The origin of the 95 GeV excess in the flavor-dependent U(1)X model

This study investigates the excesses observed in the CMS diphoton and ditau data around 95 GeV within the framework of the flavor-dependent U(1)X model. The model introduces a singlet scalar to explain the nonzero neutrino masses. This newly introduced Higgs interacts directly with the quark sector, motivated by the aim to explain the flavor numbers of the fermion sector. Additionally, it undergoes mixing with the SM-like Higgs boson. The study suggests that designating this singlet Higgs state in this model as the lightest Higgs boson holds great potential for explaining the excesses around 95 GeV. In the calculations, we maintained the masses of the lightest and next-to-lightest Higgs bosons at around 95 GeV and 125 GeV respectively. It was found that the theoretical predictions on the signal strengthes {\mu}(h95)_{\gamma}{\gamma}, {\mu}(h95)_{\tau}{\tau} in the flavor-dependent U(1)X model can be fitted well to the excesses observed at CMS.


I. INTRODUCTION
The discovery of a 125 GeV Higgs boson at the Large Hadron Collider (LHC) in 2012 [1,2] stands as one of the most remarkable achievements in theoretical physics.Its properties align well with the predictions of the standard model (SM) [3,4], suggesting the observation of all fundamental particles anticipated by the SM.
The current focus of the LHC program is to determine whether the detected Higgs boson is the sole fundamental scalar particle or part of a new physics (NP) theory with an extended Higgs sector.As of now, no new scalars have been discovered at the LHC.However, there have been several intriguing excesses observed in searches for light Higgs bosons below 125 GeV, accompanied by increasing precision in the measurements of the Higgs couplings to fermions and gauge bosons.
Recently, a new analysis of Higgs-boson searches in the diphoton final state by CMS has further confirmed the excess at approximately 95 GeV.The results are reported in [10].
The authors of Ref. [35] explore the viability of the radion mixed Higgs to be the 125 GeV boson along with the presence of a light radion which can account for the CMS diphoton excess well in the Higgs-radion mixing model.Considering the one-loop corrections to the neutral scalar masses of the µνSSM, the authors of Refs.[36,37] demonstrate how the µνSSM can simultaneously accommodate two excesses measured at the Large Electron-Positron [38] and LHC at the 1σ level.Based on the analysis in Ref. [39], extending the scalar sector with a SU(2) L triplet with hypercharge Y = 0 can well provide the origin of the 95 GeV excesses.Whether certain model realizations could simultaneously explain the two excesses while being in agreement with all other Higgs-boson related limits and measurements were reviewed in Refs.[40,41].
In the flavor-dependent U(1) X model, the new U(1) X charge is related to the baryon and lepton number, and the origin of the number of observed fermion families can be well explained by imposing a relation involved by the color number 3 [42].Because of the Z 2 conservation, the model can contain several scenarios for single-component dark matter.In addition, the nonzero neutrino masses can be obtained elegantly by type-I see-saw mechanism by the new introduced singlet scalar and the nonzero U(1) X charges of neutrinos.As a result, the new introduced CP-even scalar may be assigned to account for the excesses at about 95 GeV.Based on the characters of the new introduced CP-even scalar in the flavor-dependent U(1) X model, we focus on investigating the diphoton and ditau excesses at about 95 GeV in this work 1 .
The paper is organized as follows.The scalar sector and fermion masses terms of the flavor-dependent U(1) X model are given in Sec.II.The numerical results are present and analyzed in Sec.III.Finally, a summary is made in Sec.IV. 1 As analyzed in Refs.[43,44], the light CP-even Higgs does suffers strict constraints from the LHC search for the top-quark associated production of the SM Higgs boson that decays into τ τ , and the possibility to explain the ditau excess by the CP-even scalar is excluded according the analysis in Ref. [44].However, they consider the 1σ range of µ(Φ 95 ) τ τ in the analysis, it is found that this constraint can be relaxed if the 2σ range of µ(Φ 95 ) τ τ is considered.And the coupling properties of 125 GeV Higgs in the flavor-dependent U (1) X model are different from the ones of 125 GeV Higgs in the SM, so the 125 GeV signal strength constraints are also taken into account in the analysis.

