]>PLB34558S0370-2693(19)30238-210.1016/j.physletb.2019.04.006The AuthorsPhenomenologyFig. 1Feynman diagram to generate the masses of μL.Fig. 1Fig. 2The running of g2 in terms of a reference energy of μ, where the black line corresponds to mth=10 TeV, the red line corresponds to mth=1.0 TeV, and the blue one does mth=0.1 TeV.Fig. 2Fig. 3Relic density of DM as a function of DM mss fixing mϕ = 400 GeV, vφ = 2000 GeV and sinα=0.1.Fig. 3Fig. 4A line of the maximum absolute value of yD(=Max[|yD|]) in terms of the DM mass MX≡Mχ1, where the left(right)-hand side shows the bench mark point 1(2), and the horizontal line represents the perturbation limit; 4π.Fig. 4Fig. 5Line of Δaμ in terms of MX, where the left(right)-hand side shows the bench mark point 1(2). The green region is expected to be detected by the experiment that covers over Δaμ = (26.1 ± 16.0)×10−10 at 2σ C.L.Fig. 5Table 1Charge assignments of the our lepton and scalar fields under SU(2)L × U(1)Y × U(1)L × Z2 with ℓ ≠ 0, where the upper index a is the number of family that runs over 1-3, all of them are singlet under SU(3)C, and the quark sector is same as the SM one.Table 1LLaeRaψaχRaH2H3H4φ

SU(2)L21412341

U(1)Y−12−1−120120120

U(1)Lℓℓℓℓ000−2ℓ

Z2+++−++−+

Table 2Some final states from doubly charged lepton pair production with values of σ(pp → ψ++ψ−−)BR fixing M1 = 500 GeV.Table 2Signal4ℓ+4ℓ−E̸T3ℓ+3ℓ−2jE̸T2ℓ+2ℓ−4jE̸T4ℓ±3ℓ∓2jE̸T3ℓ±2ℓ∓4jE̸T3ℓ+3ℓ−4j

σ ⋅ BR [fb]0.00970.190.970.0530.0530.072

Inverse seesaw model with large SU(2)L multiplets and natural mass hierarchyTakaakiNomuraa⁎nomura@kias.re.krHiroshiOkadabokada.hiroshi@apctp.orgaSchool of Physics, KIAS, Seoul 02455, Republic of KoreaSchool of PhysicsKIASSeoul02455Republic of KoreabAsia Pacific Center for Theoretical Physics, Pohang, Geyoengbuk 790-784, Republic of KoreaAsia Pacific Center for Theoretical PhysicsPohangGeyoengbuk790-784Republic of Korea⁎Corresponding author.Editor: G.F. GiudiceAbstractWe propose an inverse seesaw model with large SU(2)L multiplet fields which realizes natural mass hierarchies among neutral fermions. Here, lighter neutral fermion mass matrices are induced via two suppression mechanisms; one is small vacuum expectation value of SU(2)L triplet required by rho parameter constraint and the other is generation of Majorana mass term of extra singlet fermions at one-loop level. To realize the loop masses, we impose Z2 symmetry which also guarantees stability of a dark matter candidate. Furthermore, we discuss anomalous magnetic moment and collider physics from interactions of large multiplet fields.1IntroductionsA model of inverse seesaw [1,2] or linear seesaw [2–4] is well-known as one of the elegant mechanisms to generate Majorana masses for active neutrinos, including both the left and right handed heavier neutral fermions. Thus, it is frequently discussed in a larger gauge theory such as SU(2)L×SU(2)R [5], (SU(2)L×SU(2)R⊂)SO(10) [6], SO(10) with supersymmetry [7] etc., as an unified theory. On the other hand, there are several issues which should be improved in these models. A representative issue is how to describe more natural hierarchies among neutral fermion mass matrices. For example we need to assume small Majorana mass for singlet fermion in realizing inverse seesaw mechanism unless there is a way to