Neutrino mass models and sizable 13 Christoph Luhn Prologue - PowerPoint PPT Presentation

GGI neutrino workshop Florence – July 3rd, 2012 Neutrino mass models and sizable θ 13 Christoph Luhn

Prologue � remarkable results from neutrino oscillation experiments � tri-bimaximal lepton mixing (until recently) � family symmetries like A 4 and S 4 � origin of the Klein symmetry in the neutrino sector � strategies of implementing a sizable reactor angle θ 13 (post T2K) · tri-bimaximal mixing plus corrections (from extra ingredient) · new family symmetries · non-standard vacuum configurations Neutrino mass models and sizable θ 13 1 of 22

A brief history of neutrino mixing � atmospheric neutrinos · ν µ / ν µ disappear – Super-Kamiokande (1998) � accelerator neutrinos · ν µ disappear – K2K (2002), MINOS (2006) · ν µ converted to ν τ – OPERA (2010 & 2012) · ν µ converted to ν e – T2K, MINOS (2011) � solar neutrinos · ν e disappear – Chlorine (1998), Gallium (1999 - 2009), Super-Kamiokande (2002), Borexino (2008) · ν e converted to ( ν µ + ν τ ) – SNO (2002) � reactor neutrinos · ν e disappear – Double Chooz (2011), Daya Bay, RENO (2012) · ν e disappear – KamLAND (2002) Neutrino mass models and sizable θ 13 2 of 22

2011/2012 story of non-zero θ 13 T2K [arXiv:1106.2822] · θ 13 � = 0 disfavored at ∼ 2 . 5 σ MINOS [arXiv:1108.0015] · θ 13 � = 0 disfavored at ∼ 1 . 6 σ Double Chooz [arXiv:1112.6353] · θ 13 � = 0 disfavored at ∼ 2 σ —————— Daya Bay [arXiv:1203.1669] · θ 13 � = 0 disfavored at ∼ 5 . 2 σ · 7 . 9 ◦ � θ 13 � 9 . 6 ◦ RENO [arXiv:1204.0626] · θ 13 � = 0 disfavored at ∼ 4 . 9 σ · 8 . 7 ◦ � θ 13 � 10 . 8 ◦ Neutrino mass models and sizable θ 13 3 of 22

Three neutrino flavor mixing (in diagonal charged lepton basis) flavor PMNS mixing mass       ν e U e 1 U e 2 U e 3 ν 1  =      ν µ U µ 1 U µ 2 U µ 3 ν 2 ν τ U τ 1 U τ 2 U τ 3 ν 3 atmospheric reactor + Dirac solar Majorana         0 s 13 e − iδ 1 0 0 0 1 0 0 c 13 c 12 s 12 α 2         U PMNS = 0 c 23 s 23 0 1 0 − s 12 c 12 0 0 e 0 2 − s 13 e iδ 0 α 3 0 − s 23 c 23 0 0 1 0 0 c 13 e 2 Neutrino mass models and sizable θ 13 4 of 22

Tri-bimaximal lepton mixing vs. global neutrino fits   − 2 1 0 √ √ 6 3   1 1 1 ≈ ≡ U PMNS U TB   √ √ √ 6 3 2 1 1 1 − √ √ √ 6 3 2   PMNS-angles tri-bimax. 1 σ exp . 1 σ exp .      sin 2 θ 12 : 1  0 . 303 − 0 . 335 0 . 291 − 0 . 325 3 ⇒ sin 2 θ 23 :  1 0 . 44 − 0 . 58 0 . 37 − 0 . 44   2     sin 2 θ 13 : 0 0 . 022 − 0 . 030 0 . 021 − 0 . 028 Forero et al. Fogli et al. (2012) (2012) · TB mixing fits relatively well → family symmetry, e.g. A 4 , S 4 · how to accommodate sizable θ 13 ∼ 8 ◦ − 10 ◦ ? Neutrino mass models and sizable θ 13 5 of 22

Non-Abelian family symmetries · unify three families in multiplets of family symmetry · group should have three-dimensional representations SU (3) PSL 2 (7) ∆(96) SO (3) → ∆(27) Z 7 ⋊ Z 3 S 4 → A 4 Neutrino mass models and sizable θ 13 6 of 22

