Neutrino masses : beyond d=5 tree-level operators Florian Bonnet - PowerPoint PPT Presentation

Neutrino masses : beyond d=5 tree-level operators Florian Bonnet Würzburg University based on arXiv:0907 .3143, JHEP 10 (2009) 076 and arXiv:1205.5140 to appear in JHEP In collaboration with Daniel Hernandez, Martin Hirsch, Toshi Ota and Walter Winter What’ s ? Invisibles12, Firenze, July 2012 ν F . Bonnet 1 July 2012 - GGI

Seesaw Mechanism Standard Model (SM) does not explain masses ν Call for New Physics (NP) > EW Model independent approach : effective theories L eff = L SM + δ L d =5 + δ L d =6 + . . . Lowest order: unique d=5 operator H H Weinberg operator Neutrino masses L L Recent review A. Abada et al. ’07 F . Bonnet 2 July 2012 - GGI Identifying NP ∼ constraining new parameters

Seesaw Mechanism H H ? L L F . Bonnet 3 July 2012 - GGI Identifying NP ∼ constraining new parameters

Seesaw Mechanism H H µ ∆ H H H H N R Σ R Y T Y T Y Σ Y N Σ N ∆ L L L L Y ∆ L L Type I Type II Type III Minkowski 1977 Magg, Wetterich 1980, Foot, Lew, He and Joshi 1989 Yanagida 1979 Schechter, Valle 1980, Gell-Mann et al. 1979 Wetterich 1980, Mohapatra, Senjanovic 1980 Cheng, Li 1980, Lazarides, Shafi, Wetterich 1981 Mohapatra, Senjanovic 1981, F . Bonnet 4 July 2012 - GGI Identifying NP ∼ constraining new parameters

Seesaw Mechanism H H µ ∆ H H H H N R Σ R Y T Y T Y Σ Y N Σ N ∆ L L L L Y ∆ L L Type I Type II Type III v 2 v 2 v 2 Y T Y T Y ∆ µ ∆ Y Σ Y N m ν ∝ m ν ∝ m ν ∝ Σ N M 2 M Σ M N ∆ Problem : ⇢ Y ∼ O (1) , M ∼ GUT No LHC access m ν < eV ⇒ small couplings Y ∼ 10 − 5 , M ∼ TeV F . Bonnet 5 July 2012 - GGI Identifying NP ∼ constraining new parameters

Way out Goals : New Physics @ TeV large couplings (LFV) Means : need of additional source of suppression Radiative generation of neutrino masses d>5 operator Small lepton number violating contributions ◆ n ⇣ v m ν ∝ v 2 ✓ ⌘ d − 5 1 Λ × × ✏ LNV × 16 ⇡ 2 Λ F . Bonnet 6 July 2012 - GGI Identifying NP ∼ constraining new parameters

Small lepton number violation contributions

Inverse/Linear Seesaw Type II : natural H H µ ∆ ∆ Y ∆ L L v 2 Y ∆ µ ∆ m ν M 2 ∆ LFV Y † ∆ Y ∆ F . Bonnet 8 July 2012 - GGI Identifying NP ∼ constraining new parameters

Inverse/Linear Seesaw Type II : natural Type I/III : extra fermion Mohapatra, Valle 1986 N 2 N 1 ν H H ν   ! Y N 0 0 µ ∆ N 1 Inverse Seesaw Y T Λ 0   N Λ 0 µ N 2 ∆ H H µ Y T Y ∆ Y N N L L N 1 N 2 N 1 L L v 2 µ − Y T Λ 2 Y N v 2 Y ∆ µ ∆ m ν m ν N M 2 ∆ Y † LFV LFV Y † N Y N ∆ Y ∆ F . Bonnet 8 July 2012 - GGI Identifying NP ∼ constraining new parameters

Inverse/Linear Seesaw Type II : natural Type I/III : extra fermion Akhmedov et al. 1995 N 2 N 1 ν H H ν   ε Y 0 0 Y N ! µ ∆ N N 1 Y T Linear Seesaw Λ 0  N  T ε Y 0 Λ 0 N 2 N ∆ H H Y T Y 0 Y ∆ ε N N L L N 1 N 2 L L v 2 T v 2 v 2 ✓ ◆ Λ Y N + Y T Y 0 Λ Y 0 Y ∆ µ ∆ m ν m ν ε N N N M 2 ∆ Y † LFV LFV Y † N Y N ∆ Y ∆ F . Bonnet 8 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operators

