]>NUPHB114621114621S0550-3213(19)30101-410.1016/j.nuclphysb.2019.114621High Energy Physics – PhenomenologyFig. 1The diagram inducing active neutrino mass.Fig. 1Fig. 2The running of g2 in terms of a reference energy of μ, where the red line corresponds to mth=0.5 TeV, while the blue one does mth=5 TeV. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)Fig. 2Fig. 3μγγ ≡ BR(h→γγ)SM+exotic/BR(h→γγ)SM as a function of λHΦ assuming they are same value for Φ = H4,H5,H7 and masses of corresponding multiplets are (1,5,1) TeV. The shaded region is 1σ region from the LHC data [27].Fig. 3Fig. 4Various LFV processes and Δaμ in terms of mR, where BR(μ → eγ), BR(τ → eγ), BR(τ → μγ), and Δaμ are respectively colored by red, magenta, blue, and black. The black horizontal line shows the current upper limit of the experiment [33,34], while the green one does the future upper limit of the experiment [33,35].Fig. 4Fig. 5The lifetime of DM in terms of mR, where we fix v7 ≈ 1.03 GeV, and λ0 = (10−7,10−9,10−11) with (red, green, blue). The black horizontal line shows the current age of Universe τ0.Fig. 5Fig. 6Cross section for pp→ϕ7++++ϕ7−−−− at the LHC 14 TeV where dashed line indicate the cross section from only Drell-Yan process and solid line corresponds to the cross section including both Drell-Yan and photon fusion processes.Fig. 6Fig. 7Cross section for pp → ψ+++ψ−−− at the LHC 14 TeV where dashed line indicate the cross section from only Drell-Yan process and solid line corresponds to the cross section including both Drell-Yan and photon fusion processes.Fig. 7Table 1Charge assignments of the our lepton and scalar fields under SU(2)L × U(1)Y, where the upper index a is the number of family that runs over 1-3 and all of them are singlet under SU(3)C.Table 1LLaeRaψaH2H4H5H7

SU(2)L2142457

U(1)Y−12−1−12121201

A one-loop neutrino mass model with SU(2)L multiplet fieldsTakaakiNomuraanomura@kias.re.krHiroshiOkadab⁎okada.hiroshi@apctp.orgaSchool of Physics, KIAS, Seoul 02455, Republic of KoreaSchool of PhysicsKIASSeoul02455Republic of KoreabAsia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790-784, Republic of KoreaAsia Pacific Center for Theoretical PhysicsPohangGyeongbuk790-784Republic of Korea⁎Corresponding author.Editor: Tommy OhlssonAbstractWe propose a one-loop neutrino mass model with several SU(2)L multiplet fermions and scalar fields in which the inert feature of a scalar to realize the one-loop neutrino mass can be achieved by the cancellation among Higgs couplings thanks to non-trivial terms in the Higgs potential and to present it in a simpler way. Then we discuss our typical cut-off scale by computing renormalization group equation for SU(2)L gauge coupling, lepton flavor violations, muon anomalous magnetic moment, possibility of dark matter candidate, neutrino mass matrix satisfying the neutrino oscillation data. Finally, we search for our allowed parameter region to satisfy all the constraints, and discuss a possibility of detecting new charged particles at the large hadron collider.1IntroductionsRadiatively induced neutrino mass models are one of the promising candidates to realize tiny neutrino masses with natural parameter spaces at TeV scale and to provide a dark matter (DM) candidate, both of which cannot be explained within the standard model (SM). In order to build such a radiative model, an inert scalar boson plays an important role and its inert feature can frequently be realized by imposing additional symmetry such as Z2 symmetry [1–4] and/or U(1) symmetry [5–7], which also play an role in stabilizing the DM. On the other hand, once we introduce large SU(2)L multiplet fields such as quartet [8,9], quintet [10,11], septet fields [12–14], we sometimes can evade imposing additional symmetries [15,16]. Then, the stability originates from a remnant symmetry after the spontaneous electroweak symmetry breaking due to the largeness of these multiplets. In addition, the cut-off scale of a model is determined by the renormalization group equations (RGEs) of SU(2)L gauge coupling, and it implies that a theory can be within TeV