Theoretical Models of neutrino parameters. G.G.Ross, Paris, September PDF Free Download

Theoretical Models of neutrino parameters. G.G.Ross, Paris, September 2008

Theoretical Models of neutrino parameters. G.G.Ross, Paris, September 2008 Number of light neutrinos 3? Masses + Mixing Angles 6 (15) CP violating phases 3 (6)

Theoretical Models of neutrino parameters. G.G.Ross, Paris, September 2008 q l See-saw with sequential domination Symmetry GUT Family Abelian, Non-Abelian, Discrete, String? Tri-bi-maximal mixing Non-Abelian discrete symmetry

Masses DATA :? ν i i l di u i 12 10 10 9 10 6 3 Mixing Quarks 1 10 10 3 Leptons GeV V CKM 1 0.218 0.224 0.002 0.005 0.218 0.224 1 0.032 0.048 0.004 0.015 0.03 0.048 1 V MNS 0.79 0.88 0.48 0.61 < 0.2 = 0.27 0.49 0.45 0.71 0.52 0.82 0.28 0.5 0.51 0.65 0.57 0.81 10-1 10-2 10-3 10-4 ev 2 1 3 3 0 1 1 1 6 3 2 1 1 1 6 3 2 Bi-Tri Maximal Mixing Discrete Non Abelian Structure?

DATA : L = Y Q u H + Y Q d H u i c, j d i c, j Yukawa ij ij M u ij = Y ij u < H 0 > M d ij = Y ij d < H 0 > M u = V u L M Diag V R M d = U d L M Diag U R V CKM = V L U L The data for quarks is consistent with a very symmetric structure : M d,u m b,t < ε 4 ε 3 ε 3 ε 3 ε 2 ε 2 ε 3 ε 2 1 ε d = 0.15 ε u = 0.05

q l symmetry? Charged leptons are consistent with a similar form M d,l,u b,τ,t m < ε 4 ε 3 ε 3 ε 3 aε 2 aε 2 ε 3 aε 2 1 ε d = 0.15, a d = 1 ε l = 0.15, a l = 3 ε u = 0.05, a u = 1

Symmetry 1. GUT relations e.g. ψ α SU(4) SO(10) d d = d l

Symmetry GUT relations e.g. ψ α SU(4) SO(10) d d = d l Det( M l ) = Det( M d ) M X ψ α ψ α m b m τ ( M X ) = 1 M d,l m 3 = < ε 4 ε 3 ε 3 ε 3 aε 2 aε 2 ε 3 aε 2 1 ε d = 0.15, a d = 1 ε l = 0.15, a l = 3

Symmetry 1. GUT relations e.g. SU(4) SO(10) ψ α d d = d l ψ α 1 Σ 45 = 1 1 3 ψ α m s m µ ( M X ) = 1 3 Georgi Jarlskog M d,l m 3 = < ε 4 ε 3 ε 3 ε 3 aε 2 aε 2 ε 3 aε 2 1 ε d = 0.15, a d = 1 ε l = 0.15, a l = 3

Neutrinos??? L ν eff = m 3 φ i 23 ν i φ j i j 23 ν j + m 2 φ 123 ν i φ 123 ν j i < φ > = (0,1, 1), < φ > = (1,1,1) i 23 123

Neutrinos??? L ν eff = m 3 φ i 23 ν i φ j i j 23 ν j + m 2 φ 123 ν i φ 123 ν j i < φ > = (0,1, 1), < φ > = (1,1,1) i 23 123 Can one have a unified description of quark, charged lepton and neutrinos? q,l c. f. L Dirac = m 3 φ 3 i ψ i φ 3 j ψ j c +... < φ 3 > i = (0,0,1)???

Neutrinos??? L ν eff = m 3 φ i 23 ν i φ j i j 23 ν j + m 2 φ 123 ν i φ 123 ν j i < φ > = (0,1, 1), < φ > = (1,1,1) i 23 123 See-Saw Quarks, charged leptons, neutrinos can have similar Dirac mass : q,l,ν i = α ψ i φ 3ψ c j i j φ 3 + β ψ i φ 123 ψ c φ j j 23 L Dirac i + ψ i φ 23 ψ c φ j i j 123 + γ ψ i φ 123 ψ c φ j j 23 Σ 45 α > β M Dirac m 3 = < ε 4 ε 3 + ε 4 ε 3 + ε 4 ε 3 + ε 4 aε 2 + ε 3 aε 2 + ε 3 ε 3 + ε 4 aε 2 + ε 3 1 ε d = 0.15, a d = 1 ε l = 0.15, a e = 3 ε u = 0.05, a u = 1 ε ν = 0.05, a ν = 0

