Status of neutrino mass models G. Ross, Invisibles 13, Lumley - PowerPoint PPT Presentation

Status of neutrino mass models G. Ross, Invisibles 13, Lumley Castle,July 2013

Neutrino mixing Symmetry or anarchy? Tri-bi-maximal mixing: tan Θ = 1/ Harrison, Perkins, Scott 2 tan Θ = 2 /(1 + 5) ≡ 1/ φ Golden ratio mixing: Datta et al; Kajyama et al Barger et al; Fukugita et al tan Θ = 1 Bi 2 -maximal mixing: Davidson, King

Neutrino mixing Gonzalez-Garcia, Maltoni, Salvado, Schwetz see also: Forero, Tortola, Valle Fogli, Lisi, Marrone, Montanino, Palazzo, Rotuno

Symmetries of the mass matrices M l = h T M l h * e . g . Z 3 , h = Diag (1, e 2 i π /3 , e 4 i π /3 ) M l = Diag ( m e , m µ , m τ ) Klein symmetry M ν = S T M ν S Z 2 × Z 2 M ν = U PMNS Diag ( m ⊥ , m  , m @ ) U PMNS T Diag ( ± 1, ± 1, ± 1) U PMNS , det S = 1 S = U PMNS *

Symmetries of the mass matrices M l = h T M l h * e . g . Z 3 , h = Diag (1, e 2 i π /3 , e 4 i π /3 ) M l = Diag ( m e , m µ , m τ ) Klein symmetry M ν = S T M ν S Z 2 × Z 2 M ν = U PMNS Diag ( m ⊥ , m  , m @ ) U PMNS T Diag ( ± 1, ± 1, ± 1) U PMNS , det S = 1 S = U PMNS * Z 2 × Z 2 ⇒ Choice of symmetry mass matrix structure e.g. ¡ ⎛ ⎞ ( − , − ) ν @ = ( ν µ − ν τ ) / 1 0 0 2 { ¡ ⎜ ⎟ µ ↔ τ U = Bi-maximal 0 0 1 θ 13 = 0 ⎜ ⎟ ⎝ ⎠ 0 1 0 ( + , + ) ⎛ ⎞ ν  = ( ν e + ν µ + ν τ ) / − 1 3 2 2 { ¡ S TBM = 1 Tri-maximal ⎜ ⎟ − 1 2 2 ( ) ⎜ ⎟ ( + , − ) 3 ν ⊥ = 2 ν e − ( ν µ + ν τ ) / 2 − 1 ⎝ ⎠ 2 2

Origin of symmetries Direct: φ ν ⎯ ⎯ → Z 2 × Z 2 G family φ l ⎯ → ⎯ l Z 3 l ⊂ S 4 ≅ ( Z 2 × Z 2 ) × S 3 ⊂ SU (3), U ⊂ A 4 ( S TBM "accidental") e . g . U , S TBM , Z 3 | Emergent: Z 2 × Z 2 ⊂ G family G family = Δ (27) ⊂ SU (3) e . g . ν = a ψ i φ 123 i ψ j φ 123 j + b ψ i φ 23 i ψ j φ 23 j L eff Symmetric under { ¡ T,S TBM φ 123 ∝ (1,1,1), φ 2 ∝ (1,0,0), φ 3 ∝ (0,0,1) Vacuum alignment

⇒ Symmetries ¡ ¡ Tr-Bi-Maximal, Golden Ratio, … θ 13 ≠ 0 ??? Anarchy? ⇒ Symmetry breaking perturbations ? New symmetries ?

Symmetry breaking perturbations ν = m @ ( ν a + ε ab ν b + ..) 2 + m  ( ν b − ε ab ν a + ..) 2 + m ? ( ν c + ..) 2 L m ( ) ν a = 1 { ¡ ν µ − ν τ ( ) { ¡ ν a = 1 ν µ − ν τ 2 ( ) 2 ν b = 1 TBM GR ν e + ν µ + ν τ t θ = 1/ φ ν b = s θ ν e + c θ ( ν µ + ν τ ) / 2 3 ( ) ν c = c θ ν e − s θ ( ν µ + ν τ ) / ν c = 1 2 2 ν e − ν µ − ν τ 6 θ 13 ≠ 0 ⇒ must break U ⇒ ν a , b ν a , c mixing and / or

