symmetries and unification

Transcription

1 Right unitarity triangles and tribimaximal mixing from discrete symmetries and unification Martin Spinrath FLASY th July Based on collaborations with S. Antusch, S.F. King, C. Luhn and M. Malinsky: PRD 81 (2010) , PRD 83 (2011) , NPB 850 (2011) 477

2 Outline Motivation Quark Mixing Sum Rules Discrete Vacuum Alignment Examples Summary and Conclusions

3 Outline Motivation Quark Mixing Sum Rules Discrete Vacuum Alignment Examples Summary and Conclusions

4 The CKM Unitarity Triangle η 1 γ V bi V id =0 β Δ m d Δmd ε K V ub V cb Δm s Fit result [UTfit]: α = (87.8 ± 3.0) sin(2β+γ) -0.5 α -1 Plot and number taken from the UTfit collaboration summer 2010 results (pre-ichep) ρ

5 The CKM Unitarity Triangle η 1 γ V bi V id =0 β Δ m d Δmd ε K V ub V cb Δm s Fit result [UTfit]: α = (87.8 ± 3.0) sin(2β+γ) -0.5 α Accident??? -1 Plot and number taken from the UTfit collaboration summer 2010 results (pre-ichep) ρ

6 Outline Motivation Quark Mixing Sum Rules Discrete Vacuum Alignment Examples Summary and Conclusions

7 Assumptions[Antusch, King, Malinsky, MS 2010] Hierarchical Quark Mass Matrices Texture Zeros in the 1-3 Elements

8 The Sum Rules [Antusch, King, Malinsky, MS 2010] θ12 u = θ 13 =(4.96 ± 0.30) θ 23 θ12 d = θ 12 θ 13 e iδ CKM θ = α = δ d 12 δ u 12 = [Numbers based on PDG] Idea: Mass matrices with purely real/imaginary elements! [Antusch, King, Malinsky, MS 2010] see also [Fritzsch and Xing; Masina and Savoy 2006; Harrison, Dallison, Roythorne, Scott 2009]

9 Outline Motivation Quark Mixing Sum Rules Discrete Vaccum Alignment Examples Summary and Conclusions

10 Ingredients [Antusch, King, Luhn, MS 2011] Discrete Family Symmetry (A4, S4,...) Discrete Shaping Symmetry (Zn`s) Spontaneous CP violation SUSY GUT (SU(5),...)

11 The Method I [Antusch, King, Luhn, MS 2011] Use family symmetry to align flavon, e.g.: φ (0, 0,x) T or φ (x, x, x) T Add term to W compatible with shaping symmetry: Solve F-term condtions ( FP =0) arg(φ) = arg(x) = P φ n Λ n 2 M 2 2π n q, q=1,...,n for 2π n q + π n, q =1,...,n for +

12 Outline Motivation Quark Mixing Sum Rules Discrete Vacuum Alignment Examples Summary and Conclusions

13 First Example: Ingredients [Antusch, King, Luhn, MS 2011] Symmetries: SU(5) x A4 x Gshaping 5 Flavons Matter sector: F, T1,2,3, N1,2 Higgs Fields in 5-, 24-, 45-dim. SU(5) Reps. New GUT relations!!! [Antusch, MS 09]

14 First Example: Alignment [Antusch, King, Luhn, MS 2011] We use the following flavon alignment: φ 1 1 0, φ 2 0 φ i, φ 3 0, φ , 1 For details of the alignment, see paper...

15 The Matter Sector [Antusch, King, Luhn, MS 2011] We work in an SU(5) GUT: F i = dr c d c B dg c e ν i, T i = ug c ub c u R d R ug c 0 ur c u B d B ub c ur c 0 u G d G u R u B u G 0 e c d R d B d G e c 0 i, N 1,2 We know the family and the shaping symmetries...

16 The Quark Sector [Antusch, King, Luhn, MS 2011] For the Yukawa matrices in the quark sector we find: Y d = Y u = 0 i , a 11 a 12 0 a 12 a 22 a a 23 a 33 The sum rule is applicable and we have a right-angled CKM unitarity triangle!!!

17 The Lepton Sector [Antusch, King, Luhn, MS 2011] M R = Y T e = 3 2 In the lepton sector we find: MR1 0 0 M R2, Y ν = 0 a ν2, a ν1 a ν1 a ν2 a ν2 0 i New GUT relations No unitarity triangle Small deviations from tri-bimaximal mixing

18 Another Model (same same, but different) [Antusch, King, MS 2010] Symmetries: SU(5) x A4 x Gshaping Matter sector as before: F, T, N Flavons: φ 23, φ 123 and φ 3 as before New Flavon: φ 23 0 i w T H 15 for type-ii-seesaw

19 The SM Yukawas [Antusch, King, MS 2010] Y u = Y d = Y T e = 2a a a (w2 1)ã a a a a i w i w Phase Sum Rule not valid!!

20 What about the CKM CP phase? [Antusch, King, MS 2010] From ye, ym, and q12 we can determine it to: δ CKM 69.9 This is in perfect agreement with experiment: δ CKM ( ) This is only due to the 9/2!!

21 The Neutrino Sector [Antusch, King, MS 2010] The effective neutrino mass matrix: m ν = m mi mi We predict (at the GUT scale): θ MNS , θ MNS 23 = 45, θ MNS , δ MNS 90, α 1 9.1, α 2 =0 At low energies (RGE effects below 1 ): [Gonzalez-Garcia, Maltoni, Salvado 2010] θ MNS 12 = (34.5 ± 1.0), θ MNS 23 = ( ), θ MNS 13 = ( ), δ MNS?, α 1?, α 2 =?

22 Neutrinoless Double Beta Decay 0.50 Disfavoured by 0ΝΒΒ 0.20 GERDA I m m ee ev GERDA II m Disfavoured by Cosmology m lightest ev [Antusch, King, MS 2010]

23 Outline Motivation Quark Mixing Sum Rules Discrete Vacuum Alignment Examples Summary and Conclusions

24 Summary & Conclusions Quark Phase Sum Rule Simple method to fulfill this Phase Sum Rule - Spontaneous CP violation - Family Symmetry: A4, S4,... - Shaping Symmetries: Z2 s and/or Z4 s In combination with GUTs: - (Small) Deviations from Tri-Bimaximal Mixing - Predictions for Leptonic CP Phases

25 Backup

26 Symmetries (Flavon Sector) Flavons SU(5) A 4 Z (1) 4 Z (2) 4 Z (3) 4 Z (4) 4 Z (1) 2 Z (2) 2 U(1) R φ φ φ φ φ ξ Driving Fields P i A A A A O 1; O 1; O 2; O 1; O 123; Proof of Principle! [Antusch, King, Luhn, MS 2011]

27 Symmetries (Matter and Higgs Sector) [Antusch, King, Luhn, MS 2011] SU(5) A 4 Z (1) 4 Z (2) 4 Z (3) 4 Z (4) 4 Z (1) 2 Z (2) 2 U(1) R Matter Fields F T T T N N Higgs Fields New GUT relations!!! [Antusch, MS 09] H H H H H