In this section, we focus on contribution of non-fermions which provide kinetic mixing in the model. Our set of model will discuss in Sec.VI C which consider a renormalizable model, thus the anomaly cancellation and wave function renormalizable is discussed. Phe-nomenology based on similar model has been studied before. Further detail could find in references, especially in Refs. [24, 31–34]. In Sec.VI D, we discuss the possible decay modes of the SM-Higgs(h1) outside those of the SM and SM Z boson decay to non-SM particles process with constraint from LHC experiment. In Sec.VI E, we compare each fix target beam dump experimental searchs range [35, 36, 38–55] with our estimation of constraints, and the perturbative yukawa coupling, neutral pseudoscalar meson decay also considered.
A. Kinetic Mixing
Suppose our world exist non-Standard Model gauge symmetry U (1)D and consider two fermions which carry the Standard Model U (1)Y hypercharges Y1 and Y2, and those fermions also having the U (1)D charges Q1 and Q2. If we assume the charges satisfy the relation[5]:
Q1Y1 = −Q2Y2. (203)
In this way, the Fig.26 will contribute a scale independent effective Lagrange term(gauge field kinetic terms):
Lef f ective = −
2FYµνFD,µν, (204)
and where kinetic mixing factor is a scalar quantity which depend on mass of fermions and charges, and the scale depend part and infinite term was canceled by two fermion contribution. The U (1)D probable having the interaction with other non-Standard parti-cles(may Dark Matter(DM) candidate), therefore this is a way to contact SM particle with non-Standard particles. In this paper, we assume the 1.
FIG. 26: In our model, the propagators at the loop are non-Standard model fermions F , which provide the kinetic mixing term in Eq. 204.
B. Experiment Data
1. Fixed Target and Beam Dump Experiments
For small kinetic mixing factor range( 1), we can write the approximately interaction form[34]:
Lint ' −eJemµ γD,µ (205)
where Jemµ is Standard Model charged current. This effective Lagrange is via a loop diagram like Fig.26. The interaction between γD is indirect from factor . Through this effective interaction form, thus we can draw that the experiment searching area Fig.27.
We are interesting in searching for a new light U (1)D massive gauge boson in fixed target and beam dump experiments [39–41, 43–48], that focus an electron scatters off the target it bremsstrahlung a light gauge boson which subsequently decays to a lepton pair [50]. The low energy e+e− experiments [43, 49] and meson decays experiments [43, 51] also can be used to search new light vector boson. These searches typically depend on finding resonances in the resulting di-lepton spectrum [26]. In Fig.27 we show the experiment search areas from low energy e+e− experiments [43, 49], meson decays experiments KLOE [51] and BaBar [39, 43]
(an estimation results [26, 52]), fixed target experiments MAMI(Mainz) [46] and APEX [47], the beam dump experiments E137, E141, and E774 [52], the ae(aµ) is consistent electron and muon anomalous magnetic moment experiment result areas [34], and the parameter space can be probed by several proposed experiments, including by DarkLight [53], HPS [54], VEPP-3 [55].
In this paper, we will also discuss that the Standard Model Higgs decays and Z boson decays mode constraints(using LHC[35, 36] and Particle Data Group(PDG)[61] results) to
FIG. 27: we show in more detail the parameter space for larger values of . This parameter space can be probed by several proposed experiments, including APEX[47], HPS[54], VEPP-3[55],
DarkLight[53], Mainz[46], Babar[39], KLOE[51] and E774, E141, E137[52]. The ae(aµ) is consistent electron and muon anomalous magnetic moment experiment result areas [34]
our parameter space, and then compare the Fig.27 to point out that probable kinetic factor
and mass of light U (1)D range.
Very small strength is possible existed, that may imply which two-loop or three-loop is dominant for kinetic mixing. In very small range 10−10 . . 10−7 exist the constraint from supernova cooling [72], and fermion Dark Matter(only carry dark charge) annihilate analysis [73] which discussed the three possible cooling phases, the very low DM density, the intermediate DM density and the sufficiently high DM density.
2. ATLAS and CMS Results
The latest experimental values of LHC results are given in Refs. [35, 36, 58] for the ATLAS Collaboration and the CMS Collaboration, giving the averaged signal strengths [58]11
µexpγγ = 1.22 ± 0.31, µexpZZ∗ = 1.21 ± 0.35, (206)
11 The search for the SM Higgs boson in the decay of Zγ mode has also been done by the CMS result [37].
The observed 95% C.L. upper limit for the cross cestion are between about 4 and 25 times the standard model crosse section times the branching fraction. The observed and expected limits for invariant mass at 125GeV.