II. THE U (1) X MODEL AND ITS HIGGS SECTOR
The flavor-dependent U(1) X model [42] is one of the simplest extension of the SM that introduces a flavor-dependent additional gauge group U(1) X .The gauge group of the model X in the model, and local U(1) X gauge group is not family universal.The new charge X, combines lepton (L) and baryon (B) numbers, are defined as and X depends on family.For each flavor i, X = x i b + y i L, where x i and y i are functions of i for i = 1, 2, ..., N f , while B and L denotes the total baryon or lepton numbers, respectively.
The SM fermions transform under the gauge symmetry as where x i are family dependent, and y i do not.The charges of all fields in this model are presented in Table I, where a = 1, 2, 3, α = 1, 2, and z is arbitrarily nonzero.
This model can explain the origin of the observed number of fermion families and potentially offer solutions for both neutrino mass and dark matter, which differs from the traditional U(1) B−L extension.The total scalar potential in this model is given by [42] where λ's are dimensionless,and µ's have mass dimension.To ensure the stability of the scalar potential, the free parameters The local gauge symmetry SU(2) L ⊗ U(1) Y ⊗ U(1) X breaks down to the electromagnetic symmetry U(1) em as the scalar fields receive nonzero vacuum expectation values (VEV): [42].
Substituting them into the scalar potential Eq. ( 6), the tadpole equations give Due to Z 2 conservation, the dark scalars S 3 and A 3 do not mix with the other scalars and are degenerate in mass.On the basis (S 1 , S 2 , S 3 ), the squared mass matrix of Higgs can be written as where S 1 and S 2 are mixed by the term λ 4 vΛ.The squared mass matrix M 2 h in Eq. ( 10) can be diagonalized by the unitary matrix where m h 1 , m h 2 , m h 3 are the physical Higgs masses.And under the assumption v/Λ ≪ 1, λ 2 ≪ 1 and λ 4 ≪ 1, we can obtain Z h can be parameterized as where the mixing angle cos where a, b = 1, 2, 3, α, β = 1, 2. The fermion-antifermion-higgs couplings on the interactional basis can be written as It is worth noting the presence of additional terms compared to the quark mass matrices in the SM, such as 2M (vū 3L S 2 u αR + Λū 3L S 1 u αR ) in the up-quark sector and etc.Under the minimal flavor violation assumption [45][46][47][48][49] which can release the model from the experimental constraints on the processes mediated by flavor-changing neutral currents (FCNCs), the fermion-antifermion-higgs couplings on the physical basis h 1 f m i f m i , (q = u, d, e) can be written as Here, the contributions from the additional terms in the quark sector are absorbed into the constants κ 1 and κ 2 with where m q i denotes the i − th quark q mass, Z q L and Z q R are the unitary matrices which diagonalize the mass matrix of quark q, and (i, i) denotes the i − th diagonal element of matrix.It is obvious that κ 1 , κ 2 depend on the parameters Λ, M and the Yukawa coupling constant complicatedly.For simplicity, as shown in Eq. ( 16), we take the diagonal elements of the matrices defined as κ 1 m d i , κ 2 m u i as inputs to carry out the analysis.
As defined in the introduction sector, the diphoton and ditau signal strength are where [50] Γ SM tot,95 ≈ 0.00259 GeV, BR(h and the top quark loop is considered in calculating the production cross section of the 95 GeV Higgs at the LHC for simplicity.The contributions from NP can be written as [24] Γ NP tot,95 ≈ C where the coefficients C h 95 uu , C h 95 dd , C h 95 ee are the normalized couplings of 95 GeV Higgs in NP models with SM particles (in units of the corresponding SM couplings).In the conventional U(1) X model, we have As shown above, the extra scalar singlet (which is designed to be the 95 GeV scalar state) couples to the SM quarks at the tree level, and the corresponding effects are collected to the newly defined parameters κ 1 , κ 2 .Hence, there are two sources to accommodate the excesses in the diphoton and ditau channels in the model.The first one comes from the tree level couplings between the extra scalar singlet with the SM quarks, and the second one comes from the mixing of the 95 GeV scalar state with the 125 GeV one.It indicates that the 125 GeV Higgs boson signal strength measurements should to be considered in the analysis.
