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

Transcription

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

2 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)

3 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

4 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 parameter constraints

5 Masses DATA :? ν i i l di u i Mixing Quarks Leptons GeV V CKM V MNS < 0.2 = ev Bi-Tri Maximal Mixing Discrete Non Abelian Structure?

6 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

7 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

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

9 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

10 Symmetry 1. GUT relations e.g. SU(4) SO(10) ψ α d d = d l ψ α 1 Σ 45 = 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

11 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

12 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 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)???

13 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 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 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

14 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 β 2 ψ M i φ i j 23 ψ j φ (α + β)2 ψ M i φ i j 3 ψ j φ 3 3

15 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 β 2 ψ M i φ i j 23 ψ j φ (α + β)2 ψ M i φ i j 3 ψ j φ 3 3

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

17 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

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

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

20 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 c.f. Georgi-Jarskog (1,3) (1,3) (1,3) ( 45,1) ε 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

21 Neutrino Parameters

22 Neutrino Parameters Tri-bi-maximal mixing Degenerate and normal spectra favoured ev? Degenerate Normal Inverted

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

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

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

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

27 See saw parameters

28 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

29 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 > GeV (hierarchical spectrum) / / ββ phase CP = CP(δ,φ ',φ i=1,2,3 ) see saw phases ν factory phase

30 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 > 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

31 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

32 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

33 Sequential see saw and (1,1) texture zero (1,1) texture zero Lepton sector zero sin 2 θ , 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

34 Sequential see saw and (1,1) texture zero (1,1) texture zero Lepton sector zero sin 2 θ , 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

35 Summary Sequential see saw consistent with quark-lepton unification

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

37 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?

38 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)