For µexpγγ of the CMS Collaboration, we take the value based on the MVA method [36]. Where the signal strengths is defined by
µRefX ≡ ρRefh × Br(h → X)Ref
ρSMh × Br(h → X)SM, (207)
where ρRefh (ρSMh ) and Br(h → X)Ref(Br(h → X)SM) are the reference value(SM prediction) of the Higgs production cross section and that of the branching fraction of the h → X decays, respectively.
3. Higgs and Z boson Decay to Invisible
The global fits [60] for the signal strengths of the various SM Higgs decay channels from the LHC data imply the total width of the SM Higgs is about 4.03 MeV and the non-standard (decay to invisible) width for the SM Higgs can be at most 1 MeV. In other words, the non-standard branching ratio for the SM Higgs must be less than 22%. One can use this result to constrain the parameter space of the model, and another one can constrain our model for Z boson decay [32, 61, 62] and Dark matter annihilating [23–25, 31, 63–65]. Experiment give us the constraint of Z decay to invisible must be less than 20%. The decay of Z boson to left hand neutrino is Eq. 208
Γν = Γ(Z → ¯νν) = 4Γ0(gAν2 + g2V ν) = 8Γ0gν2 (208) The parameter gν and Γ0 is equal to 0.5 [61] and 82.94 GeV [62], respectively. We can estimate Z decay to other(without left hand neutrino) invisible particles is
Γ(Z → invisible) − Γ(Z → ¯νν) = 499 − 82.94 × 3 × 8 × 0.52 ∼ 1.36M eV,
where 499 MeV is decay width of Z → invisible, and the factor 3 is family of neutrinos.
That implies Br(Z → other invisible) ∼ 0.052%. This value is allowed by the LEP bound Γ(Z → other invisible) < 2.0 MeV [42].
Another one thing is constrained from Dark matter annihilating [24], in our model U (1)D gauge boson(γD) is a Dark matter candidate , that can annihilating to mediator matter then create Standard Model particles.
We will compute the following non-standard processes h1 → γDγD, h1 → h2h2, h1 → ¯FiFi and Z → γDγD, Z → γDh2, Z → ¯FiFi12, which shown in Fig. 28. The light of F had discussed [32]. Other authors in [68] have looked at hidden-valley like models or
milli-FIG. 28: Possible processes for H and Z bosons decay into invisible particle at one loop level triangle diagram.
charged [69] dark matter are concentrating their study to heavy γD, which assume mass of γD is bigger than few (or more) GeV, and the discussion of effective Lagrangian could be found in Ref.[59]. Here we assume mass of γD is less than 2 GeV, because we had absence of any observed proton excess from cosmic-ray, with a dark boson γD that has a mass below the proton-antiproton kinematic threshold of ∼ 2 GeV. Such low-mass dark photons can decay to electrons, muons, and pions, whereas decays to protons are kinematically forbidden [35].
Our Model exist process Z → γDγD and H → ZγD that given a possibility to predict more lepton,quark or pion jets signal in future from experiment LHC or ILC [29]. Vertex HZγD
also given a possibility process to produced the Higgs.
Limitation for invisibly decay of a dark Higgs boson with mass as low as 1 GeV had been reported by OPAL [38]. For a 1 GeV dark Higgs boson mass, an upper limit for the mixing angle of sin2α ≤ 10−3 can be extracted from the discussion in Ref. [70]. However, the exclusion curve on the Higgs mass versus mixing angle plot also given in [70] was obtained under the assumption would lead to larger mixing angle for a given Higgs mass. Other decays of Z boson will be shown in next section.
C. The Model
In this section, we consider that the gauge boson exist an interaction with fermions Fi from the hidden sector. Here we assume an extra dark gauge U1 in our model which mass could produce from dark Higgs(hD) via spontaneous symmetry breaking [1]13.