• General mixing (TBM case): c’s random Altarelli, Feruglio, Merlot

• Restricted (bilinear) mixing (TBM case): ν = m @ ( ν a + ε ab ν b + ..) 2 + m  ( ν b − ε ab ν a + ..) 2 + m ? ( ν c + ..) 2 L m ( ) ν a = 1 { ¡ ⎛ ⎞ ν µ − ν τ 3 e − i δ 2 c s 2 ⎜ ⎟ 6 3 ( ) ν b = 1 TBM ν e + ν µ + ν τ ⎜ ⎟ − 1 3 − 2 e i δ 2 + 3 e − i δ U = c s c s 3 ⎜ ⎟ 6 ( ) ν c = 1 2 e i δ 3 e − i δ ⎜ − 1 3 + − c 2 + ⎟ 2 ν e − ν µ − ν τ c s s ⎝ ⎠ 6 6 θ 13 ≠ 0 ⇒ must break ⇒ ν a , b ν a , c mixing U or ≡ δθ 12 small ⇒ residual symmetry bilinear mixing Z 2 S TBM ⇒ ν a , b , S TBM T ⇒ ν a , c S GR ⇒ ν a , b , S GR T ⇒ ν a , c Hall, GGR Luhn

ν = 1 + e − i δ s 13 s 23 2 2 ⎛ ⎞ ( ) ν = m 3 2 2 + s 13 e − i δ ( ν e + ν µ + ν τ ) 2 s 13 e i δ ( ν µ − ν τ ) @ ( ν µ − ν τ ) / + m  ( ν e + ν µ + ν τ ) / 3 − L m ⎜ ⎟ ⎝ ⎠ θ 13 ⎛ ⎞ 3 e − i δ 2 c s ⎜ ⎟ 6 3 ⎜ ⎟ 2 e i δ 3 e − i δ U = − 1 3 − 2 + c s c s ⎜ ⎟ 6 ⎜ − 1 3 + 2 e i δ − c 2 + 3 e − i δ ⎟ c s s ⎝ ⎠ 6

θ 13 charged lepton or neutrino origin? ν − θ 23 l c 23 ν e i δ 23 s 23 ≈ s 23 ν − θ 12 l c 23 ν c 12 ν e i δ 12 s 12 ≈ s 12 ν − θ 12 θ 13 e − i δ 13 = θ 13 ν + δ 12 ν e − i δ 13 l s 23 ν e − i ( δ 23 e ) (1,1) texture zero †  θ C m e Cabibbo haze: m µ 3 { ¡ θ C M q , l : small mixing …dominated by ν ≈ θ 12 l ν = 0, l s 23 θ 13 θ 13 ≈ θ 12 M ν : tri-bi-maximal 2 2 + m  ν = m @ 2 ⎡ ⎤ ⎡ ⎤ 2 ( ν µ − ν τ ) 3 ( ν e + ν µ + ν τ ) L m 1 1 ⎣ ⎦ ⎣ ⎦ Datta, Everett, Ramond l = θ C (GUT?), θ 13 = 9 0 ! If θ 12 Marzocca, Petkov, Romanino, Spinrath Antusch et al l = θ C † θ 12 …but inconsistent with other plausible GUT relations

Symmetry fights back - I ' : Z 2 × Z 2 S TBM , GR , ( U × CP ) Diag Klein symmetry: Harrison, Scott Feruglio, Hagedorn, Ziegler Ding, King, Luhn, Stuart Talbert, GGR S ,( U × CP ) Diag SU ,( U × CP ) Diag S , U ν a ( + , − ) ( + ,  ) ( − ,  ) ν b ( + , + ) ( + , ± ) ( + , ± ) ν c ( − , + ) ( − , ± ) ( − , ± ) − ν a , ± i ν b ν a , ± i ν c Mixing ⎛ ⎞ 3 e ± i π /2 2 c s ⎜ ⎟ 6 3 ⎜ ⎟ 2 e  i π /2 3 e ± i π /2 U = − 1 3 − 2 + c s c s ⎜ ⎟ 6 ⎜ − 1 3 + 2 e  i π /2 − c 2 + 3 e ± i π /2 ⎟ c s s ⎝ ⎠ 6

Symmetry fights back - I ' : Z 2 × Z 2 S TBM , GR , ( U × CP ) Diag Klein symmetry: Feruglio, Hagedorn, Ziegler Ding, King, Luhn, Stuart ( ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡) ¡ Generalised CP I. ¡ II. ¡ III. ¡

Symmetry fights back - II ' × Z 3 ⊂ G family Z 2 × Z 2 Direct: G family = Δ (600): sin 2 θ 13 = 0.028, sin 2 θ 23 = 0.38 Lam G family = Δ (6 n 2 ) ≅ ( Z n × Z n ) × S 3 , n even | δ = 0, π Trimaximal mixing, King, Neder, Stuart

Symmetry fights back - III Emergent: King 2 ν R (1,1) Texture Zero 1 parameter fit ( m 2 / m 3 ) , η = 2 π , ¡ 5

Vacuum alignment (A 4 model) , η = 2 π 5 King ¡

Symmetry fights back - IV Mixing and masses from an extremum principle ? 5 ⊗ O (3) local = SU (3) [ ] ⎯ ⎯ → Y i Alonso, Gavela, Isidori, Maiani G family Alonso, Gavela, Hernandez, Merlo, Rigolin Grinstein, Redi, Villadoro Y i dynamical variables- “Natural extrema” e.g. x SU(3) adjoint: I 1 = Tr ( x 2 ), I 2 = Det ( x ) V ( I 1 , I 2 ):

