Radiative Neutrino Mass Generation and Dark Matter - Institute for ...

OutlineOutline1 Introduction2 Neutrino Mass Generation3 Dark Matter4 A Concrete Model of Radiative SeesawConstraintsCoannihilation Effect of DMDirect Detection of (Leptophilic) DM5 Further Extension of Radiative SeesawSUSY with anomalous U(1)Indirect detection of DM with flavor symmetry6 SummaryTakashi Toma (IPPP) Internal Seminar 7th June 2013 2 / 34

Neutrino Mass GenerationNeutrino Mass Generation at Tree LevelInverse seesaw mechanismSmall lepton number violation (L/) → light neutrino masses.Three singlets S L are added.L = −ν L m D N R −NR cMSL c − 1 2 S LµSLcMass matrix⎛0 m D 0⎝ mDT 0 M0 M T µ⎞⎠ →m ν ∼ m D M −1 µM T−1 m T D(if µ ≪ m D , M)Typical scale of µ is keV.M ∼ 10 TeV, m D ∼ 100 GeV → m ν ∼ 0.1 eV.Note : generally 1 2 N cR µ′ N R also exists.Takashi Toma (IPPP) Internal Seminar 7th June 2013 5 / 34

Neutrino Mass GenerationExamples of ModelsExamples of ModelsZee modelSU(2) L U(1) Yφ 2 2 1h + 1 1· neutrino mass (1-loop level)Ma modelSU(2) L U(1) Y Z 2N i 1 0 −1η 2 1/2 −1· neutrino mass (1-loop level)· DM candidates (N 1 or η 0 )V = µφ T 1 φ 2h −V = λ 52(φ † η ) 2Takashi Toma (IPPP) Internal Seminar 7th June 2013 7 / 34

Dark MatterDark MatterTakashi Toma (IPPP) Internal Seminar 7th June 2013 9 / 34

Dark MatterNature of DM· stable (or long lifetime)· non-relativistic particle· electrically neutral· no electromagnetic interaction (at tree level)DM candidateIn order to include DM we have to stabilize a particle.→ Z 2 parity· Neutralino, Lightest KK Particle, Right-handed neutrino,Gravitino, Axion etc..Takashi Toma (IPPP) Internal Seminar 7th June 2013 10 / 34

Dark MatterDM Thermal ProductionDM Thermal ProductionY = n/sDM number density is determined by decoupling from thermalbath in the universe.Number density follows the Boltzmann equation.dYdz = −ΓY eqHz[ ( YY eq) 2−1], z ≡ m T , Γ ≡ 〈σv〉n eq, Y ≡ n sapproximate solutionΩh 2 ≈ 1.04×109 [GeV −1 ]√g∗ m pl 〈σv〉= 0.12 (Planck)z = m/T↔ 〈σv〉 ≈ 3×10 −26 [cm 3 /s]= 3×10 −9 [GeV −2 ]Takashi Toma (IPPP) Internal Seminar 7th June 2013 11 / 34

Dark MatterNon-thermal ProductionNon-thermal production of DM arXiv:0810.4147· a metastable particle (χ 2 ) decays into DM (χ 1 )· simuletaneous Boltzmann equationdY 1dzdY 2dz= − Γ A1Y 1eqHz= − Γ A2Y 2eqHz[ ( ) ] 2 Y1−1Y 1eq[ ( ) ] 2 Y2−1Y 2eq+N decΓ 2Hz Y 2− Γ 2Hz Y 210 0 10 -2 10 0 10 2 10 4 10 6 10 8Y i = n i (z)/s(z)10 -210 -410 -610 -810 -1010 -1210 -1410 -16z = m 1 /TY 1Y 1eqY 2χ 2 → N dec χ 1 +XY 2eq〈σv〉 > 3×10 −26 [cm 3 /s]m 1 = 130 [GeV]m 2 = 300 [GeV] = 3.0x10 -25 [GeV -2 ] = 3.0x10 -26 [GeV -2 ]Γ 2 = 1.0x10 -24 [GeV]Γ −12 0.1 sExplaination of the positronand gamma-ray excess incosmic-ray observations?Takashi Toma (IPPP) Internal Seminar 7th June 2013 12 / 34

Concrete ModelA Concrete Model of Radiative SeesawTakashi Toma (IPPP) Internal Seminar 7th June 2013 13 / 34