12 Decay to ¯FiFi may forbid by kinetics 2mF>mZ
13 We assume the mass of non-SM fermions is from hidden Higgs χ, because the SM Higgs(v = 246 GeV ) can’t afford too much heavy particles, which the limitation is from perturbative constraint, and allow maximal masses of fermions can be raised to 246√
4π/√
2 ∼ 650 GeV. [56]
1. Scalar and Vector Bosons
L = LSM+ LDarkU1 + LFermion (209) with
LDarkU1 = |DµΦ|2+ |Dµχ|2− Vscalar(Φ, χ) − 1
4CµνCµν −
2BµνCµν , (210) LHidden ⊃X
f,b
a ¯Ffγµ(Vf,b− Af,bγ5)Ff Vµb (211)
and
DµΦ =
∂µ+ ig1
2σaWaµ+ i1 2gYBµ
Φ , (212)
Dµχ = (∂µ+ igDCµ) χ , (213)
Vscalar = −µ2ΦΦ†Φ + λΦ Φ†Φ2
− µ2χχ∗χ + λχ(χ∗χ)2+ λΦχ Φ†Φ (χ∗χ) . (214) We pick the unitary gauge and expand the scalar fields around the vacuum,
Φ(x) = 1
√2
0
v + h(x)
, χ(x) = 1
√2(vD+ hD(x)) (215) with the VEVs v and vD. Where f is index of non-SM fermions, and the index b is gauge boson B, W0 or C. Bµ being the gauge field for the hypercharge, and Cµ is the gauge field of extra U1. The couplings are defined such that a = 1(1/2) for Dirac(Majorana) fermion. Eq. (211) build the interaction between non-SM fermions with gauge bosons. Here the interaction term could neatly write after spontaneous symmetry breaking:
JFµVµ = ¯Ff[γµQf(Vf0− A0fγ5)γD,µ+ γµ(Vf − Afγ5)Zµ+ γµVfaAµ]Ff (216) where the vector vertex Vf and Af is define in next subsection(VII), The U (1)D charge Qf should satisfy anomaly cancellation [57], that will discuss in next subsection also. The Vfa → 0 for neutral particle. When the 1 the Vf, Af and Vfa is approximated
Vf ' g cosθW(1
2Tf3− Qesin2θW), Af ' g cosθW
1
2Tf3, Vfa ' Qee. (217) where g is SU (2)L coupling constant.
2. Kinetic Mixing and Fermions
We have to make sure that the non-SM fermions will contribute the kinetic mixing term and all of our model is renormalizable. All the anomalies that involve only the SU (3)c, SU (2)L, U (1)Y and U (1)D factor vanish identically, and the anomaly places an important constraint on model building: The theory must be anomaly-free[66] thus the anomaly can-cellation is request. We can easily to write the restriction:
• Anomaly-free U (1)D
Holdom Kinetic Mixing and wave function renormalizable request14 U (1)D–U (1)Y : X
f
QfYf = 0 (218)
U (1)D–SU (2)L : X
f
QfTf3 = 0 (219)
Anomaly cancellation
U (1)D–SU (2)L–SU (2)L : X
f
Qftr[Ti(2)Tj(2)] = 0 (220) U (1)Y–SU (2)L–SU (2)L : X
f
Yftr[Ti(2)Tj(2)] = 0, (221)
as easily to know that at least existing two fermion having U (1)D charge(Qf) for Anomaly-free U (1)D Model, and the simplest model is that one of the two fermions having posi-tive charge, another one having negaposi-tive charge and all the fermions don’t carry Weak-Isospin(Tf3) (showing VII). In this way, the fermions are satisfy all the restriction. As above formulae, existing a freedom is that we can chose the difference sign either Qf 1, Qf 2 or hyperchange(Yf 1, Yf 2), which will affect a few decay mode, for example: the two fermions contribute a addition of h1 → h2γD amplitude by difference sign between Yf 1, Yf 2, another case is subtraction.
14 Here we assume the fermions having no SU (3)c colors.
• Anomaly U (1)D
Holdom Kinetic Mixing and wave function renormalizable request15 U (1)D–U (1)Y : X G(3) = SU (3) algebras respectively, specifically If3 is fermion’s weak-isospin(±12). In our no-tation T r[TiaTka] = 12δij. All the remaining anomalies that involve U (1)0s vanish identically due to group theoretical arguments (see Chapter 22 of [86] and [57]). If the fermions simul-taneously carry SU (2)L Weak-Isospin and U (1)D charge (Qf) but no hypercharge(thus no kinetic mixing), we have four fermions at leastN, and then if the fermions are charged under SU (2)L, U (1)Y and U (1)D, at least our model exist eight fermions to meet all the require-ments of the formulae, and where assume that all the charges quantum number is integer.
