Models for Neutrino Masses and Physics Beyond Standard Model Salah - PowerPoint PPT Presentation

Models for Neutrino Masses and Physics Beyond Standard Model Salah Nasrj The 2nd Toyama International Workshop on ”Higgs as a Probe of New Physics 2015” (HPNP2015), Toyama, Japan February 12, 2015 1 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 1/27 . .

Introduction . The standard model is not the final theory . • Dark matter . Ω DM h 2 ] ( obs ) = 0 . 1199 ± 0 . 0027 . [ [Planck Collaboration (2013)] • Matter- antimatter asymmetry of the universe . η B : n B = ( 6 . 047 ± 0 . 074 ) × 10 − 10 . [Planck Collaboration (2013)] n γ • Neutrino Oscillations (masses and mixings) • Hierarchy problem • Strong CP problem • Gauge coupling unification • ect.. 2 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 2/27 . .

Global Fit [Gonzalez-Garcia, Maltoni and Schwetz (2014)]. 3 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 3/27 . .

Why m e >> m ν ̸ = 0? . SM is an effective theory . . ef f + L ( 6 ) L = L SM + L ( 5 ) ef f + .. [ Weinberg ( 1979 )] . . . . Λ ∼ 10 14 GeV ef f ∼ 1 m ν ∼ υ 2 . Λ L Φ L Φ ⇒ ⇒ L ( 5 ) . . Λ NP . Can be written in . 3 diff. forms : ....... + C αβ ( ¯ α i σ 2 Φ )( L T L c Type I = β i σ 2 Φ )+ h . c 2 Λ NP .... − C αβ σ L β )( Φ T i σ 2 ⃗ ( ¯ L c α i σ 2 ⃗ Type II = σ Φ )+ h . c 4 Λ NP .... + C αβ ( ¯ σ Φ )( L T Type III = L c α i σ 2 ⃗ β i σ 2 ⃗ σ Φ )+ h . c 2 Λ NP 4 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 4/27 . .

. Seesaw mechanisms . . . Φ Y ν N R + 1 . Type I L ˜ 2 N T = ... + ¯ R C M R N R + h . c ⇒ . C αβ ν M − 1 Y ν = Y T Λ NP [ Minkowski; Yanagida; Ramond and Gell-Mann; Mohapatra and Senjanovic ] . . ∆ Tr ( ∆ † ∆ )+ µ ∆ Φ T i τ 2 ∆ † Φ + h αβ . Type II = ... + M 2 L T Ci τ 2 ∆ L β + h . c = h αβ µ ∆ . C αβ 2 Λ NP M 2 ∆ [ Maag, Watterich, Shafi, Lazaridis; Mohapatra, Senjanovic; Schechter, Valle ] . . Type III = .... + 1 . Σ R i M Σ i Σ c R M ∗ + h α i ¯ L α Σ R i ˜ [ R i + Σ c ] m ν = C αβ υ 2 Σ Σ R Φ + h . c ⇒ 2 . Λ NP [ Foot, He, Lew, Joshi; Ma ] 5 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 5/27 . .

Leptogenesis. Ex: Type I . • Generate a B-L asymmetry through the . out-of-equilibrium decays of N iR into leptons and anti-leptons. ฀ [Fukugita and Yanagida (86)] • The CP-asymmetry from the decay of N i into lepton and anti-leptons: L ¯ ε i = Γ ( N i → L Φ ) − Γ ( N i → ¯ Φ ) [ Flanz et al , 94; Covi, Roulet, Vissani , 94 ] Γ ( N i → L Φ )+ Γ ( N i → ¯ L ¯ Φ ) • Part of it get converted to a baryon asymmetry via sphaleron transitions. 6 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 6/27 . .

Leptogenesis. Ex: Type I • Wash out effects (in addition to the inverse decay) . . ∆ L = 1 scatterings involving top quark: 1. off-shell N 1 ¯ ( s-channel ) ↔ q , L ↔ t ¯ N 1 L t ¯ q ¯ ( t-channel ) ↔ L q , N 1 ¯ t ↔ L ¯ N 1 t q . . ∆ L = 2 scatterings 2. L ¯ ¯ L L ↔ ¯ Φ ¯ L ¯ ¯ L Φ ↔ Φ , Φ , L ↔ Φ Φ . • The final baryon asymmetry : Y B : = n B s ≃ − 4 × 10 − 3 × ε 1 × κ f × C s . . C s = 28 79 : [ Conversion factor ] ; κ f ( ˜ m 1 ) [ Efficiency factor ] ; m 1 = ( YY † ) 11 υ 2 . ˜ M 1 7 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 7/27 . .