Concrete ModelInteractions and Neutrino MassesThe Simplest Model (Ma Model)New particlesSU(2) L U(1) Y Z 2N i 1 0 −1η 2 1/2 −1InteractionsNeutrino mass generation at1-loop levelInclude DM candidatesN 1 and η 0L = (D µ η) † (D µ η)+N i i∂/N i − M i2 Nc i N i +h αi l α η † N i +h.c.−V (φ,η)V (φ,η) = mφ 2 |φ|2 +mη|η| 2 2 + λ 12 |φ|4 + λ 22 |η|4)( )+λ 3 |φ| 2 |η| 2 +λ 4(φ † ηη † φ+ λ 52〈η〉 = 0 is assumed.φ and η do not mix after the symmetry breaking.assumed that new particles are less than a few TeV.[ ( 2 ( ) ] 2φ η) † + η † φTakashi Toma (IPPP) Internal Seminar 7th June 2013 14 / 34

Concrete ModelNeutrino Massesη 0 split after electroweak symmetry breaking.η 0 = 1 √2η R + i √2η I , mass eigenstates (η R ,η I )(m ν ) αβ=3∑ h αi h βi M i[mR2(4π) 2 mR 2 −M2 ii=1) m2log(RMi2 −∼ ( hΛh T) αβΛ = diag(Λ 1 ,Λ 2 ,Λ 3 )m 2 Im 2 I−M 2 i)] m2log(IMi2When λ 5 ≪ 1, m 2 R ≈ m2 I = M 2 η3∑ 2λ 5 h αi h βi 〈φ 0 〉 2 ( ) M2(m ν ) αβ≃(4π) 2 I iMi=1 iMη2I(x) = x (1+ x logx )1−x 1−xTakashi Toma (IPPP) Internal Seminar 7th June 2013 15 / 34

Concrete ModelConstraintsThe parameters are constrained by various aspects.Neutrino mass scale m ν ∼ 10 −1 eVNeutrino mixingU T PMNS m νU PMNS = diag(m 1 ,m 2 ,m 3 )Lepton flavor violation (LFV)µ → eγ : Br(µ → eγ) ≤ 2.4×10 −12 → 5.7×10 −13 (now)µ → 3e?Thermal relic density of DM· N 1 is assumed to be DM here.· Leptophilic DM.· degenerated with N 2 .Takashi Toma (IPPP) Internal Seminar 7th June 2013 16 / 34

Concrete ModelConstraintsTo derive the neutrino mass scale(λ 5 h 210 −11 ∼ M √ )i ∆m 2〈φ〉 0.05 eVThe structure of the neutrino mass matrix is determined by theYukawa matrix h αi .The flavor structure:⎛ ⎞ǫ 1 ǫ 2 h 3′h αi = ⎝ h 1 h 2 h 3⎠, ǫ i ≪ h ih 1 h 2 −h 3ǫ i are understood as deviations from the Tri-bimaximal mixing.→ sin 2 θ 12 = 1 3 +ǫ, sin2 θ 23 = 1 2 +ǫ′ , sin 2 θ 13 = 0+ǫ ′′ .U T PMNS m νU PMNS = diag(m 1 ,m 2 ,m 3 )Takashi Toma (IPPP) Internal Seminar 7th June 2013 17 / 34

Concrete ModelConstraintsConstraints from LFVBr(l α → l β γ) = 3α em64πG 2 F M4 η3∑∣i=1The experimental boundsBr(µ → eγ) < 2.4×10 −12Br(τ → µγ) < 4.4×10 −8Br(τ → eγ) < 3.3×10 −8( Mhαi ∗ 2) ∣ 2h i ∣∣∣βiF 2Mη2 Br(l α → l β ν α ν β )where Br(µ → eν µ ν e ) ≃ 1, Br(τ → µν τ ν µ ) ≃ 0.174,Br(τ → eν τ ν e ) ≃ 0.178.→ Yukawa couplings h αi should be small.orSpecial structure of Yukawa matrix.Takashi Toma (IPPP) Internal Seminar 7th June 2013 18 / 34

