A SUSY SU (5) T 0 Uni ed Model of Flavour with large θ13

Transcription

1 A SUSY SU (5) T 0 Uni ed Model of Flavour with large θ13 What's nu? Invisibles12, Florence, June 2012 Aurora Meroni (SISSA) In collaboration with S. T. Petcov and M. Spinrath arxiv:

2 Outline of the talk Motivations for a SU(5) T Unied Model of Flavour General Setup of the Model Neutrino Sector Conclusions Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

3 Experimental values and Open questions Global t analysis including the Daya Bay and RENO results D. V. Forero, M. Tortola, J. W. F. Valle ArXiV: Parameter best-t (±1σ) 3σ m 2 [10 5 ev 2 ] 7.62± ma 2 [10 3 ev 2 ] ( ) -( ) sin 2 θ sin 2 θ sin θ Open Questions in Neutrino Physics Majorana or Dirac? Absolute values of neutrino masses Hierarchy (normal m 1 < m 2 < m 3 or inverted m 3 < m 1 < m 2) CP-phases: δ, α 31 and α 21 Normal Inverted Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

4 Motivations GUT: SU(5) SU(5), Unied picture of quarks and leptons possibly leads to sizeable θ 13 discrete symmetry: T treats quarks and lepton mixing simultaneously can allow spinorial unitary irreducible reps geometrical CP violation corrections to U TBM via lepton sector 2/3 1/3 0 U TBM = 1/6 1/3 1/2 1/6 1/3 1/2 Unied model of avour Model based on SU(5) T In this model sin 2 θ 13 = 0.02 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

5 Discrete symmetry: the group T' T is the Double-valued group of T A 4 (even permutations of 4 objects) inequivalent UIRs : 1, 1, 1, 3 }{{} + 2, 2, 2 }{{} TBM for Neutrinos 2+1 assignments for q and l Complex CG coecients when spinorial UIRs are involved! Clebsch-Gordan coecients can be complex geometrical origin of CP violation! ( x1 x 2 ( x1 x 2 ) ) 2(2 ) 2 ( ) x 1 x 2 u 1 u 2 u 3 2(2 ) 3 = [( ( ) x1x 2 x 2x 1 2 (1 + i )x 2 u 2 + x 1 u 1 (1 i )x 1 u 3 x 2 u 1 ) 2 1 ( (1+i) 2 (x 1x 2 + x 2x 1) x 1x 1 ix 2x 2 (1 + i )x 2 u 3 + x 1 u 2 (1 i )x 1 u 1 x 2 u 2 )2 ( 3 )2 ] (1 + i )x 2 u 1 + x 1 u 3 (1 i )x 1 u 2 x 2 u 3 M.-C. Chen, K.T. Mahanthappa Phys.Lett. B652 (2007) F. Feruglio, C. Hagedorn, Y. Lin, L. Merlo, Nucl.Phys. B775 (2007) Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

6 Conventions and Assignments: Matter and Higgs elds Fundamental Symmetries SU(5) T (SUSY!) Shaping symmetry Z 12 Z 3 8 Z 2 6 Z 4 U(1) R Continuous version of the usual R-parity Matter Content 10(Q, u c, e c ) L : ten-plets into (T 1, T 2) 2, T 3 1 5(d c, l) L : ve-plets into (F 1, F 2, F 3) 3 Three Heavy RH Majorana N k, (N 1, N 2, N 3) 3 light active neutrinos via Type I See-Saw Higgs sector: copies of 5, 5 and 24 assigned to 1, 1 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

7 Conventions and assignments: Flavon elds up and down quark sector ψ ψ ( ) 1, 0 ψ ψ 0 φ φ 0, singlets e.g. ζ 1 1 in the ν sector ξ = 1 ξ 0, ρ = ρ 0, ρ = ρ 0 1 ( ) 0 1 Flavons elds take all real vevs when T' is broken! Flavon Alignment problem!!! S. Antusch, S. King, C. Luhn, M. Spinrath ArXiv: Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

8 Flavon vacuum alignement Auxiliary Fields: ɛ i SU(5) T 1 and Q U(1)R = 0 transform in a non trivial way under the shaping symmetries they appear only in the avon superpotential W ɛ = S ɛi ( ɛ 2 i M 2 ɛ i ) + Sɛj ( 1 Λ ɛ3 j M 2 ɛ j ) Driving Fields: {S x 1, D x 3} SU(5) 1 and Q U(1)R = 2 transform in a non trivial way under T and shaping symmetries W ξ,ρ, ρ = D ξ Λ for example in the neutrino sector ( ξ 2 ) ( ɛ 9 + ξρɛ 9 + ξ ρɛ 9 + Sξ ξ 2 M 2 ) ( ξ + Sρ ρ 2 + ρ 2 Mρ) 2 ξ i = ξ 0 0 if ρ 0 = ρ 0 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