Consider a mixing self-energy between U (1)D and SU (2)Ldiagram, and it’s contribution Γµν form a fermion is
15 N In order to U (1)D–SU (2)L is renormalizable only if the fermion mass satisfy relationship Eq.231.
FIG. 29: The mixing between anomaly gauge boson U (1)D and SU (2)Lvia the fermion loop is shown.
and the infinite term is QfIf3
δ
(gµνk2− kµkν)(vfv0f + afa0f)
12π2 − afa0f m2f 2π2
(229) where δ → 0 and the Λ is energy scale, vf(v0f) and af(a0f) is vector coupling and axial vector coupling between SU (2)L(U (1)D) and fermion, respectively. The first term in Eq.229 is cancelled by Eq.222, thus the infinite term can be rewritten to
inf inite term ∝ QfIf3m2f (230) as the result, in order to the mixing self-energy diagram of anomaly U (1)D-SU (2)L is finite only if the fermion mass satisfy relationship
X
f
QfIf3m2f = 0, (231)
which probably imply some symmetry is existed. By the way, if U (1)D couple to left hand neutrino[100] at tree level, at least we need three(or more) non-SM fermions in the model, and the particles carry very small coupling constant gD . 10−5[85].
In order to estimate the impact on the phenomenology of the fermions, this subsection consider the two simple case(see Table VII)
• Toy Model I
In first case, We added extra two fermions in the model, and we also assume that those fermions are Dirac fermion and the U (1)D is a anomaly-free gauge symmetry, therefore we have the coupling form:
Vf0 ' gD, A0f ' 0, (232)
TABLE VII
Type U (1)D Anomaly Field SU (3)c rep. SU (2)L rep. U (1)D(Qf) I3(SU (2)L) Y (L,R) Electric(Qe) Mass[GeV][61]
F1 1 1 +1 0 +1 1 mf 1 > 102.6
Toy I × F2 1 1 +1 0 -1 -1 mf2 > 102.6
F1 1 1 +1 0 +1 +1 mf 1 > 102.6
F2 1 1 +1 0 -1 -1 mf 2 > 102.6
Toy II X F3 1 1 -1 0 +1 +1 mf 3 > 102.6
F4 1 1 -1 0 -1 -1 mf 4 > 102.6
and the kinetic mixing term L ⊃ −1
2BµνCµν− mf 1
vD/√
2χ0F1F¯1− mf 2
vD/√
2χ0F2F¯2, (233) with
= gYgD
6π2 log(mf 1
mf 2), (234)
where the gY is U (1)Y coupling constant. We also assume that the mf 1 > mf 2, and those values must be heavier then 102.6 GeV[61]. In order to satisfy gauge invariance, we adding a extra singlet scalar Higgs(χ0) in the last two term of Eq.233, and it don’t couple to other particles but it have the mixing term in scalar potential Eq.214. In order to simplify the parameter space, where we assume either the mass eigenstate of non-SM higgs is very lighter( mz) particles16 or all the scalar mixing angles are much smaller than 1, otherwise our some results are failed, those are only process h2 in the external legs.
• Toy Model II
The Toy Model II consider four non-SM fermions, and a anomaly gauge boson γD, thus we can write
Vf0 ' gD, A0f ' gD, (235)
and the Lagrange non-SM fermions part is L ⊃ −2
2BµνCµν −
4
X
i
mf,i vD/√
2χFi,RF¯i,L+ h.c. (236)
16 Therefore sinα is represented two mixing angle(χ0− h and χ − h) both for the following article.
with the kinetic mixing factor
= gYgD
6π2 log(mf 1mf 4
mf 2mf 3). (237)
In the Toy Model I, the process of gauge boson decay to two gauge boson via the fermions loop is vanish by anomaly cancellation[57], unless the model exist chiral vertex between the fermions and gauge boson(as Eq.235), therefore this model exists process Z → γγD and Z → γDγD (Z → γγ is forbidden by [82]), those don’t exist in Toy Model I. For ease of discussion, we assume that the mf 1 ' mf 3 ' mf 4 in our paper, and the yukawa terms are gauge invariance in Eq.236.