Concrete ModelConstraintsConstraint from DM Relic DensityThe lightest right-handed neutrino N 1 is assumed to be DMcandidate.The channel: N 1 N 1 → l α l β (t, u-channel)Expansion in terms of v 2 , σv = a+bv 2 +O(v 4 )Fermionic DM is often suppressed by chiral suppression.The annihilation cross section has no s-wave due to chiralsuppression.σv =τ∑α=e|h α1 | 424πM 2 1(M41 +M 4 η)( )M21 +Mη2 4v 2 ∝ v 2→ the Yukawa couplings h αi should be large.Takashi Toma (IPPP) Internal Seminar 7th June 2013 19 / 34

Concrete ModelCoannihilation of DMCoannihilation of DMIf N 2 is degenerated with N 1 (M 1 ≈ M 2 ), they can coannihilate:The effective annihilation cross section σ eff includesN 1 N 2 → l α l β , N 2 N 2 → l α l β .s-wave appears due to the coannihilation processN 1 N 2 → l α l β if the Yukawa h αi are complex.σ eff v = a eff +b eff v 2 , a eff ∝ Im(h ∗ 1h 2 ) ≠ 0.→ It is possible to be consistent with LFV and DM relic abundance.Takashi Toma (IPPP) Internal Seminar 7th June 2013 20 / 34

Concrete ModelAllowed parameter region fromNeutrino mass and mixing Perturbativity |h i | < 1.5LFVDM relic abundance Ωh 2 = 0.12ξ ≡ Im(h ∗ 1 h 2)A: 2.00 < M η /M 1 < 9.80B: 1.20 < M η /M 1 < 2.00C: 1.05 < M η /M 1 < 1.20D: 1.00 < M η /M 1 < 1.051 DM mass 3 TeVTakashi Toma (IPPP) Internal Seminar 7th June 2013 21 / 34

Concrete ModelDirect Detection of DMDirect DetectionDetection RatedRdE R= ∑ nuclei∫ρ ⊙ 1m DM m detNuclei are made of quarks.→ Interactions with quarks areimportant.Many direct detectionexperiments are performed.XENON100, CDMSII, DAMA,CoGeNT, CRESST, KIMS etc.v>v mindσdE Rvf ⊙ (v+v e )d 3 vdσ/dE R : cross section (Particle physics dependence)ρ ⊙ , v: DM local density, velocity (Astrophysics dependence)Takashi Toma (IPPP) Internal Seminar 7th June 2013 22 / 34

Concrete ModelDirect Detection of DMElastic scattering N 1 A → N 1 A is highly suppressed.Scattring with nuclei occurs inelastically in the model likeN 1 A → N 2 A.We need the effective coupling of N 1 N 2 γ.N 2γ ∗ =N 2γ ∗ +N 2η +l αl αl αη +η +γ ∗N 1N 1(L eff = ia 12 N 2 γ µ N 1 ∂ ν µ12)F µν +i N 2 σ µν N 1 F µν +ic 12 N 2 γ µ N 1 A µ2There are three types of interactions. a 12 , µ 12 , c 12 ∝ ξ ≡ Im(h2 ∗h 1)→ Charge int. a 12 and c 12 , Dipole int. µ 12 .N 1Takashi Toma (IPPP) Internal Seminar 7th June 2013 23 / 34

Concrete ModelDirect Detection of DMScattering with nucleiN 1l −N 2N 1η +N 2η + η +l −l −γγAAAAInelastic Scattering with nuclei occurs when δm 100 keVPhoton has small transter energy E R .Three types of cross sections are obtained.Charge-Charge coupling: σ CC ∼ (a 12 +c 12 ) 2 Z 2Dipole-Charge coupling: σ DC ∼ µ 2 12 Z2Dipole-Dipole coupling: σ DD ∼ µ 2 12 µ2 Nσ CD is suppressed.Takashi Toma (IPPP) Internal Seminar 7th June 2013 24 / 34

Concrete ModelDirect Detection of DMComparison of the couplings for M η /M 1 = 1.5CC coupling is dominant for rather small mass range.DD coupling is larger than DC coupling for DAMA and KIMS.→ dependence of µ NTakashi Toma (IPPP) Internal Seminar 7th June 2013 25 / 34

Concrete ModelDirect Detection of DMδ = 0 keVδ = 40 keVThe inelastic cross section (CC coupling) is enhanced if DM andη are highly degenerated (light blue region).→ the behavor of the loop function in the effective couplings.Enhanced by a 12 ∝ M2 1m 2 lwhen M 1 ≈ M ηSome parameter space can be investigated by XENON1T.Takashi Toma (IPPP) Internal Seminar 7th June 2013 26 / 34