See-saw with sequential domination M M M 1 M2 M 3 M M 1 < M 2 << M 3 ν = M ν D M 1 M M νt D H H ν R ν L ν L Minkowski Gell-Mann, Ramond, Slansky; Yanagida, King ν L Dirac i = α ψ i φ 3ψ c j i j φ 3 + β ψ i φ 123 ψ c φ j j 23 i + ψ i φ 23 ψ c φ j j 123 α > β ν L eff = β 2 i j ψ M i φ 123 ψ j φ 123 1 + β 2 ψ M i φ i j 23 ψ j φ 23 2 + (α + β)2 ψ M i φ i j 3 ψ j φ 3 3

See-saw with sequential domination M M M 1 M2 M 3 M ν M 1 << M 2 << M 3 = M ν D M 1 M M νt D Minkowski Gell-Mann, Ramond, Slansky; Yanagida, King ν L Dirac i = α ψ i φ 3ψ c j i j φ 3 + β ψ i φ 123 ψ c φ j j 23 i + ψ i φ 23 ψ c φ j j 123 α > β small ν L eff = β 2 i j ψ M i φ 123 ψ j φ 123 1 + β 2 ψ M i φ i j 23 ψ j φ 23 2 + (α + β)2 ψ M i φ i j 3 ψ j φ 3 3

Symmetry 2. Family symmetry Non-Abelian family symmetry Promote φ i to fields transforming under SU(3) family Vacuum alignment φ 3 = 0 0 1 φ 23 = 0 1 1 1 φ = 1 123 1 Discrete non Abelian symmetry

List of models with discrete flavour symmetry (incomplete, by symmetry) S 3 :Pakvasa et al.(1978), Derman(1979), Ma(2000), Kubo et al.(2003), Chen et al.(2004), Grimus et al.(2005), Dermisek et al (2005), Mohapatra et al.(2006), Morisi(2006), Caravaglios et al.(2006), Haba et al(2006), S 4 :Pakvasa et al.(1979), Derman(1979), Lee et al.(1994), Mohapatra et al.(2004),ma(2006), Hagedorn et al.(2006), Caravaglios et al.(2006), Lampe(2007), Sawanaka(2007), A 4 :Wyler(1979), Ma et al.(2001), Babu et al.(2003), Altarelli et al.(2005-8), He et al.(2006), Bazzocchi, Morisi, et al.(2007/8), King et al.(2007), D 4 :Seidl(2003), Grimus et al.(2003/4), Kobayashi et al.(2005), D 5 :Ma(2004), Hagedorn et al.(2006), D n :Chen et al.(2005), Kajiyama et al.(2006), Frampton et al.(1995/6,2000), Frigerio et al (2005), Babu et al.(2005), Kubo(2005),... T :Frampton et al.(1994,2007), Aranda et al.(1999,2000),feruglio et al.(2007), Chen et al.(2007), Δ n :Kaplan et al.(1994), Schmaltz(1994), Chou et al.(1997), de Madeiros Varzielas et al(2006/7). T 7 :Luhn et al.(2007). Adapted from Lindner, Manchester

Symmetry 2. Family symmetry Non-Abelian family symmetry Promote φ i to fields transforming under SU(3) family Vacuum alignment φ 3 = 0 0 1 φ 23 = 0 1 1 1 φ = 1 123 1 Discrete non Abelian symmetry e.g. Δ(27) SU(3) f, φ i triplets φ i Z 3 φ i Z ' 3 φ i φ 1 φ 2 φ 1 φ 2 φ 3 αφ 2 φ 3 φ 1 α 2 φ 3

Symmetry 2. Family symmetry Non-Abelian family symmetry Promote φ i to fields transforming under SU(3) family Vacuum alignment φ 3 = 0 0 1 φ 23 = 0 1 1 1 φ = 1 123 1 Discrete non Abelian symmetry e.g. Δ(27) SU(3) f, φ i triplets φ i Z 3 φ i Z 3 ' φ i Δ 27 φ 1 φ 2 φ 1 φ 2 φ 3 αφ 2 ( ) { Z3 Z 3, < φ > = (1,1,1) λ > 0 ', <φ> = (0,0,1) λ < 0 φ 3 φ 1 α 2 φ 3 V (φ) = m 2 φ φ +...+ λ m 2 φ i φ i φ i φ i

A complete model Δ(27) SO(10) G (G = R U (1)) Varzielas, GGR c i i ( ) ψ, ψ 16, 3 No mass while SU(3) unbroken Spontaneous symmetry breaking i i i φ, φ, φ, H 3 23 123 45 c.f. Georgi-Jarskog (1,3) (1,3) (1,3) ( 45,1) 0 0 1 0 1 ε 1 1 1 1 2 M ε M M 1 i j c 1 i j c 1 i j c 1 i j c PY = φ 2 3ψ iφ3 ψ j H + φ 3 23ψ iφ23ψ j HH 45 + φ 2 23ψ iφ123ψ j H + φ 2 123ψ iφ23ψ j H M M M M only terms allowed by G

Neutrino Parameters

Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra favoured 10 10 0 10-1 10-2 10-3 10-4 ev? Degenerate Normal Inverted

Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra favoured 10 10 0 10-1 10-2 10-3 10-4 ev? Degenerate Normal Inverted Mixing angles sin 2 θ 12 1 3 ± 0.03 sin 2 θ 23 1 2 ± 0.03 sinθ 13 m e 2m µ = 0.053 ± 0.05 (3 ± 3 o ) From charged lepton mixing King; GGR, Varzielas

Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra favoured 10 10 0 10-1 10-2 10-3 10-4 ev? Degenerate Normal Inverted Mixing angles 3cos(δ π ) sin 2 θ 12 1 3 ± 0.03 θ θ 12 + 1 C 2 3 cos( δ π ) 35.26 ± 2o Antusch, King sinθ 13 sin 2 θ 23 1 2 ± 0.03 m e 2m µ = 0.053 ± 0.05 (3 ± 3 o ) From charged lepton mixing King; GGR, Varzielas

Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra possible Neutrinoless double β decay (3 light neutrinos) 10 10 0 10-1 10-2 10-3 10-4 ev? Degenerate Normal Inverted

Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra possible Neutrinoless double β decay (3 light neutrinos) 10 10 0 10-1 10-2 10-3 10-4 ev? Degenerate Normal Inverted?

See saw parameters

See saw parameters Masses + Mixing Angles 6 (15) CP violating phases 3 (6) κ = Y ν T M 1 Y ν P = Y ν Y ν Insufficient information RGE for sleptons (SUSY) In principle all parameters determined by neutrino structure and radiative corrections (assuming degenerate sleptons at GUT scale) Davidson, Ibarra Thermal Leptogenesis (Baryogenesis) M νr > 10 9 GeV, T Reheat > 10 10 GeV (hierarchical spectrum) / / ββ phase CP = CP(δ,φ ',φ i=1,2,3 ) see saw phases ν factory phase

See saw parameters Masses + Mixing Angles 6 (15) (8) CP violating phases 3 (6) (3) κ = Y ν T M 1 Y ν P = Y ν Y ν Insufficient information RGE for sleptons (SUSY) In principle all parameters determined by neutrino structure and radiative corrections (assuming degenerate sleptons at GUT scale) Davidson, Ibarra Thermal Leptogenesis (Baryogenesis) Fukugita, Yanagida M νr > 10 9 GeV, T Reheat > 10 10 GeV (hierarchical spectrum) / / ββ phase CP = CP(δ,φ ',φ i=1,2,3 ) see saw phases ν factory phase Sequential see saw and symmetry (texture zero) simplifies structure

Sequential see saw and (1,1) texture zero (1,1) texture zero M Dirac m 3 = < ε 4 ε 3 + ε 4 ε 3 + ε 4 ε 3 + ε 4 aε 2 + ε 3 aε 2 + ε 3 ε 3 + ε 4 aε 2 + ε 3 1

Sequential see saw and (1,1) texture zero (1,1) texture zero Quark sector zero V us = m d m s e iδ m u m c M Dirac m 3 = < ε 4 ε 3 + ε 4 ε 3 + ε 4 ε 3 + ε 4 aε 2 + ε 3 aε 2 + ε 3 ε 3 + ε 4 aε 2 + ε 3 1

Sequential see saw and (1,1) texture zero (1,1) texture zero Lepton sector zero sin 2 θ 23 1 2, sinθ 13 m e 2m µ M Dirac m 3 = < ε 4 ε 3 + ε 4 ε 3 + ε 4 ε 3 + ε 4 aε 2 + ε 3 aε 2 + ε 3 ε 3 + ε 4 aε 2 + ε 3 1

Sequential see saw and (1,1) texture zero (1,1) texture zero Lepton sector zero sin 2 θ 23 1 2, sinθ 13 m e 2m µ M Dirac m 3 = < ε 4 ε 3 + ε 4 ε 3 + ε 4 ε 3 + ε 4 aε 2 + ε 3 aε 2 + ε 3 ε 3 + ε 4 aε 2 + ε 3 1 Y B sin 2 θ 13 sin( 2δ φ) Abada et al

Summary Sequential see saw consistent with quark-lepton unification

Summary Sequential see saw consistent with quark-lepton unification Discrete non Abelian family symmetry readily generates near Tri-Bi-Maximal mixing

Summary Sequential see saw consistent with quark-lepton unification Discrete non Abelian family symmetry readily generates near Tri-Bi-Maximal mixing Neutrino parameters strongly constrained: Mixing angles to ±3 o m ββ Number of see saw parameters reduced measureable? Sign of matter-antimatter asymmetry sin(2δ-φ) - measureable? Other model implications SUSY models: sparticles have related mass structure (m 2 φ i φ i... degeneracy split by small fermion mass related terms) FCNC : L i, B i violation close to present bounds (µ eγ, mercury EDM within a factor of 10 of present limits)