scale, depending on the number of multiplet fields. Thus a good testability could be provided in such a scenario.Then, using large SU(2)L multiplet fields, we would like to realize one-loop neutrino generation by inert scalar field without imposing additional symmetry such as Z2. In this case scalar quintet H5 is minimal choice for inert multiplet since scalar multiplet smaller than quintet easily develop a vacuum expectation value (VEV) by renormalizable interaction with SM Higgs field H like H4HHH for the quadruplet H4. In addition we need quadruplet fermion ψ4 to interact H5 with the SM lepton doublet and septet scalar H7 is also required to get Majorana mass term from ψ4 by its VEV (Higgs triplet is also possible but it allows type-II seesaw mechanism [17,18]). We find that scalar quadruplet H4 is needed to realize vacuum configuration in which the VEV of H5 to be zero; in addition we can avoid dangerous massless Goldstone boson from scalar multiplets by non-trivial terms with these multiplets. Although number of exotic fields is smaller in other one-loop neutrino mass models like scotogenic model [1] they usually require additional discrete symmetry such as Z2. We show the realization of one-loop neutrino mass without additional symmetry which result in introduction of several exotic multiplets.In this letter, we introduce several multiplet fermions and scalar fields under the SU(2)L gauge symmetry. As a direct consequence of multiplet fields, our cut-off scale is of the order 10 PeV that could be tested by current or future experiments. In our model we do not impose additional symmetry and search for possible solution to obtain inert condition for generating neutrino mass at loop level. Then required inert feature can be realized not via a remnant symmetry but via cancellations among couplings in our scalar potential thanks to several non-trivial couplings [19]. In such a case, generally DM could decay into the SM particles, but we can control some parameters so that we can evade its too short lifetime without requiring too small couplings. Therefore our DM is long-lived particle which represents clear difference from the scenario where the stability of DM is due to an additional or remnant symmetry. We also discuss lepton flavor violations (LFVs), and anomalous magnetic moment (muon g−2), and search for allowed parameter region to satisfy all the constraints such as neutrino oscillation data, LFVs, DM relic density, and demonstrate the possibility of detecting new charged particles at the large hadron collider (LHC).This letter is organized as follows. In Sec. 2, we review our model and formulate the Higgs sector, neutral fermion sector including active neutrinos. Then we discuss the RGE of the SU(2)L gauge coupling, LFVs, muon g−2, and our DM candidate. In Sec. 3, we explore the allowed region to satisfy all the constraints, and discuss production of our new fields (especially charged bosons) at the LHC. In Sec. 4, we devote the summary of our results and the conclusion.2Model setup and constraintsIn this section we formulate our model. As for the fermion sector, we introduce three families of vector-like fermions ψ with (4,−1/2) charge under the SU(2)L×U(1)Y gauge symmetry. As for the scalar sector, we respectively add an SU(2)L quartet (H4), quintet (H5), and septet (H7) complex scalar fields with (1/2,0,1) charge under the U(1)Y gauge symmetry in addition to the SM-like Higgs that is denoted by H2, where the quintet H5 is expected to be an inert scalar field. Here we write the nonzero vacuum expectation values (VEVs) of H2, H4, and H7 by 〈H2〉≡vH/2, 〈H4〉≡v4/2 and 〈H7〉≡v7/2, respectively, which induces the spontaneous electroweak 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+fab[L¯LaH5(ψR)b]+gLaa[(ψ¯Lc)aH7ψLa]+gRaa[(ψ¯Rc)aH7ψRa]+MDaaψ¯RaψLa+h.c., where SU(2)L index is omitted assuming it is contracted to be gauge invariant inside bracket [⋯], upper indices (a,b)=1-3 are the number of families, and yℓ and either of gL/R or MD are assumed to be diagonal matrix with real parameters without loss of generality. Here, we assume gL/R and MD to be diagonal for simplicity. The mass matrix of charged-lepton is defined by mℓ=yℓv/2. Here we assign lepton number 1 to ψ so that the source of lepton number violation is only the terms with coupling gab and gab′ in the Lagrangian requiring the lepton number is conserved at high scale.2.1Scalar sectorScalar potential and VEVs: The scalar potential in our model is given by(2)V=−M22H2†H2+M42H4†H4+M72H7†H7+λH(H2†H2)2+μH2[H52]+μ1[H2H˜4H5]+μ2[H4TH˜7H4]+λ0[H2TH2H5H7⁎]+λ1[H2H4H5H˜7]+λ2[H2†H2H4†H2]+h.c.