Symmetries of the mass matrices charged leptons M ℓ = diag ( m e , m µ , m τ ) symmetric under diagonal phase transformation h M ℓ = h T M ℓ h ∗ 4 πi 2 πi 3 ) 3 , e e.g. h = diag (1 , e M ν = U PMNS diag ( m ν 1 , m ν 2 , m ν 3 ) U T neutrinos PMNS symmetry of M ν depends on U PMNS M ν = k T M ν k k = U ∗ PMNS diag ( ± 1 , ± 1 , ± 1) U T PMNS require det k = 1 four different k → generate Z 2 × Z 2 symmetry group Klein symmetry K = { 1 , k 1 , k 2 , k 3 } for U PMNS = U TB : − 1 2 2 1 0 0     1  ,  , k 1 = 2 − 1 2 k 2 = − 0 0 1 k 3 = k 1 k 2   3 − 1 2 2 0 1 0 Neutrino mass models and sizable θ 13 7 of 22

Origin of the Klein symmetry � “direct” models · Klein symmetry K ⊂ family symmetry G · flavon fields φ break G down to K in neutrino sector · for TB mixing ( k 1 , k 2 , h ) generate S 4 � “indirect” models · Klein symmetry K not necessarily ⊂ family symmetry G · G responsible for generating particular flavon VEV configurations · for TB mixing – from e.g. ∆(27), Z 7 ⋊ Z 3 − 2 1 0       � φ 1 � ∝ 1 � φ 2 � ∝ 1 � φ 3 � ∝ 1       1 1 − 1 ν ( φ 1 φ T 1 + φ 2 φ T 2 + φ 3 φ T ⇒ L ν ∼ 3 ) ν H H Neutrino mass models and sizable θ 13 8 of 22

Typical model setup ingredients: M Pl M GUT family symmetry broken M seesaw → M R / Yukawas generated Majorana ν L electroweak symmetry broken M EW seesaw → light fermion masses generated Neutrino mass models and sizable θ 13 9 of 22

Implementing sizable θ 13 direct models indirect models TB plus corrections TB plus corrections other family symmetries with non-standard K non-standard flavon VEV configurations Neutrino mass models and sizable θ 13 10 of 22

TB plus non-diagonal charged leptons

Charged lepton corrections to TB mixing · charged lepton mass matrix might not be diagonal (GUTs) · U PMNS = V ℓ L V † V † and ν L = U TB ν L       1 0 0 0 ˆ ˆ 0 c 13 s 13 c 12 s 12       s ∗ U PMNS = 0 c 23 s 23 ˆ 0 1 0 − ˆ c 12 0 12 s ∗ s ∗ 0 − ˆ − ˆ 0 0 0 1 c 23 c 13 23 13 � 23 ) � e iδ ν 12 e iδ ℓ 13 e i ( δ ℓ 13 − δ ν c ij = cos θ ij 12 − θ ℓ 12 + θ ℓ s 12 e iδ 12 1 ≈ √ 3 � � s ij = sin θ ij e − iδ ij ˆ e iδ ν 23 e iδ ℓ 23 − θ ℓ s 23 e iδ 23 1 ≈ √ 23 2 � � 23 ) − θ ℓ 12 e i ( δ ℓ 12 + δ ν 13 e iδ ℓ s 13 e iδ 13 1 − θ ℓ ≈ √ 13 2 · θ ℓ θ 13 ∼ 9 ◦ 12 ∼ θ C ∼ 0 . 22 → · not (easily) compatible with Georgi-Jarlskog relations Neutrino mass models and sizable θ 13 11 of 22

TB plus new TB breaking flavon

An S 4 model of leptons τ c µ c e c N c matter L H u H d King, Luhn (2011) 1 ′ S 4 3 1 1 3 1 1 Z ν 1 2 2 2 2 0 0 3 Z ℓ 0 2 1 0 0 0 0 3 � 0 � flavons ϕ ℓ η µ η e ϕ ν η ν ξ ν ζ ν   � η µ � = 0 3 ′ 3 ′ 1 ′ w µ S 4 2 2 2 1   � ϕ ℓ � = v ℓ � w e � Z ν 0 0 0 2 2 2 0 3 0 � η e � = 0 Z ℓ 1 1 2 0 0 0 0 3   1 � 1 �   � ϕ ν � = v ν � η ν � = w ν � ξ ν � = u ν � ζ ν � = z ν 1 1 1 Neutrino mass models and sizable θ 13 12 of 22