9 Yukawa couplings: Eective Operators - arxiv: RL convention, i.e. L = Y ij f i R f j L H + H.c. (1 i)a u i b u 0 Y u = i b u c u (1 + i)d u, 0 (1 + i)d u e u (1 + i) a d i b d (1 + i) a d (1 i) b d 0 Y d = (1 i) b d c d 0 and Y l = 6 i b d 6 c d d d d d Talk by M. Spinrath. S. Antusch, M. Spinrath arxiv: V us b d c d θ12 e = 6ib d 6c d b d b d θc, (b d = 0.9 b d ) θ 13 = 1 θ12 e = 0.9 θ c 2 2 D. Marzocca, S. T. Petcov, A. Romanino, M. Spinrath arxiv: Antusch, Maurer arxiv: Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

10 Fit Results 2Σ 1Σ 0Σ 1Σ 2Σ e Μ Τ s d s b u c t Θ CKM 12 Θ CKM 13 Θ CKM 23 CKM A. M., S. T. Petcov, M. Spinrath arxiv: Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

11 Neutrino Sector: Description y ν W ν = λ 1NNξ + NN(λ 2ρ + λ 3 ρ) + }{{} Λ (N F )1(H (2) 5 ρ)1 + ỹν Λ (N F )1(H (2) 5 ρ)1 }{{} RH Majorana Mass M R Dirac Yukawa coupling M D 1 ξ = 1 ξ 0, ρ = ρ 0, ρ = ρ 0 1 2Z + X Z Z M R = Z 2Z Z + X, M D = ρ Λ Z Z + X 2Z X, Z and ρ are real parameters M R is form diagonalizable U T TBM M R U TBM = Diag(3Z + X, X, 3Z X ) Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

12 Neutrino Sector: Masses for Light Neutrinos Diagonal Majorana Mass Matrix 3Z + X αe i φ e i φ X 0 X 0 e i φ Z X αe i φ e i φ 3 α 3Z/X > 0, φ arg(z) arg(x ) φ i = 0, π Light neutrino Majorana mass term via type I see-saw mechanism: M ν = MD T M 1 R M D = Uν Diag (m 1, m 2, m 3) U ν (e ) i φ1/2, e i φ2/2, e i φ 3/2 U ν = i U TBM Diag ( ) ρ 2 1 m i =, i = 1, 2, 3 m i > 0 Λ M i Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

13 Neutrino Sector: Imput Parameters for Light Masses (remember : α > 0 cos φ = ±1!) ( ρ m 2 31 m 2 A = 1 X 2 { for cos φ = +1 for cos φ = 1 Λ ) 4 4α cos φ 1 + α e i φ 2 1 α e i φ 2 mass spectrum with NO mass spectrum with IO m 2 21 m 2 = 1 X 2 ( ρ Λ ) 4 α (α + 2 cos φ) 1 + α e i φ 2 r = m2 m 2 A = 1 4 (α + 2 cos φ) ( 1 2α cos φ + α 2) = ± Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

14 Neutrino Spectrum NO m 1 < m 2 < m 3 - arxiv: NO Solution A NO Solution B m 1 = ev m 2 = ev m 3 = ev RH Majorana N k : M 3 < M 2 < M 1 M 1/M 3 = 11.0 M 2/M 3 = 5.0 m 1 = ev m 2 = ev m 3 = ev RH Majorana N k : M 3 < M 2 < M 1 M 1/M 3 = 8.33 M 2/M 3 = m1, m2, m3 ev m1, m2, m3 ev Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

15 Neutrino Spectrum IO m 3 < m 1 < m 2 - arxiv: IO m 1 = ev m 2 = ev m 3 = ev RH Majorana N k : M 1 = M2 < M 3 M 1/M 2 = M 3/M 2 = m1, m2, m3 ev Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

16 Charged lepton correction to U TBM, angles and phases - arxiv: U PMNS = U el Uν U el = diag(1, e i ϕ, 1) R 12(θ e 12), U ν U TBM Uappx PMNS = e i β sin θ12 e e i(π θ e 12)/2 2 e i β θ 12 = arcsin(1/ 3) + 2/8(θ e 12) 2 θ 13 = θ e 12/ 2 θ 23 = π/4 1/4(θ e 12) 2 δ = π θe 12 β 1 = 2π 2θ e 12 + φ 3 β 2 = 2π + θ e 12 + φ 3 φ 2 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