Extensions of Radiative SeesawExtensions of Radiative SeesawTakashi Toma (IPPP) Internal Seminar 7th June 2013 27 / 34

Extensions of Radiative Seesaw1. Supersymmetry with anomalous U(1) AA pair of inert Higgs η u and η d is required.Break gauge coupling unification at GUT scale because ofadditional inert Higgs doublets ηU(1) A anomaly cancellation by Green-Schwarz mechanismδL = − g2 A TrQ A32π 2 α(x)ǫ µνρσ F µν F ρσL = aǫ µνρσ F µν F ρσ , a → a+δ GS α(x)Remain accidental Z 2 parity after the U(1) A breakingTakashi Toma (IPPP) Internal Seminar 7th June 2013 28 / 34

Extensions of Radiative SeesawInteresting featuresZ 2 is softly broken → metastable DMlifetime is determined by charge assignment of U(1) Aτ ∝ exp(δ −1GS ), δ GS = TrQ A48π 2We have Multi-component DM (R-parity and softly broken Z 2 )Neutralino and the lightest Z 2 odd particle.The positron excess of AMS-02 and PAMELA is explained bythe decay of DM.l αψ N1¯l βχTakashi Toma (IPPP) Internal Seminar 7th June 2013 29 / 34

Extensions of Radiative Seesaw2. Flavor SymmetryIntroduce flavor symmetry to derive neutrino mixing.θ 12 = 34 ◦ , θ 23 = −45 ◦ , θ 13 = −9 ◦DM decay channel is also controlled by the symmetry.Allowed interaction of DMs X and X ′Decay rateL = λ XΛ 2LLEc X c + λ X ′Λ 2 LLEc X c′dΓ Xdx = |λ X| 2 m 5 X48(4π) 3 Λ 4x2 (21−16x), x = 2E em XΓ X = |λ X| 2 m 5 X16(4π) 3 Λ 4Takashi Toma (IPPP) Internal Seminar 7th June 2013 30 / 34

Extensions of Radiative SeesawPositron flux from DMdΦdE =v e ρ(r)4πb(E)m X∫ mX /2EAstrophysical dependences are in I(E,E ′ )e + /(e + +e - ) [GeV -1 cm -2 s -1 sr -1 ]10 0 10 0 10 1 10 2 10 310 -110 -2arXiv:1304.2680PAMELAAMS-02BackgroundBackground + Dark MatterE [GeV]dE ′dΓ XdE ′ I(E,E′ )small dump around 120 GeVe : µ : τ = 1 : 1 : 1 becauseof the flavor symmetryTwo-component DMBest fit :m X = 244 GeV, Γ X = 1.2×10 28 s.m X ′ = 1360 GeV, Γ X ′ = 2.4×10 27 s.Takashi Toma (IPPP) Internal Seminar 7th June 2013 31 / 34

SummarySummary1 The SM should be extended to include neutrino masses and DM.2 In some Radiative Seesaw models, neutrino masses and DM arerelated.3 Coannihilation plays an important role to be consistent with allthe constraints.4 Due to small mass difference between N 1 and N 2 , inelasticscattering between DM and nuclei is possible even if the DM isleptophilic.Takashi Toma (IPPP) Internal Seminar 7th June 2013 32 / 34

Future WorksFuture Works1 Gamma-ray from DM annihilation.E 2 · dJ/dE [GeV/cm 2 /s/sr]10 -510 -610 -710 0 10 1 10 2E [GeV]Required cross section :σv ∼ 10 −27 [cm 3 /s]↔ relic density of DMσv ∼ 10 −26 [cm 3 /s]Large cross section is required ↔ DM relic density2 Lepton Flavor Violation µ → 3e.When Yukawa coupling is large enough, µ → 3e can be largerthan µ → eγ→ Radiative Seesaw or Inverse Seesaw3 The other extensions of the SM.(model building of new radiative seesaw)Takashi Toma (IPPP) Internal Seminar 7th June 2013 33 / 34

Thank you for your attention!Takashi Toma (IPPP) Internal Seminar 7th June 2013 34 / 34