Charged lepton sector � M 2 ( Lϕ ℓ ) 2 η e e c � M ( Lϕ ℓ ) 1 ′ τ c + M 2 ( Lϕ ℓ ) 2 η µ µ c + 1 1 1 W ℓ ∼ H d · Z ℓ 3 controls pairing of flavons with right-handed charged fermions · different S 4 contractions of ( Lϕ ℓ ) pick out different L i components ( Lϕ ℓ ) 1 ′ = L 1 ϕ ℓ 1 + L 2 ϕ ℓ 3 + L 3 ϕ ℓ 2 → L 3 � L 1 ϕ ℓ 3 + L 2 ϕ ℓ 2 + L 3 ϕ ℓ 1 � � L 2 � ( Lϕ ℓ ) 2 = → L 1 ϕ ℓ 2 + L 2 ϕ ℓ 1 + L 3 ϕ ℓ 3 L 1 · mass matrix diagonal by construction · m τ heavier than m µ and m e · hierarchy between m µ and m e due to hierarchy of VEVs w µ and w e · just a toy model of charged lepton sector (with GUTs off-diagonals) Neutrino mass models and sizable θ 13 13 of 22

Neutrino sector W ν ∼ LN c H u + ( ϕ ν + η ν + ξ ν ) N c N c + 1 M ζ ν η ν N c N c · trivial Dirac neutrino Yukawa � · neutrino mixing governed by heavy right-handed neutrinos · S 4 multiplication rule ( N c ∼ 3 ) 3 ⊗ 3 = ( 3 ′ + 2 + 1 ) s · three TB conserving flavons ϕ ν η ν ξ ν · ζ ν flavon is neutral except for S 4 ( ζ ν ∼ 1 ′ ) 1 ′ ⊗ ( 3 ⊗ 3 ) = ( 3 + 2 + 1 ′ ) s · only one extra term involving ζ ν · this breaks TB structure (at higher order) ... Neutrino mass models and sizable θ 13 14 of 22

Breaking of the TB Klein symmetry K Dirac term LN c H u respects K ⊂ S 4 � � N c N c respect k 1 but break k 2 1 Majorana terms ϕ ν + η ν + ξ ν + M ζ ν η ν S 4 irrep k 1 k 2 alignment       − 1 2 2 1 0 0 1 1       3 ′ 2 − 1 2 0 0 1 � ϕ ν � ∝ 1 3 2 2 − 1 0 1 0 1 � 1 � 0 � 1 � � � 0 1 � η ν � ∝ 2 0 1 1 0 1 1 1 � ξ ν � ∝ 1 1 1 ′ 1 − 1 � ζ ν � ∝ 1 Neutrino mass models and sizable θ 13 15 of 22

Resulting mixing − 1 − 1  2   0 1 1   1 0 0  M 1 + M 3  + 2 M 2 + M 3 − M 1  + M 1 + M 2 − M 3 − 1 − 1 M R = 2 1 1 0 0 0 1     6 6 3 − 1 − 1 2 1 0 1 0 1 0 − 1 0 1   − 1 ← + ∆ 1 0 small TB breaking term   − 1 0 1   − 2 1 − 2 6 α ∗ √ √ √ 6 3   1 1 1 1 1 6 α ∗ 6 − 2 + = ⇒ U PMNS ≈ 2 α  √ √ √ √ √  3 1 1 1 − 1 1 6 α ∗ 6 + 2 + 2 α √ √ √ √ √ 3 � � � Im  M 1 + M 3  √ � ∆ � � ∆ M 1 − M 3 ≈ − 3 · Re α  Re + Im  � � M 1 − M 3 M 1 − M 3 M 1 + M 3 Re M 1 − M 3 � � ∆ Im √ M 1 − M 3 ≈ 3 · Im α � � M 1 + M 3 Re M 1 − M 3 Neutrino mass models and sizable θ 13 16 of 22