Leptogenesis. Ex: Type I After solving the Boltzmann equations: . 3 M 1 . ε 1 ≤ υ 2 ( m 3 − m 1 ) 16 π [ Davidson and Ibarra ( 2002 )] . M 1 > 10 9 GeV ⇒ . [ Buchmuller, Di Bari, Plumacher ( 2004 )] . Wash-out from ∆ L = 2 processes → √ . ¯ m 2 1 + m 2 2 + m 2 m : = 3 < 0 . 2 eV . . ⇒ ฀ m i < 0 . 11 eV 8 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 8/27 . .

Some remarques • A super-heavy RHN is not accessible to collider experiments. • If one take naturalness seriously, then a super-heavy RH neutrinos distablises the EW scale (hierarchy problem): m ν M 3 1 1 < υ 2 ⇒ M < 10 7 GeV | δµ 2 | ≃ | Y α i | 2 M 2 4 π 2 ∑ i ; 4 π 2 υ 2 α , i [ De Gouvea, Hernandez and Tait ( 2014 )] • Super-heavy RHN could render the SM Higgs vacuum stability issue worse. • M 1 > 10 9 GeV ⇒ T RH > 10 9 GeV ⇒ Gravitino problem (if SUSY). • No relation or correlation between ε 1 and the low energy CP violation in the ν -sector. ⇒ Need to reduce the number of parameters: Flavor Symmetries/Textures/Ansatz. [E.g: Frampton, Glashow, Yanagida; Branco, Felipe, Joaquim, Masina, Rebelo and Savoy; Mohapatra, S. N, Yu, ....] 9 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 9/27 . .

Radiative Neutrino Masses . M ν at One loop . (a) Zee Model [(1980)] S (+) ∼ ( 1 , 1 , + 1 ) , Φ 2 ∼ ( 1 , 2 , + 1 / 2 ) , ; A ∝ µ cot β f m 2 l + m 2 l f T ] [ M ν = A 16 π 2 M 2 2 ( ∆ m 2 ) 2 sin 2 2 θ 12 ≥ 1 − 1 [ Koide; Frampton, Oh, Yoshikawa; He ] 12 ∆ 2 m 23 16 . sin 2 2 θ 12 > 0 . 999 ⇒ . Ruled out by solar neutrino oscillation data . 10 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 10/27 .

. Radiative Neutrino Masses . M ν at One loop . (b) Scotogenic Model [Ma (2006)] SU ( 2 ) L × U ( 1 ) Y × Z 2 : N i ∼ ( 1 , 0 , − 1 ) , η ∼ ( 2 , + 1 / 2 , − 1 ) with < η 0 > = 0 , ( M ν ) αβ ≃ λ 5 υ 2 M 2 ln m 2 h α n M n h β n [ ] n 0 If λ 5 << 1 8 π 2 ∑ 1 − m 2 m 2 M 2 0 − M 2 0 − M 2 n n n n . M 2 n ln m 2 [ ] i ∼ 10 − 10 ( ) For . ∼ 1 ⇒ λ 5 h 2 M i 1 − n 0 m 2 M 2 0 − M 2 TeV n The possible DM candidates: • The lightest N i if min ( M i ) < m R , I , or • η R if m R < m I , min ( M i ) , or • η I if m I < m R , min ( M i ) . 11 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 11/27 .

. Radiative Neutrino Masses . M ν at One loop . (c) Scotogenic Model [Ma (2013)] SU ( 2 ) L × U ( 1 ) Y × U ( 1 ) D : η 1 ∼ ( 2 , + 1 / 2 , + 1 ) , η 2 ∼ ( 2 , + 1 / 2 , − 1 ) , N i = 1 , 2 , 3 ∼ ( 1 , 0 , + 1 ) . L , R [ ] m 2 ln m 2 m 2 ln m 2 ( h 1 ) n α M n ( h 2 ) n β + 1 ↔ 2 [ ] ( M ν ) αβ ∝ λ 5 ∑ 1 1 2 2 − 8 π 2 m 2 1 − M 2 M 2 m 2 2 − M 2 M 2 n n n n n The possible DM candidates: • The lightest N i if U ( 1 ) D is unbroken, or • The lightest neutral scalar mass eigenstate χ 1 if U ( 1 ) D is spontaneously broken and m χ 1 < min ( M i ) . 12 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 12/27 .

