Neutrino Mass Models Mu-Chun Chen, University of California, Irvine - PowerPoint PPT Presentation

Neutrino Mass Models Mu-Chun Chen, University of California, Irvine NuFact 2015, CBPF , Rio de Janeiro, Brazil, August 10, 2015

Theoretical Challenges (i) Absolute mass scale: Why m ν << m u,d,e ? • seesaw mechanism: most appealing scenario ⇒ Majorana • GUT scale (type-I, II) vs TeV scale (type-III, double seesaw) • TeV scale new physics (SUSY, extra dimension, U(1)´) ⇒ Dirac or Majorana (ii) Flavor Structure: Why neutrino mixing large while quark mixing small? • neutrino anarchy: no parametrically small number Hall, Murayama, Weiner (2000); de Gouvea, Murayama (2003) • near degenerate spectrum, large mixing • still alive and kicking de Gouvea, Murayama (2012) Buchmüller, Hamaguchi, Lebedev, Ramos-Sánchez, Ratz (2007); • possible heterotic string connection Feldstein, Klemm (2012) • family symmetry: there’s a structure, expansion parameter (symmetry e ff ect) • mixing result from dynamics of underlying symmetry • for leptons only (normal or inverted) • for quarks and leptons: quark-lepton connection ↔ GUT (normal) • Alternative? • In this talk: assume 3 generations, no LSND/MiniBoone/Reactor Anomaly 2

Origin of Mass Hierarchy and Mixing • In the SM: 22 physical quantities which seem unrelated • Question arises whether these quantities can be related • No fundamental reason can be found in the framework of SM • less ambitious aim ⇒ reduce the # of parameters by imposing symmetries • Grand Unified Gauge Symmetry • seesaw mechanism naturally implemented • GUT relates quarks and leptons: quarks & leptons in same GUT multiplets • one set of Yukawa coupling for a given GUT multiplet ⇒ intra-family relations • Family Symmetry • relate Yukawa couplings of di ff erent families • inter-family relations ⇒ further reduce the number of parameters ⇒ Experimentally testable correlations among physical observables 3

Origin of Flavor Mixing and Mass Hierarchy • Several models have been constructed based on t t t u u c c u c GUT Symmetry SU(10) • GUT Symmetry [SU(5), SO(10)] ⊕ Family Symmetry G F d s d d s s b b b SU(5), SO(10), ... • Family Symmetries G F based on continuous groups: e e µ µ µ " " " e ! ! µ ! ! e ! ! • U(1) ! ! ! " e µ µ e " " • SU(2) SU(2) F family symmetry • SU(3) (T ′ , SU(2), ...) • Recently, models based on discrete family symmetry groups have been constructed • A 4 (tetrahedron) • T´ (double tetrahedron) Motivation: Tri-bimaximal • S 3 (equilateral triangle) (TBM) neutrino mixing • S 4 (octahedron, cube) • A 5 (icosahedron, dodecahedron) • ∆ 27 • Q 4 4

Tri-bimaximal Neutrino Mixing Latest Global Fit (3 σ ) sin 2 θ 23 = 0 . 437 (0 . 374 − 0 . 626) Capozzi, Fogli, Lisi, Marrone, Montanino, Palazzo (2014) • Latest Global Fit (3 σ ) sin 2 θ 12 = 0 . 308 (0 . 259 − 0 . 359) sin 2 θ 13 = 0 . 0234 (0 . 0176 − 0 . 0295) • Tri-bimaximal Mixing Pattern Harrison, Perkins, Scott (1999) ⇤ ts sin 2 θ atm , TBM = 1 / 2 an ts sin 2 θ ⇥ , TBM = 1 / 3 ⌥ d sin θ 13 , TBM = 0. • Leading Order: TBM (from symmetry) + higher order corrections/contributions • Is TBM a good starting point? 5 m

⇒ SU(5) Compatibility ⇒ T ′ Family Symmetry M.-C.C, K.T. Mahanthappa (2007, 2009) • Double Tetrahedral Group T´: double covering of A4 • Symmetries ⇒ 10 parameters in Yukawa sector ⇒ 22 physical G F e.g. A 4 observables • neutrino mixing angles from group theory (CG coe ffi cients) � Φ e � � Φ ν � • TBM: misalignment of symmetry breaking patterns • neutrino sector: T ′ → G TST2 , G e G ν • charged lepton sector: T ′ → G T • GUT symmetry ⇒ contributions to mixing parameters from charged lepton neutrino sector sector charged lepton sector e.g. Z 3 e.g. Z 2 subgroup of A 4 subgroup of A 4 ⇒ deviation from TBM related to Cabibbo angle θ c � Φ ν � ∝ (1,1,1) � Φ e � ∝ (1,0,0) ⇧ CG’s of ⌅ 13 ⌅ ⌅ c / 3 2 δ ⋍ 227 o tan 2 θ ⇤ ⌃ tan 2 θ ⇤ ,T BM + 1 SU(5) & T´ 2 θ c cos δ • large θ 13 possible with one additional singlet flavon M.-C. C., J. Huang, K.T. Mahanthappa, A. Wijiangco (2013) 6

Neutrinoless Double Beta Decay 1 Current Bound or Positive Indication our model prediction 10 − 1 sum rule among masses • ⇒ small predicted region IS Cosmological Limit |m ββ | [eV] 10 − 2 NS 10 − 3 1 σ 2 σ [P 3 σ [Plot taken from C. Giunti, LIONeutrino2012] 10 − 4 10 − 4 10 − 3 10 − 2 10 − 1 1 m min [eV] 7

