 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 ≈ 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 χ 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.
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.

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 SM discovered at the LHC with m H SM ≈ 125 GeV.In this scenario the lighter CP-even Higgs, h, is the source of the observed excess in γγ, τ τ and b b channels around 95 GeV, which we previously labelled as h SM .
To explore this scenario, we conducted a systematic random scan across the parameter ranges specified in Tab. 3 7 .We then investigate parameter spaces that satisfy the condition χ  95min 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 χ 2  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 ≈ 125 GeV Higgs state to t t (left) and to b b (right).The explanation of the three excesses simultaneously requires an enhancement of up to 12% and 8% in c h 125 t t and c h 125 b b, respectively.The reason for the enhancement in c h 125 t t can be understood as follows.The requirement of fitting the three excesses at 1.3σ C.L. restricts sin(β − α) in the range ≈ [-0.18,-0.13].This makes the s α /s β term in the c h 125 t t coupling (see second row, Tab. 1) slightly larger than one.The χ u 33 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 b originates from both terms, as χ d 33 is larger, contributing substantially to the coupling.A typical set of values for the χ f ij 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 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 γγ [7] analysis data.The light green colour represents the parameter points that fit the excesses within a three-dimensional C.L. from 1.5σ up to 1.3σ, whereas the points that fit the excesses at 2σ 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.Fig. 5 depicts the correlation between the normalised couplings of the ≈ 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 bb, τ τ and γγ channels requires an enhancement of the h 125 tt and h 125 bb couplings deviating by ∼ 11.5% from the SM for t t and by ∼ 8% for b b.In contrast, a decrease can be seen in the Higgs coupling to τ τ (c h 125 τ τ ), deviating from the SM value by about 11%.Furthermore, the plot includes green dashed lines representing the current 1σ uncertainties of the normalised couplings c h 125 i 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.with colours corresponding to those in Fig. 4, are illustrated.Also presented are the current 1σ 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 , σ tth 125 /σ SM tth ) plane.The black dashed line corresponds to the observed value from CMS [62] and the lime green (yellow) band represents instead the 1σ (2σ) range.The hatched area denotes the 95% C.L. probability sensitivity of the HL-LHC [63] to the normalised cross section σ tth 125 /σ SM tth , 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 1.5σ C.L or better.represented by the light green colour, fall within the 2σ measurement range of CMS.Additionally, as seen in Fig. 5, these points exhibit an enhancement in the h 125 t t coupling.In fact, due to such an enhancement, these points deviate significantly from the 2σ 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 t coupling.[62] while the lime green (yellow) band denotes the 1.5σ (2σ) range around the observed value.The hatched area illustrates the 95% probability sensitivity of the HL-LHC [63] to the normalised cross section σ tth 125 /σ SM tth , 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 γγ, τ τ and b b anomalies at 1.3 σ C.L. and can be tested at the LHC.On the one hand, c h 125 t t and c h 125 b b are consistently larger than 1, while c h 125 τ τ is consistently smaller than 1.Among these couplings, c h 125 t 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 t pairs, which could then be tested at the (HL-)LHC, via pp → t th 125 , and an ILC 500, via e + e − → t th 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 χ u 33 parameter.This, in combination with the small negative sin(β − α) values preferred in our parameter scan gives rise to the observed enhancement in the h 125 t t couplings (see Tab. 1).

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 γγ, τ τ and b 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 τ τ and γγ as well as produced by Higgs-strahlung at LEP and decaying into b b.
By assuming that the heaviest CP-even Higgs state, H, is the one discovered at the LHC with mass ≈ 125 GeV, we have identified parameter space regions where the lightest CP-even state, h, with a mass of ≈ 95 GeV, can explain simultaneously the observed excesses through a χ 2 analysis at approximately 1.3 σ 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 µ γγ , µ τ τ and µ b b at 1σ 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 → t tH 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 − → t tH 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 tH coupling.Finally, one should stress that the precise measurement of the t tH 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.

Figure 1 :
Figure 1: The colour map of χ 2 γγ+τ τ +b b in the (µ γγ − µ τ τ ), (µ γγ − µ b b) and (µ b b − µ τ τ ) planes of the signal strength parameters for 2HDM Type-III parameter space under study.The ellipses define the regions consistent with the excess at 1σ C.L. The contribution from µ γγ to χ 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 χ 2 from µ τ τ (left frame) comes from CMS data while the contribution from µ b b (middle frame) comes from LEP data.Grey points are excluded by σ(ttϕ) × BR(ϕ → τ τ ) [61].The position of χ 2 95min is marked by a green star.

Figure 3 :
Figure 3: As in Fig. 2, but the colour coding indicates the value of |c h 125 t t| (left) and |c h 125 b b| (right).

Figure 4 :
Figure 4: Allowed points, following the discussed theoretical and experimental constraints, superimposed onto the results of the CMS 13 TeV low-mass γγ [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 1.5σ (χ 2 95 ≤ 5.59) or better, reaching up to 1.3σ, whereas the points that fit the excesses at 2σ or more are shown in red.

Figure 5 :
Figure 5: Correlations between the normalized couplings |c h 125 τ τ |, |c h 125 V V |, |c h 125 t t|, and |c b 125 t b|,with colours corresponding to those in Fig.4, are illustrated.Also presented are the current 1σ 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.

Figure 6 :
Figure 6: Predicted signal strength σ tth 125 /σ SM tth 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 1.5σ (2σ) range around the observed value.The hatched area illustrates the 95% probability sensitivity of the HL-LHC[63] to the normalised cross section σ tth 125 /σ SM tth , centred on the value of the SM (depicted as a solid red line).The colours correspond to those in Fig.4.

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

Table 4 :
The full description of the best fit point χ 2 95,min (green star).