justify the smallness. In addition, small Yukawa couplings are required to obtain Dirac mass term among SM neutrinos and singlet fermion to fit neutrino oscillation data with TeV scale heavy neutrinos. It could not be well explained by simple gauge extended scenarios of the standard model (SM).11In ref. [8], small Majorana mass in inverse seesaw mechanism is induced by a small VEV generated by supersymmetry breaking renormalization group equation effect in a supersymmetric model.In this letter, we realize the inverse seesaw mechanism of natural hierarchies among neutral fermion mass terms by introducing extra fields with larger SU(2)L representations and applying radiatively induced mass mechanism for Majorana mass term. In order purely to realize inverse seesaw, we impose a global U(1) lepton number that forbids linear seesaw. A scalar field with larger SU(2)L representations restricts their vacuum expectation values (VEVs) to be or less than the order of 1 GeV by constraint from ρ-parameter [9–15]. In this model SU(2)L triplet scalar develops a VEV which provides Dirac mass among the SM neutrino and singlet fermion which are typically 1 GeV or less because of the restricted VEV. The Majorana mass term of singlet fermion is generated at one loop level providing an additional loop suppression factor [16] where we impose a Z2 symmetry to realize the mechanism. As a bonus of this additional symmetry, we have a dark matter (DM) candidate. Furthermore, we also explain anomalous magnetic moment of muon and discuss collider physics focusing on interactions of large multiplet fields.This letter is organized as follows. In Sec. 2, we review our model and formulate the Yukawa sector and Higgs sector, remormalization group equations (RGEs), lepton flavor violations (LFVs), muon anomalous magnetic moment, and DM candidate. In Sec. 3, we show numerical analysis at a benchmark point including all the constraints and discuss collider physics. Finally we devote the summary of our results and the conclusion.2Model setup and constraintsIn this section we introduce our model. First of all, we introduce a global U(1)L symmetry to obtain a successful inverse seesaw model, which will be spontaneously broken. Also we impose Z2 symmetry in order to realize natural hierarchies among neutral fermions and assure a stable DM candidate, as we will discuss below. As for the fermion sector, we introduce three families of vector fermions ψ with (4,−1/2,ℓ,+), and right-handed fermions χR with (1,0,ℓ,−), where each of content in parentheses represents the charge assignment of (SU(2)L,U(1)Y,U(1)L,Z2) symmetry. As for the scalar sector, we add a triplet scalar field H3 with (3,0,0,+), a quartet inert scalar field H4 with (4,1/2,0,−), and a singlet scalar field φ with (1,0,−2ℓ,+), where SM-like Higgs field is denoted as H2. Here we write vacuum expectation values (VEVs) of H2,3 and φ by 〈H2,3〉≡v2,3/2 and 〈φ〉≡vφ/2 which induces the spontaneously electroweak and U(1)L symmetry breaking. All the field contents and their assignments are summarized in Table 1, where the quark sector is exactly the same as the SM. The renormalizable Yukawa Lagrangian under these symmetries is given by(1)−Lℓ=yℓaaL¯LaH2eaR+yDab[L¯LaH3ψRb]+gab[ψ¯LaH4⁎χRb]+Maaψ¯LaψRa+yφaa2φ(χ¯Rc)aχaR+h.c., where we