3. Mass Eigenstate
In our model having the two scalar bosons h(x) − h∗D(x)17 mixing and the three gauge bosons Bµ− Wµ3 − Cµ, this section try to diagonal the mass matrix and work out the form of mixing angles. Finally, we show the Feynman Rules which are used in our calculation.
Scalar Mixing
The mass matrix MS2 from Eq. (214) for the scalar bosons is given by MS2 =
17 Where assume taht the h∗D is the one which will couple to non-SM fermions in Toy Model, and we don’t consider the other two mixing angles because they are don’t effect to our phenomenology results if either all the mixing angles between scalars is much smaller than 1 or two lighter scalars mass are very light( mz).
The heavier Higgs h1 is identified as the new boson observed recently at the LHC[35, 36]
having a mass m1 = 126 GeV, while the lighter one h2 has yet to be discovered by experi-ments.
Vector Boson Mixing
In additional to the mass mixing of the three neutral gauge bosons arise from the spon-taneously electroweak symmetry breaking given by
Lm = 1
with the following mass mixing matrix
M2 =
The following mixed transformation diagonalizes the above mass mixings and the kinetic mixing from the last term in Eq. (210) simultaneously [76]
where AD, , Z and A are the physical dark photon, Z boson and the photon respectively.
Here K is a general linear transformation that diagonalizes the kinetic mixing
K = with the mixing angles defined as
tan θ = gY
After the K transformation, the gauge bosons mass matrix is
The O matrix diagonalize this ˜M2 matrix
MDiag2 = OT · ˜M2· O =
with the following eigenvalues (assuming mγD ≤ mZ18) m2γ = 0, m2z,γ For small kinetic parameter mixing , the Z and γD masses can be approximated by mz ≈p(g2+ gY2)v/2 and mγD ≈ gDvD. is based on this Feynman Rules.
18 For the case of mγD > mz, we will have m2z,γ
D = (q ∓ p)/2 the case which has been studied previously [76], which diagonal method is different with [33, 34]
D. Phenomenology
In this section, we do calculate and discuss the non-SM process for h1 and Z boson decay modes, and all the numerical results are based on toy Model I. Only if the three gauge boson external legs diagram(for example Z → γγD) is vanish by anomaly cancellation in Toy Model I, therefore the Toy Model II is used in three gauge bosons process. The non-SM parameter sinα, , mγD, mf 1 and mf 2 are focused in our discussion.
1. Standard Higgs h1 decay modes
Non-SM process in h1 decay modes have h1 → γγ and h1 → ZZ∗ via non-SM fermions loop, and the h1 → non-SM invisible(h2 or γD) particles.
h1→ γγ
The decay width for h1 → γγ can be adapted from an earlier calculation in a different context [87, 88]
i indicates all possible diagrams, and the Qi(Nc) is the electric charge(colors) of the particle at the loop.
with
τ± ≡ 1
2(1 ±√
1 − τ ). (258)
Since the SM particles W±, t-quark19 and the non-SM particles F in Eq.253, therefore we separate the SM amplitude and non-SM amplitude as
Γ(h1 → γγ) = Gfm3h
Recall the Sec.VI C 3 and Table.VII Model I, as we know that non-SM parameter sinα, mγD and is only depends on h1F F coupling, thus we find
AnonSM ∝ sinα ×
mγD × AF(mf 1, mf 2), (260) and the numerical results are shown by Fig.30. We use the LHC h1 → γγ result and the blue line is taken mγD = 10−2.5, = 10−4.5, the green line is taken mγD = 10−3, = 10−4.5, the
200 400 600 800 1000
200 mγD = 10−3, = 10−4 and the lighter color is theirs experimental error-bar. In particular, the yellow area is error-bar for parameter mγD = 10−3, = 10−3.6, and all the color areas is taken
sinα = 10−3.
19 Ignore other lighter particles.
red line is taken mγD = 10−3, = 10−4 and the lighter color is theirs experimental error-bar.
In particular, the yellow area is error-bar for parameter mγD = 10−3, = 10−3.6, and all the color area is taken sinα = 10−3. As the Fig.30 shown, we could estimate that at least the constraints from LHC 2013 result(Recall the Sec.VI B) h1 → γγ is
sinα ×
mγD . 10−3.4GeV−1 (261)
Otherwise parameter space is Rule-Out, and the estimating is taken the region of fermions mass 0 . mf 1, mf 2. a few TeV.
h1→ ZZ∗
The non-SM fermion also couples to Z boson thus that contribute the process h1 → ZZ∗ in Next-Leading-Order(NLO).