+Vtri, where Vtri is the trivial quartic terms containing H4,5,7. From the conditions of ∂V/∂v5=0 and 〈H5〉=0, we find the following relation:(3)v4=310v7v2λ030v7λ1+15μ1. Then, the stable conditions to the H4 and H7 lead to the following equations:(4)v2=38(λ2λHv4+λ22λH2v42+64M229λH),v4=5v23λ223(10M42+30μ2),v7=−310v42μ22M72, where we have ignored contributions from terms in Vtri assuming corresponding couplings are negligibly small; we can always find a solution satisfying the inert condition including such terms. Solving Eqs. (3) and (4), one rewrites VEVs and one parameter in terms of the other parameters. In addition to the above conditions, we also need to consider the constraint from ρ parameter, which is given by the following relation at tree level:(5)ρ≈v22+112v42+22v72v22+v42+4v72, where the experimental values is given by ρ=1.0004−0.0004+0.0003 at 2σ confidential level [20]. Then, we have, e.g., the solutions of (v2,v4,v7)≈(246,2.18,1.03) GeV, where v22+v42+4v72≈246 GeV2.2.2Neutral fermion massesHeavier neutral sector: After the spontaneously electroweak symmetry breaking, extra neutral fermion mass matrix in basis of ΨR0≡(ψR0,ψL0c)T is given by(6)MN=[μRMDTMDμL], where μR≡310gRv7 and μL≡310gL⁎v7. Since we can suppose hierarchy of mass parameters to be μL/R<<MD, the mixing is expected to be maximal. Thus, we formulate the eigenstates in terms of the flavor eigenstate as follows:(7)ψR0=i2ψ1R−i2ψ2Lc,ψL0c=12ψ1R+12ψ2Lc, where ψ1R and ψ2Lc represent the mass eigenstates, and their masses are respectively given by Ma≡MD−(μR+μL)/2 (a=1-3) Mb≡MD+(μR+μL)/2 (b=4-6).Active neutrino sector: In our scenario, active neutrino mass is induced at one-loop level, where ψ1,2 and H5 propagate inside a loop diagram as in Fig. 1, and the masses of real and imaginary part of electrically neutral component of H5 are respectively denoted by mR and mI. As a result the active neutrino mass matrix is obtained such that(8)mν=∑α=16fiαMαfTαj8(4π)2[rRαlnrRα1−rRα−rIαlnrIα1−rIα], where rR/Iα≡mR/I2Mα2. Neutrino mass eigenvalues (Dν) are given by Dν=UMNSmνUMNST, where UMNS is the MNS matrix. Once we define mν≡fMfT, one can rewrite f in terms of the other parameters [21,22] as follows:(9)fik=∑α=16Uij†DνjjOjαMααVαk⁎, where O is a three by six arbitrary matrix, satisfying OOT=1, and |f|≲4π is imposed not to exceed the perturbative limit.2.3Analysis of other phenomenological formulasBeta function ofSU(2)Lgauge couplingg2:_ Here we estimate the running of gauge coupling of g2 in the presence of several new multiplet fields of SU(2)L. The new contribution to g2 from fermions (with three families) and bosons are respectively given by [13,23](10)Δbg2f=103,Δbg2b=433. Then one finds that the resulting flow of g2(μ) is then given by the Fig. 2. This figure shows that the red line is relevant up to the mass scale μ=O(1) PeV in case of mth=0.5 TeV, while the blue line is relevant up to the mass scale μ=O(10) PeV in case of mth=5 TeV.Lepton flavor violations (LFVs): LFV decays ℓi→ℓjγ arise from the term associated with coupling f at one-loop level, and its form can be given by [24,25](11)BR(ℓi→ℓjγ)=48π3αemCijGF2mℓi2(|aRij|2+|aLij|2), where(12)aRij=∑α=13fjαmℓifαi†(4π)2[−112G(ma,M±α)+G(Mα,m±)+G(M3+α,m±)+14[2G(M±α,m±±)+G(m±±,M±α)]−G(M±±α,m±)−2G(m±,M±±α)], and(13)G(ma,mb)≡∫01dx∫01−xdyxy(x2−x)mℓi2+xma2+(1−x)mb2, where aL=aR(mℓi→mℓj).New contributions to the muon anomalous magnetic moment (muon g−2: Δaμ): We obtain Δaμ from the same diagrams for LFVs and it can be formulated by the following expression(14)Δaμ≈−mμ[aLμμ+aRμμ]=−2mμaLμμ, where aLμμ=aRμμ has been