implicitly symbolize the gauge invariant contracts of SU(2)L index as bracket [⋯] hereafter, indices (a,b)=1-3 are the number of families, and (yℓ,MD,yφ) are assumed to be diagonal matrix with real parameters without loss of generality. Then, the mass eigenvalues of charged-lepton are defined by mℓ=yℓv/2=Diag(me,mν,mτ). Note here that we do not have [(ψ¯cR)aH4χRb] operator thanks to the global U(1)L symmetry, and thus the neutrino mass matrix can dominantly be induced via inverse seesaw.Scalar potential and VEVs: The scalar potential in our model is given by(2)V=−μH2|H2|2+λH2|H2|4+M32H3†H3+M42H4†H4−μφ2φ⁎φ+λφ2(φ⁎φ)2+λHφ(H†H)(φ⁎φ)+μ32(H2†H3H2+h.c.)+∑iλH4H2i[H4†H2H4†H2+h.c.]i+(other trivial terms), where sum for (H4†H2)2 term is for independent contraction patterns of SU(2)L index. Non-zero VEVs of scalar fields are obtained by solving the conditions(3)∂V∂v2=∂V∂v3=∂V∂vφ=0, where we assume VEV of H4 to be zero. Taking condition v3≪v2 as we see below, the VEVs are approximately given by(4)v2≃μH2λH,v3≃μ32v22M32,vφ≃μφ2λφ, where we ignored contributions from trivial terms in the potential like (H†H)φ⁎φ assuming their couplings are small. The SM Higgs VEV is identified as v2∼246 GeV.ρparameter_: The electroweak ρ parameter deviates from unity due to the nonzero value of v3 at the tree level as(5)ρ=v22+4v32v22, where the experimental bound is ρexp=1.0004+0.0003−0.0004 at 2σ C.L. [17]. It suggests that(6)v3≲3.25GeV, where v22+v32≈246 GeV.Exotic particles: The scalars and fermions with large SU(2)L multiplet provide exotic charged particles. Here we write components of multiplets as(7)H3=(δ+,δ0,δ′−)RT,(8)H4=(ϕ4++,ϕ4+,ϕ40,ϕ′−4)T,(9)ψL(R)=(ψ+,ψ0,ψ′−,ψ−−)TL(R). The mass of component in H4 and ψ are given by ∼M4 and ∼M respectively, where charged particles in the same multiplet have degenerate mass at tree level which will be shifted at loop level [18]. Components of H3 have also degenerated mass of ∼M3 since VEV v3 is small and masses are not much shifted. We also have extra singlet scalar φ which is written by(10)φ=12(vφ+ϕ˜+iaφ), where aφ is identified as light Goldstone boson associated with global lepton number symmetry breaking. CP-even component ϕ˜ can mix with the SM Higgs and mass term becomes(11)L⊃14(H˜ϕ˜)T(λHv2λHφvvφλHφvvφλφvφ2)(H˜ϕ˜), where H˜ is neutral CP-even component in Higgs doublet H2. This squared mass matrix can be diagonalized by an orthogonal matrix and the mass eigenvalues are given by(12)mh,ϕ2=λHv2+λφvφ24±14(λHv2−λφvφ2)2+4λHφ2v2vφ2. The corresponding mass eigenstates h and ϕ are obtained as(13)(hϕ)=(cosαsinα−sinαcosα)(H˜ϕ˜),tan2α=2λHφvvφλHv2−λφvφ2, where α is the mixing angle and h is the SM-like Higgs boson with mh≃125 GeV.2.1Neutral fermion massesNeutral sector: After the spontaneous symmetry breaking, neutral fermion mass matrix in basis of ΨL0≡(νL,ψRc,ψL)T is given by(14)MN=[0mDT0mD0M⁎0M⁎μL⁎], where mD≡yDv3/2, M†=M⁎. In our model μL is given at one-loop level in Fig. 1, and is explicitly computed by(15)μLij=2giαMχagαjT(4π)2(Mχa2−mR2)(Mχa2−mI2)×[Mχa2mR2ln(Mχa2mR2)−Mχa2mI2ln(Mχa2mI2)+mI2mR2ln(mR2mI2)], where Mχ≡yφvφ/2, mR/I is the mass of ϕ4R/4I0 which comes from real/imaginary part of ϕ40. It implies a tiny mass scale of μL is expected due to the one-loop effect. Furthermore, the mass scale of mD is of the order 1 GeV since it is proportional