d>5 operator arXiv:0907 .3143, JHEP 10 (2009) 076 concept : O d =5 = LLHH O d =7 ( LLHH )( H † H ) = O d =9 ( LLHH )( H † H ) 2 = . . . problem : H H H H H H ⇒ L L L L < 1 1 1 ( LLHH )( H † H ) ( LLHH ) ∝ ∝ Λ 3 16 π 2 Λ NP if NP Λ NP > 3 TeV F . Bonnet 10 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator concept : O d =5 = LLHH O d =7 ( LLHH )( H † H ) = O d =9 ( LLHH )( H † H ) 2 = . . . solution : genuine d=D operator as LO with all d<D forbidden new U(1) or discrete symmetry Pb : H†H singlet -> need new fields Chen, de Gouvea, Dobrescu 2006 O n +5 ∼ ( LLHH ) S n Gogoladze, Okada, Shafi, 2008 F . Bonnet 11 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator concept : O d =5 = LLHH O d =7 ( LLHH )( H † H ) = O d =9 ( LLHH )( H † H ) 2 = . . . solution : genuine d=D operator as LO with all d<D forbidden new U(1) or discrete symmetry Pb : H†H singlet -> need new fields Chen, de Gouvea, Dobrescu 2006 O n +5 ∼ ( LLHH ) S n Gogoladze, Okada, Shafi, 2008 O 2 n +5 ∼ ( LLH u H u )( H u H d ) n simplest possibility : d=7 with ( LLH u H u )( H u H d ) Z 5 F . Bonnet 11 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator decomposition : finding all possible heavy fields (mediators) for tree-level realizations of ( LLH u H u )( H u H d ) X Y L Lorentz: S (scalar), V (vector), R/L (fermion) SU(2) Hypercharge F . Bonnet 12 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator Type I (fermion singlet) 1 R/L 0 Type II (scalar triplet) 3 S − 1 Type III (fermion triplet) 3 R/L 0 F . Bonnet 12 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : first example H u H d φ ∼ 1 S µ H u H u 0 N, N 0 ∼ 1 F φ 0 Λ Λ Y ν Y ν κ N 0 N 0 N R N R L L L L F . Bonnet 14 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : first example H u H d φ ∼ 1 S µ H u H u 0 N, N 0 ∼ 1 F φ 0 Λ Λ Y ν Y ν κ N 0 N 0 N R N R L L L L m ν = v 3 u v d ν ( Λ − 1 ) T κ µ Λ − 1 Y ν Y T Masses @TeV -> Y ν ∼ 10 − 4 M 2 2 φ F . Bonnet 14 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : first example H u H d φ ∼ 1 S µ H u H u 0 N, N 0 ∼ 1 F φ 0 Λ Λ Y ν Y ν κ N 0 N 0 N R N R L L L L m ν = v 3 u v d ν ( Λ − 1 ) T κ µ Λ − 1 Y ν Y T M 2 2 φ Y T ν h H 0 u i  ν h H 0   0 0  Y T u i 0 0 Y ν h H 0 u i Λ 0 Y ν h H 0 u i Λ 0     2 κ µ φ h H 0 u H 0 d i Λ 0 M φ → ∞ Λ µ LNV 0 M 2 F . Bonnet 14 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : second example L H u H u Φ ∼ 2 S +1 / 2 N, N 0 ∼ 1 F 0 ζ Λ H d Y ν Y 0 N 0 N R Φ ν L L H u m ν = ζ v 3 u v d T Λ � 1 Y ν ⇣ ⌘ Y T ν Λ � 1 Y 0 ν + Y 0 4 M 4 ν Φ   ζ h H 0 d ih H 0 u i 2 T T   Y T ν h H 0 Y 0 Y T ν h H 0 u i ε LNV Y 0 u i 0 0 ν M 2 ν Φ Y ν h H 0 u i   Λ 0 Y ν h H 0 u i Λ 0     M Φ → ∞  ζ h H 0 d ih H 0 u i 2  ε LNV Y 0 Λ 0 Y 0 Λ 0 ν ν M 2 Φ F . Bonnet 14 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : 1 F 0 / 3 F 0 µ LNV ε LNV 1 F 0 / 3 F 1 F 0 / 3 F 0 0 1 F 0 / 3 F 0 F . Bonnet 15 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : 1 F 0 / 3 F 0 µ LNV ε LNV 1 F 0 / 3 F 1 F 0 / 3 F 0 0 1 F 0 / 3 F 0 d-5 d=7 1/ 1/ ε LNV µ LNV F . Bonnet 15 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator : Type II H u H d H u L L H u H u ( ) ( ) ∆ ∆ ∆ ∆ L H u L H u H d µ ∆ H u H u H d L L H u H u ∆ ∆ H d L L H u H u F . Bonnet 16 July 2012 - GGI Identifying NP ∼ constraining new parameters

d>5 operator d-5 M seesaw @TeV Type I/III M other @TeV Yukawa large M seesaw @TeV M seesaw @TeV M other > TeV M other > TeV Yukawa large Yukawa large 1/ 1/ ε LNV µ LNV d-5 Type II M seesaw @TeV M other @TeV Yukawa large M seesaw @TeV M other > TeV Yukawa large 1/ 1/ Y ∆ µ ∆ F . Bonnet 17 July 2012 - GGI Identifying NP ∼ constraining new parameters

Radiative neutrino masses

one-loop d=5 arXiv:1205.5140, to be published in JHEP concept : H H 1 loop only, no self-energy L L F . Bonnet 19 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 Include Dark doublet Include Zee Model Ma 2006 Zee 1980 Kubo, Ma, Suematsu 2006 Partially Studied in Ma 1998 F . Bonnet 20 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 N/ Σ ∆ ∆ ∆ N/ Σ ∆ ∆ ∆ F . Bonnet 21 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 N/ Σ ∆ ∆ F . Bonnet 21 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 Other problem : Forbid tree-level d=5 solution : It depends ... Loop Seesaw N/ Σ ∆ ∆ F . Bonnet 22 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 F . Bonnet 23 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 F . Bonnet 23 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 simple symmetry is enough Z 2 F . Bonnet 23 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 loop = singlet Z n : loop tree ⇒ solution : No LNV couplings Fermion in loop : Majorana to prevent scalar vev Z 2 F . Bonnet 24 July 2012 - GGI Identifying NP ∼ constraining new parameters

one-loop d=5 loop = singlet Z n : loop tree ⇒ solution : No LNV couplings Fermion in loop : Majorana to prevent scalar vev Z 2 F . Bonnet 24 July 2012 - GGI Identifying NP ∼ constraining new parameters