applied. In Eq. (12), one finds that the first term and the last two terms provide positive contributions, while the other terms do the negative contributions. When mediated masses are same value for all the modes; (m≡)ma=m±=m±±=M±=M±±=M±±, one simplifies the formula of aR as(15)aRij≈−13∑α=13fjαmℓifαi†(4π)2G(m,m). Thus one would have positive contribution to the muon g−2, and we use the allowed range of Δaμ=(26.1±8.0)×10−10 in our numerical analysis below.Charged scalar contribution toh→γγdecay:_ Interactions among SM Higgs field and large multiplet scalars affect the branching ratio of h→γγ process via charged scalar loop. Here we write the relevant interactions such that(16)V⊃∑Φ=H4,H5,H7λHΦ(H2†H2)(Φ†Φ)⊃∑Φ=H4,H5,H7λHΦv2h(Φ†Φ), where Φ†Φ provide sum of charged scalar bilinear terms. Then we obtain decay width of h→γγ at one-loop level as [26](17)Γh→γγ≃αem2mh3256π3|43v2A1/2(τt)+1v2A1(τW)+∑Φ∑ΦiQΦi2λHΦ2mΦ2A0(τΦ)|2, where Φi indicates components in the multiplet Φ and QΦi is its electric charge, and τf=4mf2/mh2. The loop functions are given by(18)A0(x)=−x2[x−1−[sin−1(1/x)]2],(19)A1/2(x)=2x2[x−1+(x−1−1)[sin−1(1/x)]2],(20)A1(x)=−x2[2x−2+3x−1+3(2x−1−1)[sin−1(1/x)]2] where x<1 is assumed and subscript of A0,1/2,1(x) correspond to spin of particle in loop diagram. We then estimate μγγ≡BR(h→γγ)SM+exotic/BR(h→γγ)SM assuming Higgs production cross section is the same as in the SM. In Fig. 3, we show the μγγ as a function of λHΦ assuming they are same value for Φ=(H4,H5,H7) and masses of corresponding multiplets are (1,5,1) TeV. The value of μγγ is constrained by the current LHC data [27,28] and we indicate 1σ region in the plot. We thus find that |λHΦ| is required to be less than around 1 for TeV scale scalar masses.Dark matter candidate: In our case, the lightest neutral fermion among ψ1,2 can be a DM candidate, which comes from SU(2)L quintet field with −1/2 charge under U(1)Y. Here we firstly require that higher-dimensional operator inducing decay of the DM is not induced by the physics above cut-off scale so that decay of DM can only be induced via renormalizable Lagrangian in the model. Assuming the dominant contribution to explain the relic density originates from gauge interactions in the kinetic terms, the typical mass range is MDM≳2.4 TeV where MDM=2.4±0.06 TeV is estimated by perturbative calculation [16] and heavier mass is required including non-perturbative Sommerfeld enhancement effect [29]. Then the typical order of spin independent cross section for DM-nucleon scattering via Z-portal is at around 1.6×10−45 cm2 [16] for MDM≃2.4TeV, which marginally satisfies the current experimental data of direct detection searches such as LUX [30], XENON1T [31], and PandaX-II [32]; the direct detection constraint is weaker for heavier DM mass. In the numerical analysis, below, we fix the DM mass to be 2.4 TeV as a reference value for simplicity. One feature of our model is possible instability of DM since we do not impose additional symmetry at TeV scale. We thus have to estimate the decay of DM so that the life time τDM=ΓDM−1 does not exceed the age of universe that is around 4.35×1017 second. The main decay channel arises from interactions associated with couplings f and λ0, when we neglect the effect of mixing among neutral bosons. Then the three body decay ratio of Γ(DM→νihh) via the neutral component of H5 is given by(21)Γ(DM→νihh)≈λ02|f1i|2MDM3v727680mR4π3≲λ02|Max[f1i]|2MDM3v727680mR4π3, where we assume the final states to be massless, mR≈mI, MDM is the mass of DM, and h is the SM Higgs. In the numerical analysis, we will estimate the lifetime and show the allowed region, where we take the maximum value of |f1a|.11In case where the neutral component of H5 is DM candidate, H5 decays into SM-like Higgs pairs via λ0, and its decay rate is given by λ02v72800πMX. Then the required lower bound of λ0 is of the order 10−19 so that its lifetime is longer than the age of Universe, where DM is estimated as 5 TeV [16].3Numerical analysis and phenomenologyHere we carry out numerical analysis to discuss consistency of our model under the constraints