to v3, while M can be of the order 1 TeV because of bare mass. Thus we achieve natural hierarchies among the neutral fermion mass matrices;(16)μL<<mD<M. The neutral fermions are diagonalized by a unitary matrix as follows [19]:(17)V(OMNOT)VT≈V[−2(mD⁎M⁎−1μL⁎M⁎−1mD†)3×303×606×3TM6×6′]VT≈Diag(Dν1,2,3,M⁎−μL⁎2,M⁎+μL⁎2),(18)M′≡[0M⁎M⁎μL⁎],(19)U=VO≈[UMNS3×303×606×3TΩ6×6][13×3−θ3×6θ6×3T16×6],(20)θ3×6≈[−mD⁎M⁎−1μL†M⁎−1,mD⁎M⁎−1],(21)Ω6×6≈12[i(1+μLM⁎−14)−i(1−μLM⁎−14)1−M⁎−1μL†41+μL⁎M⁎−14], where ΨL=UTNL, NL being mass eigenstates with nine components, and M±μL/2≈Diag(M±μL/2).Active neutrino sector: Here let us focus on the active neutrino sector; mν≡−2mD⁎M⁎−1μ⁎LM⁎−1mD†=UMNS†DνUMNS⁎ (UMNS≡UMNS3×3) from the above definition. Here since we define μ≡M⁎−1μL⁎M⁎−1, where μ is symmetric matrix. Then one rewrites μ≡RRT, where R is triangular matrix and R is uniquely given by each the component of μ; mν=−(2mD⁎R)(2RTmDT)≡−rrT. Applying Casas-Ibarra parametrization [20], one finds the following relation:(22)yD=iUMNS†DνOR−1v3≲4π,R−1=[1a00−dab1b0−be+dfabcfbc1c],(23)a=μ11,d=μ12a,b=μ22−d2,(24)e=μ13a,f=μ32−deb,c=μ33−e2−f2, where O is an arbitrary three by three orthogonal matrix with complex values; OOT=OTO=1.2.2Constraints from running of gauge coupling and LFVBeta function ofSU(2)Lgauge couplingg2_: Here we discuss the running of gauge coupling of g2. The new contribution to g2 for a SU(2)L quartet fermion(boson) ψ(H4), and a triplet boson H3, are respectively given by(25)Δbg2ψ=103,Δbg2H3=23,Δbg2H4=53. Then one finds the energy evolution of the gauge coupling g2 as [13,21](26)1gg22(μ)=1g2(min)−bSMg2(4π)2ln[μ2min2]−θ(μ−mth)NfψΔbg2ψ+Δbg2H3+Δbg2H4(4π)2ln[μ2mth2], where Nfψ=3 is the number of ψ, μ is a reference energy, bg2SM=−19/6, and we assume to be min(=mZ)<mth, being mth threshold masses of exotic fermions and bosons. The resulting flow of g2(μ) is then given by the Fig. 2. This figure shows that the black line is relevant up to the mass scale μ=O(1011) TeV in case of mth=10 TeV, the red one is relevant up to the mass scale μ=O(109) TeV in case of mth=1 TeV, and the blue one is relevant up to the mass scale μ=O(107) PeV in case of mth=0.1 TeV. Thus our theory is valid up to the typical energy scale of grand unified theory (GUT) ∼1015 GeV.Lepton flavor violations (LFVs): LFVs arise from the term f at one-loop level, and its form can be given by [22,23](27)BR(ℓi→ℓjγ)=48π3αemCijGF2mℓi2(|aRij|2+|aLij|2), where(28)aRij=mℓi(4π)2[∑α=19YDjαYDαi†3F(ψ0α,δ−)−∑β=13yDjβy†Dβi[2F(δ−,ψβ−−)+F(ψ−−β,δ−)+13F(δ0,ψβ−)]], aL=aR(mℓi→mℓj), YDiα≡∑j=13yDijUj+3,αT, and(29)F(a,b)≡12ma2∫01dxx(1−x)2x+(1−x)rab,rab≡mb2ma2. New contributions to the muon anomalous magnetic moment(muon_ g−2:Δaμ)_: In the model Δaμ arises from the same terms of LFVs and can be formulated by the following expression: Also another source via additional gauge sector can also be induced by(30)Δaμ≈−mμ[aLμμ+aRμμ]=−2mμaLμμ, where we use the allowed range Δaμ=(26.1±16.0)×10−10 [24] (at 2σ C.L.) in our numerical analysis below.2.3Dark matterHere we briefly discuss the feature of our DM candidate, which is assumed to be the lightest Z2 odd Majorana fermion X≡χR; MχR1≡MX. The relevant interactions are given by(31)L⊃MX2vφcosαϕX¯cX+MX2vφsinαhX¯cX+iMX2vφaφX¯cγ5X, where MX is DM mass given by MX≡M1=yφ11vφ/2. Also we have interactions