. Radiative Neutrino Masses . M ν at One loop . (c) Scotogenic Model II [Ma (2013)] 900 900 0.5 0.5 800 800 0.4 0.4 700 0.3 700 0.3 600 0.2 0.2 600 500 ∆ T 0.1 ∆ T 0.1 500 400 0 0 300 400 -0.1 -0.1 200 300 -0.2 -0.2 100 200 -0.3 -0.3 0 m H ± 100 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 m χ 1 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 ∆ S ∆ S 1 m H ± 1 ≥ 100 GeV ; m χ 1 ≥ 90 GeV [ Ahriche, Gaber, Ho, S.N, Tandean (2015)] 13 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 13/27 .

. Radiative Neutrino Masses . M ν at One loop . (c) Scotogenic Model II [Ma (2013)] 900 900 800 800 700 700 m H 1 (GeV) m H 2 (GeV) 600 600 500 500 400 400 300 300 200 100 200 100 200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900 m χ 1 (GeV) m χ 2 (GeV) The red ( 99% ), green ( 95% ), and blue ( 68% ) CL ellipsoids in the ( ∆ S , ∆ T ) plane. [ Ahriche, Gaber, Ho, S.N, Tandean (2015)] 14 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 14/27 .

. Radiative Neutrino Masses . M ν at two loops . Zee-Babu Model S + ∼ ( 1 , 1 , + 1 ) , k ++ ∼ ( 1 , 1 , + 2 ) J ( m 2 h ) k ( ln x ) 2 − 1 { 1 + 3 ( 4 π 2 ) 2 µ m 2 [ ] x >> 1 ( M ν ) αβ ≃ 3 m 2 τ M 2 f ατ h ∗ π 2 J ( x ) = ττ f βτ 2 x → 0 1 . .One of the neutrinos must be massless . .It excludes the possibility for a quasi-degenerate ν spectrum 15 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 15/27 .

. Radiative Neutrino Masses . M ν at three loops . n C l R α − 1 α C i σ 2 L β S + L ⊃ L SM + f αβ L T 1 + g α n N T 2 M n N c i N n + h . c − V ( Φ , S 1 , S 2 ) N i ∼ ( 1 , 1 , 0 ) , S + Z 2 : ( N i , S + 1 , S + 2 ) → ( − N i , S + 1 , − S + 1 , 2 ∼ ( 1 , 1 , + 1 ) ; 2 ) [L. Krauss, S. N, M. Trodden (2003)] [ Other example: Aoki, Kanemura, Seto . .Lightest of N ′ i s is a candidate for DM (2004)] 16 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 16/27 .

. . M ν at three loops: Constraints . . • Fit the observed neutrino mass squared differences and mixings; • Satisfy the bound on LFV processes; [ → Br ( µ → e + γ ) < 5 × 10 − 13 ]; . . ) 4 ( . 1 + m 2 S 2 / m 2 1 . 3 × 10 − 2 m N 1 ) 2 S 1 Ω N 1 h 2 ≃ ( N 1 N 1 → l α l β ( exchange of S ± . . 2 ) ∑ α , β | g 1 α g ∗ 1 β | 2 1 + m 4 S 2 / m 4 135 GeV S 1 m S 1 . . . m S 2 . . . . .Only 15% of the scanned points survive the µ → e + γ constraints 17 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 17/27 .

. . M ν at three loops: Type III . [Chen, McDonald, S. N (PLB 2014); Ahriche, McDonald, S. N (PRD 2014)] . E 0 = DM ; M 1 ∼ 2 . 7 TeV . . σ ( E 0 N → E 0 N ) ∼ 10 − 45 cm 2 ; below the LUX bound. . 18 / 27 . Salah Nasri Neutrino masses and Implications to Cosmology 18/27 .