discussed in previous section. Then we discuss collider physics focusing on charged scalar bosons in the model.Numerical analyses: In our numerical analysis, we assume all the mass of ψ1,2 to be the mass of DM; 2.4 TeV, and all the component of H5 except mI to be degenerate, where mI=1.1mR. These assumptions are reasonable in the aspect of oblique parameters in the multiplet fields [20]. Also we fix to be the following values so as to maximize the muon g−2:(22)O12=0.895+12.3i,O23=1.88+0.52i,O13=0.4+0.6i, where O12,23,13 are arbitral mixing matrix with complex values that are introduced in the neutrino sector [10,22]. Notice here that we also impose |f|≲4π not to exceed the perturbative limit.Fig. 4 represents various LFV processes and Δaμ in terms of mR, where BR(μ→eγ), BR(τ→eγ), BR(τ→μγ), and Δaμ are respectively colored by red, magenta, blue, and black. The black horizontal line shows the current upper limit of the experiment [33,34], while the green one does the future upper limit of the experiment [33,35]. Considering these bounds of μ→eγ, one finds that the current allowed mass range of mR∼4–20TeV can be tested in the near future. Here the upper bounds of BR(τ→eγ) and BR(τ→μγ) are of the order 10−8, which is safe for all the range. The maximum value of Δaμ is about 10−12, which is smaller than the experimental value by three order of magnitude.Fig. 5 shows the lifetime of DM in terms of mR, where we fix v7≈1.03 GeV, and λ0=(10−7,10−9,10−11) with (red, green, blue). The black horizontal line shows the current age of Universe. The figure demonstrates as follows:(23)λ0=10−7:mR∼1000TeV,λ0=10−9:100TeV≲mR,λ0=10−11:10TeV≲mR. Collider Physics: Here let us briefly comments possible collider physics of our model. We have many new charged particles from SU(2)L multiplet scalars and fermions. Clear signal could be obtained from charged scalar bosons in H7 and H4, since they can decay into final states containing only SM particles where the components in these multiplets are given by(24)H7=(ϕ7++++,ϕ7+++,ϕ7++,ϕ+7,ϕ70,ϕ7′−,ϕ′−−)T,(25)H4=(ϕ4++,ϕ4+,ϕ40,ϕ′−4)T. The quadruply charged scalar is particularly interesting since it is specific in our model and would provide sizable production cross section. We thus focus on ϕ7±±±± signal in our model.22Collider phenomenology of charged scalars from quartet is discussed in refs. [13,36–38]. The quadruply charged scalar can be pair produced by Drell-Yan(DY) process, qq¯→Z/γ→ϕ7++++ϕ7−−−−, and by photon fusion (PF) process γγ→ϕ7++++ϕ7−−−− [39–41]. We estimate the cross section using MADGRAPH/MADEVENT 5 [42], where the necessary Feynman rules and relevant parameters of the model are implemented by use of FeynRules 2.0 [43] and the NNPDF23LO1 PDF [44] is adopted. In Fig. 6 we show the cross section for the quadruply charged scalar production process pp→ϕ7++++ϕ7−−−− at the LHC 14 TeV, where dashed line indicates the cross section from only Drell-Yan process and solid line corresponds to the cross section including both Drell-Yan and photon fusion processes. We thus find that the cross section is highly enhanced including PF process due to large electric charge of the scalar boson. Thus sizable number of ϕ7±±±± pair can be produced at the LHC 14 TeV if its mass is O(1) TeV, with sufficiently large integrated luminosity. Produced ϕ7±±±± mainly decays into ϕ4±±ϕ4±± via H4TH˜7H4 interactions in the scalar potential since components in H7 have degenerate mass. Then ϕ4±± decays into W±W± via (DμH4)†(DμH4) term. We thus obtain multi W boson signal from quadruply charged scalar boson production. Mass reconstruction from multi W boson final state is not trivial and detailed analysis is beyond the scope of this paper.In addition to the charged scalar bosons, we consider production of exotic charged fermions at the LHC. The quadruplet fermion ψa is written by(26)ψa=(ψ0,ψ−,ψ−−,ψ−−−)a where the subscript indicates electric charge of components. As in the scalar sector, we focus on the component with the highest electric charge that is ψ±±± in the multiplet. Pair production of ψ±±± is estimated by MADGRAPH/MADEVENT 5 as