among ϕ and SM particles whose couplings are obtained by putting −sinα to SM Higgs couplings. Then dominant DM annihilation processes are(32)XX→ϕ/h→f¯SMf¯SM/ZZ/W+W−,(33)XX→aφaφ/aφϕ(h) where the first modes are s-channel via φ-H mixing and the second ones are t and u channels with physical GB final state. In Fig. 3, we show the relic density of X as a function of its mass fixing mϕ=400 GeV, vφ=2000 GeV and sinα=0.1, which is estimated by micrOMEGAs 4.3 [25] implementing relevant interactions. We find that relic density can be explained around 2MX∼mϕ by resonant enhancement of annihilation cross section; we also see resonance effect at 2MX∼mh but relic density is too large in this parameter setting. The relic density also decreases as MX increases since scalar interactions are proportional to MX. In addition, relic density can be explained via GB mode when vφ is smaller as can be seen in e.g. ref. [26]. The resonant point is consistent with the constraint of direct detection since DM-scalar coupling can be small [27]. But it depends on the parameter space for solution without resonance.In case of the bosonic DM candidate that is not considered as a DM one in our whole analysis, the dominant contribution to the relic density comes from kinetic terms, and the free parameter is almost the DM mass only. Thus the formulation is already established by ref. [18,28], which suggests MX∼10 TeV. As a result, any masses of new fields must be 10 TeV or larger than 10 TeV, and one cannot detect any new particles at current colliders.3Numerical analysesIn this section, we carry out numerical analysis taking into account neutrino mass and LFV constraints exploring possible value of Yukawa coupling yD and Δaμ. In addition collider physics is discussed focusing on doubly charged lepton production at the LHC.3.1Yukawa coupling and Δaμ in benchmark pointsHere we have numerical analysis in two benchmark points, where we commonly fix the following values:(34)θ23≈0.62+1.08i,θ13≈0.46+0.69i,θ12≈1.82+14.95i,(35)mν1=0.1meV,v3≈3GeV,(36)g≈[0.20.0270.0000200.0000210.0910.0830.00330.0000340.58], where θ12,13,23 is the mixings of O introduced in the analysis of neutrino mass matrix, and these values; especially θ12,13,23, are selected so as to maximize muon g−2 while minimizing LFVs.Bench mark point 1: The first bench mark point is given by(37)(Mχ2,Mχ3)=(2,2.5)TeV,(M1,M2,M3)=(0.4,0.45,0.5)TeV,(mR,mI)=(3,3.3)TeV,(mδ0,mδ±)=(0.3,0.35)TeV. Bench mark point 2: The second bench mark point is given by(38)(Mχ2,Mχ3)=(4,4.5)TeV,(M1,M2,M3)=(0.5,0.55,0.6)TeV,(mR,mI)=(5,5.5)TeV,(mδ0,mδ±)=(0.4,0.45)TeV.Fig. 4 represents the flow of maximum component of yD(=Max[|yD|]) in terms of the DM mass MX≡Mχ1, where the left(right)-hand side shows the bench mark point 1(2), and the horizontal line represents the perturbation limit; 4π. The left(right)-hand side figure suggests that the allowed region of DM mass be less than ∼190(400) GeV, satisfying the perturbative limit. Fig. 5 represents the flow of maximum component of Δaμ in terms of MX, where the left(right)-hand side shows the bench mark point 1(2). The green region is expected to be detected by the experiment that covers over Δaμ=(26.1±16.0)×10−10 at 2σ C.L. It implies that the left-bench mark point can reach the observed region of muon g−2 at 