FIG. 31: Feynman diagrams for the h1 → ZZ∗ decay mode which also define the momentum index.
We reduce the tree level contribution and effective 1-loop function in AZ and BZ20 (refer appendixVI F) which is function of off-shell Z boson momentum k1. The amplitude is21 :
M (h1 → ZZ∗) =(AZgµα+ BZTµα) −i
D(k1, mz, ΓZ)gµν − kµ1k1ν/m2z ¯uγν(gvz− gazγ5)vα,
=(AZgνα+ BZ0 Tνα0 ) −i
D(k1, mz, ΓZ)uγ¯ ν(gzv− gzaγ5)vα, (262) where we also reduce the
(AZgµα+ BZTµα)(gµν− k1µk1ν/m2z) → (AZgαν + BZ0 Tα0ν) (263)
20 In our model, the AZ and BZ include the contribution from non-SM fermion loop and SM tree level.
21 The off-shell Z boson have to decay to lighter particles and we assume those mass are ignored.
and we define
BZ0 Tα0ν ≡ − AZk1µk1ν/m2z+ BZTµα− BZk1µk1νTµα/m2z, (264) D(k1, mz,ΓZ) ≡ k21− m2z+ iΓZmz, (265) and the amplitude square is :
X The three body decay width following as :
Γh1→ZZ∗ = 1
The numerical results of Eq.266 is shown by Fig.32, which use the LHC h1 → ZZ∗ result and the Brown line is taken mf 1 = 500GeV , mf 2 = 100GeV , sinα = 10−4, the Blue line is taken mf 1 = 250GeV , mf 2= 100GeV , sinα = 10−3, the Green line is taken mf 1= 500GeV , mf 2 = 100GeV , sinα = 10−3, the Red line is taken mf 1 = 250GeV , mf 2 = 200GeV , sinα = 10−3, the Orange line is taken mf 1 = 500GeV , mf 2= 100GeV , sinα = 10−2 and the Lighter Green is error-bar of Green line. In particular, the Black Dot-Dashed is upper limit for that taken sinα = 10−3 and arbitrary combinations of (mf 1, mf 2) value22.
Comparing the Fig.27 and Fig.32, if our model can satisfy the demand of g − 2, we have a estimating
sinα . 10−6 (268)
22 The µZZ∗ = 1.21 line is always in the lower righter than upper limit, whether what value is mf 1, mf 2(smaller than a few TeV).
mf1 mf 2= 100GeV , sinα = 10−2 and the Lighter Green is error-bar of Green line. In particular, the
black dot-dashed is upper limit for that taken sinα = 10−3 and arbitrary combinations of (mf 1, mf 2) value.
at least for fermion mass in the region 0 . mf 1, mf 2 . a few TeV. We also compare Collider experiment(LHC) with the fixed target experiment, the experiment HPS, APEX, E141 search region in LHC error-bar if sinα . 10−5, and Dark Light VEPP-3 search region in LHC error-bar if sinα . 10−6.
h1→ Invisible
Our model exist the two non-standard decay modes which are h1 → h2h2 and h1 → γDγD. The decay width formulae are shown in appendixVI F, and both of two decay modes considered to Next-Leading-Order(NLO). The numerical results of h1 → γDγD are shown by Fig.33 left, another decay mode h1 → h2h2 is shown by right. The Red region is taken parameter mγD = 10−1GeV , = 10−7 and the Green region is taken parameter mγD = 10−1.5GeV , = 10−7 and the Blue region is taken parameter mγD = 10−1GeV , = 10−6 and all the region is taken sinα = 10−3. The → 0 case is already discussion in [28].
mΓD= 10- 1
200 400 600 800 1000
200
200 400 600 800 1000
200
As Fig.33, the heavier fermion mass is in the region 150GeV . mf 1 . 800GeV , and another lighter fermion mass is in the region 100GeV . mf 2 . 150GeV , if the sinα &
10−3, mγD & 10−1GeV and & 10−6. It estimating a fermion mass region, and more phenomenology are discussed in Sec.VI E.
2. Standard Z boson decay modes
Non-SM process in Z decay modes have the Z → γγD and Z → γh2 via the non-SM
Non-SM process in Z decay modes have the Z → γγD and Z → γh2 via the non-SM