Models of Neutrino Masses in View of the Large 13 Discovery Mu-Chun - PowerPoint PPT Presentation

Models of Neutrino Masses in View of the Large θ 13 Discovery Mu-Chun Chen, University of California at Irvine Flavor Physics and CP Violation (FPCP2013), Búzios, Brazil, May 19-24, 2013

Where Do We Stand? • Exciting Time in ν Physics: recent hints of large θ 13 from T2K, MINOS, Double Chooz, Daya Bay and RENO • Latest 3 neutrino global analysis (including recent results from reactor experiments): ⌅ ∆ m 2 ⇧ ⇤ 2 ⇥ sin 2 2 θ sin 2 ⇤ ⇤� ⇥⇤ P ( ν a � ν b ) = ν b | ν , t 4 E L Fogli, Lisi, Marrone, Montanino, Palazzo, Rotunno (2012) Parameter Best fit 1 σ range 2 σ range 3 σ range δ m 2 / 10 − 5 eV 2 (NH or IH) 7.54 7.32 – 7.80 7.15 – 8.00 6.99 – 8.18 sin 2 θ 12 / 10 − 1 (NH or IH) 3.07 2.91 – 3.25 2.75 – 3.42 2.59 – 3.59 ∆ m 2 / 10 − 3 eV 2 (NH) 2.43 2.33 – 2.49 2.27 – 2.55 2.19 – 2.62 ∆ m 2 / 10 − 3 eV 2 (IH) 2.42 2.31 – 2.49 2.26 – 2.53 2.17 – 2.61 sin 2 θ 13 / 10 − 2 (NH) 2.41 2.16 – 2.66 1.93 – 2.90 1.69 – 3.13 sin 2 θ 13 / 10 − 2 (IH) 2.44 2.19 – 2.67 1.94 – 2.91 1.71 – 3.15 sin 2 θ 23 / 10 − 1 (NH) 3.86 3.65 – 4.10 3.48 – 4.48 3.31 – 6.37 sin 2 θ 23 / 10 − 1 (IH) 3.92 3.70 – 4.31 3.53 – 4.84 ⊕ 5.43 – 6.41 3.35 – 6.63 δ / π (NH) 1.08 0.77 – 1.36 — — δ / π (IH) 1.09 0.83 – 1.47 — — 2

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 (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 • predictions strongly depend on choice of statistical measure • still alive and kicking de Gouvea, Murayama (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 Planck 2013 Data Release: N eff = 3.26 ± 0.35 ⇒ sterile neutrino marginally consistent 3

Origin of Mass Hierarchy and Mixing Mass spectrum of elementary particles u c t d s b LMA-MSW solution e µ ! " 3 " 2 " 1 normal hierarchy • In the SM: 22 physical quantities which seem unrelated " 2 inverted hierarchy " 3 " 1 " 3 • Question arises whether these quantities can be related nearly degenerate " 2 " 1 • No fundamental reason can be found in the framework of SM meV eV keV MeV GeV TeV • less ambitious aim ⇒ reduce the # of parameters by imposing symmetries • SUSY Grand Unified Gauge Symmetry • GUT relates quarks and leptons: quarks & leptons in same GUT multiplets • one set of Yukawa coupling for a given GUT multiplet ⇒ intra-family relations • seesaw mechanism naturally implemented • 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 4

Quarks vs Leptons, CKM vs PMNS • Quark mixings are small • Lepton mixings are large 0.12 - 0.17 • How to realize this when quarks and leptons are unified?? 5

Origin of Flavor Mixing and Mass Hierarchy • Several models have been constructed based on t t t u c u u c 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: µ " e e e µ µ " " • U(1) ! ! ! µ ! ! ! e ! ! ! " e µ µ e " " • SU(2) • SU(3) family symmetry SU(2) F (T ′ , SU(2), ...) • Recently, models based on discrete family symmetry groups have been constructed • A 4 (tetrahedron) Motivation: Tri-bimaximal (TBM) neutrino mixing • T´ (double tetrahedron) • S 3 (equilateral triangle) Discrete gauge anomaly: Araki, Kobayashi, Kubo, Ramos-Sanchez, Ratz, Vaudrevange (2008) • S 4 (octahedron, cube) Anomaly-free discrete R-symmetries: • A 5 (icosahedron, dodecahedron) simultaneous solutions to mu problem and • ∆ 27 proton decay problem, naturally small Dirac neutrino mass, M.-C.C, M. Ratz, C. Staudt, • Q 4 P . Vaudrevange, (2012) 6

Tri-bimaximal Neutrino Mixing ⌅ ∆ m 2 ⇧ • Neutrino Oscillation Parameters ⇧ ⇤ 2 ⇥ sin 2 2 θ sin 2 ⇤� ⇤ ⇥⇤ P ( ν a � ν b ) = ν b | ν , t 4 E L � ⇥ � s 13 e − i δ ⇥ � ⇥ 1 0 0 c 13 0 c 12 s 12 0 0 c 23 s 23 0 1 0 − s 12 c 12 0 U MNS = ⇤ ⌅ ⇤ ⌅ ⇤ ⌅ − s 13 e i δ 0 − s 23 c 23 0 c 13 0 0 1 • Latest Global Fit (3 σ ) Fogli, Lisi, Marrone, Montanino, Palazzo, Rotunno (2012) sin 2 θ � = 0 . 307 (0 . 259 − 0 . 359) sin 2 θ atm = 0 . 386 (0 . 331 − 0 . 637) sin 2 θ 13 = 0 . 0241 (0 . 0169 − 0 . 0313) • Tri-bimaximal Mixing Pattern Harrison, Perkins, Scott (1999) ⇤ ⌥ ts sin 2 θ ⇥ , TBM = 1 / 3 ts sin 2 θ atm , TBM = 1 / 2 an d sin θ 13 , TBM = 0. • Leading Order: TBM (from symmetry) + holomorphic Corrections/contributions • Is TBM still a good starting point? 7