“Natural extrema” Quarks : ¡ → Leptons: SU (3) l ⊗ O (3) → SU (2) l ⊗ U (1) Difference due to Majorana masses restricting redefinition of neutrinos Add ¡perturba6ons: ¡ Quasi degenerate neutrinos Normal or inverted hierarchy 2 large mixing angles Θ 13 generically small

Epilogue • Masses -Froggatt-Nielsen -Xtra-dimension/Composite

Epilogue • ( ) Masses -Froggatt-Nielsen n θ Λ -Xtra-dimension/Composite 5D mass parameters Flavour blind Flavour hierarchy Agashe, Okui, Sundrum ..Dirac neutrinos .. q, l θ 13 large 4D strongly coupled AdS/CFT analogue CFT – Walking Technicolour Leptons elementary - couple to Higgs via fermionic operators in strong sector Exponential suppression factors come from RG running with large scaling dimensions

Epilogue • Masses -Froggatt-Nielsen Majorana or Dirac } ¡ Normal/Inverted/ -Xtra-dimension/Composite Quasi-degenerate (O(3))

Epilogue • ( ) Masses -Froggatt-Nielsen n θ Majorana or Dirac } ¡ Λ Normal/Inverted/ † -Xtra-dimension/Composite Quasi-degenerate (O(3)) † Radiative generation of θ 13 Dighe, Goswami, Rodejohann Ellis, Lola …

Epilogue • Masses -Froggatt-Nielsen -Xtra-dimension/Composite -Texture (zeros) e.g. T χ M Krishnan, Harrison, Scott

Epilogue • Masses -Froggatt-Nielsen -Xtra-dimension/Composite -Texture (zeros) • Quark-lepton unification? -Spontaneous breaking (natural extrema) -Hierarchical see-saw

Hierarchical see-saw (Sequential Dominance) Quarks, charged leptons, neutrinos can have similar Dirac mass ⎛ ⎞ q , l , ν = α ψ i φ 3 i j i j i j i j L Dirac ψ j c φ 3 + β ψ i φ 123 ψ c j φ 23 + ψ i φ 23 ψ c j φ 123 ⎟ + γ ψ i φ 23 ψ c j φ 23 Σ 45 α > β ⎜ ⎝ ⎠ ε d = 0.15, a d = 1 ε 3 + ε 4 − ε 3 + ε 4 ⎛ ⎞ m b  3 m τ < ε 4 ε l = 0.15, a e = − 3 M Dirac ⎜ ε 3 + ε 4 a ε 2 + ε 3 − a ε 2 + ε 3 ⎟ ( ) m s  m µ = (1,1) T.Z. ⎜ ⎟ ε u = 0.05, a u = 1 m 3 − ε 3 + ε 4 − a ε 2 + ε 3 ⎜ ⎟ m d  9 m e 1 ⎝ ⎠ ε ν = 0.05, a ν = 0

Hierarchical see-saw (Sequential Dominance) Quarks, charged leptons, neutrinos can have similar Dirac mass ⎛ ⎞ q , l , ν = α ψ i φ 3 i j i j i j i j L Dirac ψ j c φ 3 + β ψ i φ 123 ψ c j φ 23 + ψ i φ 23 ψ c j φ 123 ⎟ + γ ψ i φ 23 ψ c j φ 23 Σ 45 α > β ⎜ ⎝ ⎠ ε d = 0.15, a d = 1 ε 3 + ε 4 − ε 3 + ε 4 ⎛ ⎞ m b  3 m τ < ε 4 ε l = 0.15, a e = − 3 M Dirac ⎜ ε 3 + ε 4 a ε 2 + ε 3 − a ε 2 + ε 3 ⎟ m s  m µ = ⎜ ⎟ ε u = 0.05, a u = 1 m 3 − ε 3 + ε 4 − a ε 2 + ε 3 ⎜ ⎟ m d  9 m e 1 ⎝ ⎠ ε ν = 0.05, a ν = 0 Majorana mass structure M 1 < M 2 << M 3 ( ) i φ 3 i + b ε 3 φ 23 i φ 23 i + c ε 2 φ 123 i φ 123 c a φ 3 i L M = θψ i c ψ j small < φ 23 >= ε (0,1, − 1), < φ 123 >= ε 2 (1,1,1) ν / H 2 = β 2 j + β 2 j + ( α + β ) 2 i ψ j φ 123 i ψ j φ 23 ψ i φ 123 ψ i φ 23 ψ i φ 3 i ψ j φ 3 j L eff ⇒ m  = O ( ε ) M 1 M 2 M 3 m @