130 GeV≲MX≲190 GeV, while the right one is below the allowed region of muon g−2 in the perturbative limit even though the allowed region of DM mass is wider than the left one.3.2Collider physicsHere we briefly discuss collider signature of the model. There are several exotic charged particles in the model coming from SU(2)L multiplet fermions and scalar fields. Interestingly we have two doubly charged particles in fermion and scalar sector. The doubly charged lepton ψ−− in quartet fermion can provide interesting signal at the LHC since it decays into SM particles and its mass could be reconstructed. On the other hand doubly charged scalar ϕ4++ in H4 decays into final state including DM due to Z2 oddness, and mass reconstruction is more difficult. We thus concentrate on doubly charged lepton production and its decay at the LHC.Firstly doubly charged lepton can be produced via electroweak interactions where we consider pair production process. Relevant gauge interactions are given by(39)L⊃−2eAμψ¯−−γμψ−−+g2cW(−32+2sW2)Zμψ¯−−γμψ−− where sW(cW)=sinθW(cosθW) with Weinberg angle θW and e is electromagnetic coupling. Taking the first generation mass as M1=500 GeV as a benchmark point we obtain pair production cross section σ(pp→ψ1++ψ1−−) around 40 fb estimated by CalcHEP [29]; here we focus on first generation ψ1±± since it provides the largest production cross section and omit generation index below. Then ψ±± decays into charged lepton and singly charged scalar δ± through the Yukawa interaction in Eq. (1) where we write by components such that(40)yDab[L¯LaH3ψRb]=yDab3[e¯La(ψR0δ′−−2ψR′−δ0+3ψR−−δ+)+ν¯L(ψR′−δ+−2ψR0δ0+3ψR+δ′−)]. For simplicity we assume ℓ=e,μ in the decay of ψ−−→ℓ−δ− in the following discussion. The singly charged scalar δ± dominantly decay into W+Z since H3 do not couple to SM fermions directly. In total we have following signal process:(41)pp→ψ++ψ−−→δ+δ−ℓ1+ℓ2+→W+W−ZZℓ1+ℓ2−. Taking into account decays of SM gauge bosons our signal at the LHC will be multi-lepton with or without jets. In Table 2, we summarize products of cross section and branching ratios (BRs) for each representative final state where we take doubly charged lepton mass as M=500 GeV as a benchmark point and final states are distinguished by number of charged lepton and jets. We find that the cross section is less than 1 fb when there are more than 4 charged leptons in final state. Thus sufficiently large integrated luminosity is required to analyze the signal at the LHC experiments. Detailed simulation study including SM backgrounds is beyond the scope of this letter and it will be given elsewhere.4Summary and discussionIn this work, we constructed inverse seesaw model with global lepton number symmetry in which Majorana mass term of extra neutral fermion from SU(2)L quartet is induced at one-loop level realizing natural hierarchy of neutral fermion masses. In our model, Z2 odd scalar quartet and fermion singlet are introduced which propagate inside a loop diagram generating the Majorana mass. Then the lightest Z2 odd particle can be a good DM candidate where we consider the Majorana fermion DM.We have formulated neutrino mass matrix, LFV and muon g−2. In addition we show that relic density can be explained by scalar exchanging interactions. Then numerical analysis is