in the charged scalar case where we consider both DY- and PF-processes. The production cross section is shown In Fig. 7 where the dashed and solid lines correspond to values from only DY process and from sum of both processes as in the scalar case. We obtain cross section σ∼0.03 fb for Mψ∼2.4 TeV which is motivated by DM relic density. In that case we can obtain ∼10(100) events for integrated luminosity of 300(3000) fb. Charged fermions in ψa decay as ψn→ψn±1W∓⁎ where n indicates electric charge and W boson is off-shell since the mass differences between components are radiatively induced and its value is around 350 MeV [16]; exotic fermions cannot decay via L¯H5ψ coupling since H5 is heavier than ψ. Thus ψ±±± production gives signature of light mesons with missing transverse momentum through decay chain of ψ±±±→W±⁎ψ±±(→W±⁎ψ±(→W±⁎ψ0)) where ψ0 is DM. Furthermore we would have displaced vertex signature since decay length of charged fermions is long as O(1) cm [16] for quadruplet fermion. Therefore analysis of displaced vertex will be important to test our scenario.4Summary and discussionsWe have proposed an one-loop neutrino mass model, introducing large multiplet fields under SU(2)L. The inert boson is achieved by nontrivial cancellations among quadratic terms. We have also considered the RGE for g2, the LFVs, muon g−2, and fermionic DM candidate, and shown allowed region to satisfy all the constraints as we have discussed above. RGE of g2 determines our cut-off energy that does makes our theory stay within the order 10 PeV scale, therefore our model could totally be tested by current or near future experiments. Due to the multiplet fields, we have positive value of muon g−2, but find its maximum value to be of the order 10−12 that is smaller than the sizable value by three order of magnitude. For the LFVs, the most promising mode to be tested in the current and future experiments is μ→eγ at the range of 3.2 TeV ≲mR≲ 11 TeV. We have also discussed possible decay mode of our DM candidate and some parameters are constrained requiring DM to be stable on cosmological time scale. Notice that the decay of DM is one feature of our model and we would discriminate our model from models with absolutely stable DM by searching for signal of the DM decay. Finally, we have analyzed the collider physics, focussing on multi-charged scalar bosons H4 and H7, and triply charged fermion ψ±±± in exotic fermion sector. For scalar sector, we find that sizable production cross section for quadruply charged scalar pair can be obtained adding the photon fusion process that is enhanced by large electric charge of ϕ7±±±±. Then possible signal of ϕ7±±±± comes from decay chain of ϕ7±±±±→ϕ4±±ϕ±±4→4W± which would provide multi-lepton plus jets at the detector. We expect sizable number of events with sufficiently large integrated luminosity to detect them at the LHC 14 TeV where the detailed analysis of the signal and background is left in future works. For exotic fermion sector, we have also find sizable production cross section for triply charged fermion pair. The triply charged fermion decay gives signature of light mesons with missing transverse momentum through decay chain of ψ±±±→W±⁎ψ±±(→W±⁎ψ±(→W±⁎ψ0)) where ψ0 is DM. In addition, would have displaced vertex signature since decay length of charged fermions is long as O(1) cm for components in quadruplet fermion, and thus analysis of displaced vertex will be important to test our scenario.AcknowledgementsThis research is supported by the Ministry of Science, ICT and Future Planning, Gyeongsangbuk-do and Pohang City (H.O.). H. O. is sincerely grateful for KIAS and all the members.References[1]E.MaPhys. Rev. D732006077301arXiv:hep-ph/0601225[2]L.M.KraussS.NasriM.TroddenPhys. Rev. D672003085002arXiv:hep-ph/0210389[3]M.AokiS.KanemuraO.SetoPhys. Rev. Lett.1022009051805arXiv:0807.0361[4]M.GustafssonJ.M.NoM.A.RiveraPhys. Rev. Lett.110212013211802arXiv:1212.4806 [hep-ph]M.GustafssonJ.M.NoM.A.RiveraPhys. Rev. Lett.112252014259902Erratum[5]H.OkadaT.TomaPhys. Rev. 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