Generally, the signal strengths for the 125 GeV Higgs decay channels can be quantified as [51] µ(h 125 where ggF and VBF stand for gluon-gluon fusion and vector boson fusion respectively.The corresponding SM decay width and fractions can be found in ref [52].The contributions from NP can be written as where the coefficients C h 125 uu , C h 125 dd , C h 125 ee and C h 125 V V are the normalized couplings of 125 GeV Higgs in NP models with SM particles (in units of the corresponding SM couplings).
In the conventional U(1) X model, we have
Because Λ affects the 95 GeV Higgs signals and 125 GeV Higgs signals mainly through the mixing effects of S 1 and S 2 as shown in Eq. ( 13).It is obvious that the dependence of A on Λ by the terms λ 4 Λ and λ 2 Λ 2 , and both the two terms depend on λ 1 for fixed m h 1 , m h 2 as shown in Eq. ( 27).Hence, the excesses are satisfied quite independent of the value of Λ, while λ 1 is strictly limited.In addition, Eq. ( 12) shows that the SM-like Higgs mass m h 2 mainly depends on λ 1 which also leads to the strict constraint on λ 1 .κ 1 and κ 2 are also limited strictly as shown in Fig. 3

Firstly, we investigate 1 versus λ 1 4 0FIG. 2 : 2 |FIG. 3 :
Fig. 1 (b).It can be observed from the plot that λ 1 and λ 2 significantly influence the masses of the two light Higgs bosons, and both m h 1 and m h 2 increase as λ 1 increases.Notably, both the 95 GeV Higgs and the SM-like Higgs with a mass of 125 GeV are attainable within the model.Fig. 1 (a) shows that λ 2 is constrained around 0.00003 with λ 1 slightly less than 0.1 for m h 1 ≈ 95 GeV and m h 2 ≈ 125 GeV in our chosen parameter space.λ 1 , λ 2 and λ 4 (a) and Fig. 3 (b), the Higgs mixing parameter |Z h,11 | versus Λ is plotted in Fig. 3 (c).
(b), by all the constrains taken into consideration.The diphoton and ditau excesses at about 95 GeV prefer the ranges 0.128 > ∼ λ 1 > ∼ 0.127, 0.52 > ∼ κ 1 > ∼ 0.45 and 0.22 > ∼ κ 2 > ∼ 0.12.Fig. 3 (c) shows that |Z h,11 | is located in the range 0.15 < ∼ |Z h,11 | < ∼ 0.17, because the 95 GeV state is dominated by the extra singlet scalar in the model and the Higgs squared mass matrix in Eq. (10) is written on the basis (S 1 , S 2 , S 3 ).Finally, provided that the excesses persist, the precision measurement of the 125 GeV Higgs couplings has potential to detect this scenario, because the introducing of a light Higgs boson below 125 GeV changes the coupling properties of 125 GeV Higgs.IV.SUMMARY Considering the diphoton and ditau excesses at a mass about 95 GeV in the CMS data, we focus on explaining these two excesses in flavor-dependent U(1) X model, because the model can produces a 95 GeV light Higgs naturally by introducing the specific singlet state.And this new scalar state interacts with the quark sector directly to explain the flavor numbers of the fermion sector, which provides great potential to explain the two excesses.Considering the specific Higgs state as the lightest Higgs boson, it is found that the specific parameters λ 1 , λ 2 , λ 4 and Λ in the model affects the theoretical predictions on the two light Higgs boson masses significantly.Taking the lightest Higgs boson mass at about 95 GeV and the nextto-lightest Higgs boson mass at about 125 GeV, the numerical results show that the specific Higgs state in flavor-dependent U(1) X model can accounts for the observed CMS diphoton and ditau excesses at about 95 GeV well.In addition, fitting µ(h 95 ) γγ , µ(h 95 ) τ τ in the CMS 1σ interval will impose stringent constraints on the parameter space of the flavor-dependent U(1) X model, and the fact can be seen explicitly in Fig. 3.
After spontaneous symmetry breaking, the fermion mass terms are given by the Yukawa couplings L ∼ h e ab laL Φe bR + h v ab laL Φν bR + 1 2 f ν ab νc aR ν bR χ + h d αβ qαL Φd βR + h u αβ qαL Φu βR