17 Results and RG corrections for mixing angles and phases Quantity Experiment (2σ ranges) Model sin 2 θ sin 2 θ sin 2 θ δ β φ 3 β φ 3 - φ 2 J CP We consider as well RG corrections The largest correction we nd is for δ= 81.2 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

18 Predictions for Mass spectrum and ββ0νdecay - arxiv: NO Solution A 3 m k = ev k=1 < m > = ev NO Solution B 3 m k = ev k=1 < m > = ev IO 3 m k = ev k=1 < m > = ev Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

19 Conclusions - arxiv: We construct a unied model of avor with large θ 13 based on S(5) T with type I See-Saw T leads to TBM in the neutrino sector + corrections coming from the charged lepton sector Geometrical CP violation via CGs of the T group Essential ingredient: real avon vev alignment Predictions: sin 2 θ δ = π/2 0.45θ c 84.3 Neutrino mass spectra: NO and IO possible unambiguous predictions for ββ0ν-decay <m > Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

20 Thank you Aurora Meroni (SISSA) SU (5) T 0 with large θ13 June / 19

21 Back up slides Aurora Meroni (SISSA) SU (5) T 0 with large θ13 June / 19

22 Literature SU(5) T Z 12 Z 12 was developped in M.C. Chen, K.T. Mahanthappa Phys. Lett. B652,34 (2007); PoS ICHEP2010:407,2010. Phys. Lett. B681, 444 (2009) Too small θ 13 θc 3 2 sin2 θ Dierent avour structure dierent values for observables! Only NO possible Flavon vacuum alignment problem Messenger sector Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

23 Discrete symmetry: UIRs of the group T' T is the Double-valued group of T A 4 (even permutations of 4 objects) inequivalent UIRs : 1, 1, 1, 3 }{{} + 2, 2, 2 }{{} TBM for Neutrinos 2+1 assignments for q and l Complex CG coecients when spinorial UIRs are involved! 3 generators: s 2 = r, r 2 = t 3 = (st) 3 = e, rt = tr : r = 0 1 0, t = 0 ω 0, s = 1 1 2ω 2ω 2 2ω 2 1 2ω ω 2 3 2ω 2ω 2 1 where 1 + ω + ω 2 = 0 conventionally. 1 Γ p = Γ p, 1 1 (1 ) = 1 (1 ), 1 1 (1 ) = 1 (1), 1 (1 ) 1 = 1(1 ) 2 1 (1 ) = 2 (2 ), 2 1 (1 ) = 2 (2), 2 1 (1 ) = 2(2 ) 2(2 ) 2(2 ) = 1 3, 2 (2) 2 (2 ) = 1 3, 2 (2) 2 (2 ) = (1 ) = 3, 3 2 = 2 2 2, 3 2 (2 ) = 2 (2 ) 2 (2) 2(2 ) 3 3 = T group: Clebsch-Gordan series Γ p Γ q = Γ q Γ p. Here Γ p = 1, 2, 3 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

24 Table of Charge Assignments: Matter and Higgs elds (1) T3 T a F N H 5 H (2) 5 H (3) 5 H (1) 5 H (2) 5 H (3) 5 H 5 24 H 24 SU(5) T U(1) R Z12 u Z8 d Z8 ν Z Z Z Z Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

25 Table of Charge Assignments: Flavons φ ψ ψ ζ ζ φ ψ ψ ζ ζ ξ ρ ρ SU(5) T U(1) R Z12 u Z8 d Z8 ν Z Z Z Z Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19

26 W Yu = y 33H (1) y23 5 T3T3 + Λ 2 (Ta φ) 2 H (2) 5 (T3 ψ ) 2 + y22 Λ 3 (Ta ψ ) 3(H (1) ζ 5 ) 1 (T ψ a ) 3 W Yd,l = y33 Λ + y21 Λ 4 (Ta φ) 2 (H (1) 5 ζ ) 1 ( ψ (T a ψ ) 3) 2 + y11 Λ 4 ((Ta φ) 2 ζ ) 2 H (3) 5 (ζ (T a φ)2 ) 2, (( H(2) 2 5 F ) 3φ) 1 (H 24T 3) 1 + y22 Λ 3 ((φta) 2 H 24) 2(ψ ( H(1) F ) 3) 2 + y12 (((Ta H Λ4 24) 2 ( F ψ ) 2 ) 3ψ ) 2 ( H(3) 5 ψ ) 2 + y21 Λ 4 (( F ψ ) 2 (ζ H(1) 5 ) 1 ζ ) 2(T aφ) 2 + y11 Λ 4 (( F ψ ) 2 (H 24ψ ) 2 H 5 ) 1 (T aψ ) 1, 5 Aurora Meroni (SISSA) SU(5) T with large θ 13 June / 19