⇒ “Large” Deviations from TBM in A 4 • Generically: corrections on the order of ( θ c ) 2 • from charged lepton sector: • through GUT relations • from neutrino sector: • higher order contributions in superpotential • Modifying the Neutrino sector: Di ff erent symmetry breaking patterns G F • TBM: misalignment of e.g. A 4 M.-C.C, J. Huang, J. O’Bryan, A. Wijangco, F. Yu, (2012) • A4 → G TST2 and A4 → G T � Φ e � � Φ ν � • A4: group of order 12 ⇒ many subgroups G e G ν • systematic study of breaking into other A4 subgroups charged lepton neutrino sector sector e.g. Z 3 e.g. Z 2 subgroup of A 4 subgroup of A 4 � Φ ν � ∝ (1,1,1) � Φ e � ∝ (1,0,0) 8

“Large” Deviations from TBM in A 4 M.-C.C, J. Huang, J. O’Bryan, A. Wijangco, F. Yu, (2012) • Di ff erent A4 breaking patterns: normal inverted non-maximal θ 23 ➩ normal hierarchy deviations correlated mass ordering ➩ symmetry breaking patterns 9

“Large” Deviations from TBM in A 4 M.-C.C, J. Huang, J. O’Bryan, A. Wijangco, F. Yu, (2012) • Correlation between Dirac CP phase and θ 13 : correlations ⇕ symmetry breaking pattern 10

Another Example: A 5 P . Ballett, S. Pascoli, J. Turner (2015) • Correlations among di ff erent mixing parameters G e θ 12 θ 23 sin α ji δ 90 � 35 . 27 � + 10 . 13 � r 2 45 � Z 3 0 270 � 0 � 45 � ± 25 . 04 � r 0 31 . 72 � + 8 . 85 � r 2 180 � Z 5 90 � 45 � 0 270 � 0 � Z 2 × Z 2 36 . 00 � − 34 . 78 � r 2 31 . 72 � + 55 . 76 � r 0 180 � 0 � 58 . 28 � − 55 . 76 � r 0 180 � TABLE I. Numerical predictions for the correlations found √ in this paper. The dimensionless parameter r ≡ 2 sin θ 13 is constrained by global data to lie in the interval 0 . 19 . r . 0 . 22 at 3 σ . The predictions for θ 12 and θ 23 shown here ne- 11 � r 4 � � r 2 � glect terms of order O and O , respectively. Following

Corrections to Kinetic Terms • Corrections to the kinetic terms induced by family symmetry breaking generically are present, should be properly included Leurer, Nir, Seiberg (1993); Dudas, Pokorski, Savoy (1995); Dreiner, Thomeier (2003) • can be along di ff erent directions than RG corrections • dominate over RG corrections (no loop suppression, copious heavy states) • only subdominant for quark flavor models • sizable for neutrino mass models based on discrete family symmetries, e.g. A 4 • Contributions from Flavon VEVs (1,0,0) and (1,1,1) M.-C.C, M. Fallbacher, M. Ratz, C. Staudt (2012) • five independent “basis” matrices                 0 0 0 0 1 1 1 0 0 0 0 0   0 i − i  ,  ,  , P II = 0 1 0 P III = 0 0 0 P IV = 1 0 1 P I = 0 0 0 P V = − i 0 i        0 0 0 1 1 0 i − i 0 0 0 1 0 0 0         • RG correction: essentially along P III = diag(0,0,1) direction due to y τ dominance • kinetic term corrections can be along di ff erent directions than RG: P I - P V • nontrivial flavor structure can be induced • non-zero CP phase can be induced 12

An Example: Enhanced θ 13 in A 4 M.-C.C., M. Fallbacher, M. Ratz, C. Staudt (2012) 8 P V 6 Correction to TBM prediction of θ 13 = 0 ∆ θ 13 [ ◦ ] 4 δ ≃ π /2 κ V v 2 / Λ 2 = (0 . 2) 2 2 ∆ θ 13 an. ∆ θ 13 num. 0 0.00 0.02 0.04 0.06 0.08 0.10 m 1 [eV] 13

Corresponding Change in θ 12 M.-C.C., M. Fallbacher, M. Ratz, C. Staudt (2012) 0.4 P V 0.3 Correction to TBM ∆ θ 12 [ ◦ ] prediction of θ 12 = 35.3º 0.2 0.1 κ V v 2 / Λ 2 = (0 . 2) 2 0.0 0.00 0.02 0.04 0.06 0.08 0.10 m 1 [eV] 14

Corresponding Change in θ 23 M.-C.C., M. Fallbacher, M. Ratz, C. Staudt (2012) � 1.4 0.4 P V � 1.6 0.3 Correction to TBM � 1.8 prediction of θ 23 = 45º ∆ θ 23 [ ◦ ] � 2.0 0.2 � 2.2 0.1 � 2.4 κ V v 2 / Λ 2 = (0 . 2) 2 � 2.6 0.0 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 0.10 m 1 [eV] 15

Origin of CP Violation • CP violation ⇔ complex mass matrices CP U R,i ( M u ) ij Q L,j + Q L,j ( M † u ) ji U R,i → Q L,j ( M u ) ij U R,i + U R,i ( M u ) ∗ ij Q L,j − • Conventionally, CPV arises in two ways: • Explicit CP violation: complex Yukawa coupling constants Y • Spontaneous CP violation: complex scalar VEVs <h> • Complex CG coe ffi cients in certain discrete groups ⇒ explicit CP violation • CPV in quark and lepton sectors purely from complex CG coe ffi cients CG coe ffi cients in non-Abelian discrete symmetries ➪ relative strengths and phases in entries of Yukawa matrices ➪ mixing angles and phases (and mass hierarchy) 16