carried out exploring allowed value of coupling constant and muon g−2. We find that sizable muon g−2 can be obtained when DM mass is 130 GeV ≤MX≤ 190 GeV taking into account perturbative limit of coupling constants. Furthermore we have discussed collider physics focusing on doubly charged lepton production at the LHC where we have shown the products of cross section and branching ratio for each final state. We could test the signals with sufficiently large integrated luminosity.Finally we discuss possibility of embedding this model in a grand unified theory such as an SO(10) model [7]. In our model, we have introduced SU(2)L quartet fermions and scalar field to realize one loop generation of Majorana mass term in inverse seesaw, and a large SO(10) multiplet is required to obtain SU(2)L quartet such as 210′ or 320 representation [30]. Thus it is non-trivial to embed our model in a SO(10) model and further investigation is left for future study.AcknowledgementsThis research is supported by the Ministry of Science, ICT and Future Planning, Gyeongsangbuk-do and Pohang City (H.O.). And H. O. is sincerely grateful for KIAS and all the members, too.References[1]R.N.MohapatraJ.W.F.VallePhys. Rev. D3419861642[2]D.WylerL.WolfensteinNucl. Phys. B2181983205[3]E.K.AkhmedovM.LindnerE.SchnapkaJ.W.F.VallePhys. Lett. B3681996270arXiv:hep-ph/9507275[4]E.K.AkhmedovM.LindnerE.SchnapkaJ.W.F.VallePhys. Rev. D5319962752arXiv:hep-ph/9509255[5]R.N.MohapatraG.SenjanovicPhys. Rev. Lett.441980912[6]H.FrizschP.MinkowskiUnified interactions of leptons and hadronsAnn. Phys.931975193266[7]M.MalinskyJ.C.RomaoJ.W.F.VallePhys. Rev. Lett.952005161801arXiv:hep-ph/0506296[8]F.BazzocchiD.G.CerdenoC.MunozJ.W.F.VallePhys. Rev. D812010051701arXiv:0907.1262 [hep-ph][9]T.NomuraH.OkadaarXiv:1808.05476 [hep-ph][10]T.NomuraH.OkadaarXiv:1807.04555 [hep-ph][11]T.NomuraH.OkadaarXiv:1806.07182 [hep-ph][12]T.NomuraH.OkadaPhys. Lett. B7832018381arXiv:1805.03942 [hep-ph][13]T.NomuraH.OkadaPhys. Rev. D9692017095017arXiv:1708.03204 [hep-ph][14]T.NomuraH.OkadaY.OrikasaPhys. Rev. D9452016055012arXiv:1605.02601 [hep-ph][15]T.NomuraH.OkadaY.OrikasaPhys. Rev. D94112016115018arXiv:1610.04729 [hep-ph][16]E.MaPhys. Rev. D732006077301arXiv:hep-ph/0601225[17]K.A.OliveParticle Data GroupChin. Phys. C382014090001[18]M.CirelliN.FornengoA.StrumiaNucl. Phys. B7532006178arXiv:hep-ph/0512090[19]Y.KajiyamaH.OkadaT.TomaEur. Phys. J. C73320132381arXiv:1210.2305 [hep-ph][20]J.A.CasasA.IbarraNucl. Phys. B6182001171arXiv:hep-ph/0103065[21]S.KanemuraK.NishiwakiH.OkadaY.OrikasaS.C.ParkR.WatanabePTEP2016122016123B04arXiv:1512.09048 [hep-ph][22]M.LindnerM.PlatscherF.S.QueirozPhys. Rep.73120181arXiv:1610.06587 [hep-ph][23]S.BaekT.NomuraH.OkadaPhys. Lett. B759201691arXiv:1604.03738 [hep-ph][24]K.HagiwaraR.LiaoA.D.MartinD.NomuraT.TeubnerJ. Phys. G382011085003arXiv:1105.3149 [hep-ph][25]G.BelangerF.BoudjemaA.PukhovA.SemenovComput. Phys. Commun.1922015322arXiv:1407.6129 [hep-ph][26]T.NomuraH.OkadaPhys. Rev. D9772018075038arXiv:1709.06406 [hep-ph][27]S.KanemuraS.MatsumotoT.NabeshimaN.OkadaPhys. Rev. D822010055026arXiv:1005.5651 [hep-ph][28]M.CirelliA.StrumiaM.TamburiniNucl. Phys. B7872007152arXiv:0706.4071 [hep-ph][29]A.BelyaevN.D.ChristensenA.PukhovComput. Phys. Commun.18420131729arXiv:1207.6082 [hep-ph][30]R.SlanskyPhys. Rep.7919811