Tri-bimaximal Neutrino Mixing θ 12 θ 13 θ 23 � √ � ≈ 35 . 3 ◦ 45 ◦ TBM prediction: arctan 0 . 5 0 � ◦ � ◦ � ◦ 33 . 6 +1 . 1 8 . 93 +0 . 46 38 . 4 +1 . 4 � � � Best fit values ( ± 1 σ ): − 1 . 0 − 0 . 48 − 1 . 2 Fogli, Lisi, Marrone, Montanino, Palazzo, Rotunno, 2012 8

Non-Abelian Finite Family Symmetry A4 • TBM mixing matrix: can be realized with finite group family symmetry based on A 4 Ma, Rajasekaran (2001); Babu, Ma, Valle (2003); ... • A 4 : even permutations of 4 objects S: (1234) → (4321) T: (1234) → (2314) • a group of order 12 • Invariant group of tetrahedron 9

Invariant Group of Tetrahedron T: (1234) → (2314) S: (1234) → (4321) [Animation Credit: Michael Ratz] 10

Non-Abelian Finite Family Symmetry A4 • TBM mixing matrix: can be realized with finite group family symmetry based on A 4 Ma, Rajasekaran (2001); Babu, Ma, Valle (2003); ... • A 4 : even permutations of 4 objects S: (1234) → (4321) T: (1234) → (2314) • a group of order 12 • Invariant group of tetrahedron • Problem: A 4 does not give rise to quark mixing 11

GUT Compatibility ⇒ SU(5) x T´ M.-C.C, K.T. Mahanthappa Phys. Lett. B652, 34 (2007); Phys. Lett. B681, 444 (2009) • Double Tetrahedral Group T´ • Symmetries ⇒ 10 parameters in Yukawa sector ⇒ 22 physical observables • neutrino mixing angles from group theory (CG coe ffi cients) • TBM: misalignment of symmetry breaking patterns • neutrino sector: T’ → G TST2 , charged lepton sector: T’ → G T • GUT symmetry ⇒ deviation from TBM related to quark mixing θ c M.-C.C, K.T. Mahanthappa, Phys. Lett. B681, 444 (2009) • complex CG’s of T´ ⇒ Novel Origin of CP Violation • CP violation in both quark and lepton sectors entirely from group theory • connection between leptogenesis and CPV in neutrino oscillation 12

M.-C.C, K.T. Mahanthappa Predictions: a SUSY SU(5) x T´ Model Phys. Lett. B652, 34 (2007); Phys. Lett. B681, 444 (2009) • Charged Fermion Sector: 7 parameters ⇒ 9 masses, 3 angles, 1 phase ⌦ ⇧ spinorial representations in charged fermion ⇤ ⇤⌦ m d /m s � e i α ⌦ ⇤ ⌦ y θ c ⇧ m u /m c m d /m s , wh ⇤ ⇤ sector ⇒ complex CGs ling constants. Even though is of the size of the ⇒ CPV in quark and lepton sectors SU(5) ⇒ M d = (M e ) T ⇒ corrections to TBM related to θ c quark CP phase: γ = 45.6 degrees Georgi-Jarlskog relations at GUT scale ↵ m e V d,L ≠ I ⇒ ⇧ 1 ↵ m d ⇤ 1 ⇧ e 3 ⇧ c . 12 ⇧ m µ 3 m s ly, m d ⌃ 3 m e , y, m µ ⌃ 3 m s is the tri-bimaximal mixing pattern 13

M.-C.C, K.T. Mahanthappa Predictions: a SUSY SU(5) x T´ Model Phys. Lett. B652, 34 (2007); Phys. Lett. B681, 444 (2009)  ✓ ◆� • Neutrino Sector: 0 1 0 1 1 0 0 2 ξ 0 + η 0 − ξ 0 − ξ 0 + η 00 0 A s 0 Λ A ζ 0 ζ 0 M RR = 0 0 1 M D = − ξ 0 2 ξ 0 + η 00 − ξ 0 + η 0 0 v u @ @ 0 0 1 0 − ξ 0 + η 00 − ξ 0 + η 0 2 ξ 0 (2+1 parameters) 0 • Prediction for MNS matrix: (for ) η 00 0 = 0 ⇧ tan 2 θ ⇤ ⌃ tan 2 θ ⇤ ,T BM + 1 CGs of ⌅ 13 ⌅ ⌅ c / 3 2 2 θ c cos δ SU(5) & T´ complex CGs: leptonic Dirac CPV ⇒ connection between neutrino mixing quark mixing 1/2 angle leptogenesis & leptonic angle CPV at low energy • sum rule among absolute masses: > 0 normal hierarchy predicted 14