SU(3)-Flavons and Pati-Salam-GUTs

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1 SU(3)-Flavons and Pati-Salam-GUTs Florian Hartmann in collaboration with Wolfgang Kilian and Karsten Schnitter Universität Siegen Theoretische Physik I Dortmund,

2 Outline 1 Running couplings in PS Multi-step breaking of Pati-Salam Gauge coupling Unification Unification Plots 2 Flavour Models Aim of Flavour Models Model of triplet Flavons Model with decuplet flavons 3 Conclusions Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

3 Multi-step breaking of SUSY-Pati Salam symmetry Pati- Salam: SU(4) SU(2) R SU(2) L Z 2 valid to M Planck Σ Left- Right: SU(3) C U(1) B L SU(2) R SU(2) L Z 2 H R Standard model: SU(3) C SU(2) L U(1) Y h M Z SU(3) C U(1) em Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

4 Pati-Salam Higgs content PS breaking Higgs Σ = (15, 1, 1) to break SU(4) E = (6, 2, 2) and T L = (1, 3, 1),T R = (1, 1, 3) } 45 L-R breaking Higgs Hu R = (4, 1, 2) and Hd R = (4, 1, 2) to break U(1) } B L SU(2) R Hu L = (4, 2, 1) and Hd L = (4, 2, 1) because of Z optional MSSM Higgs h = (1, 2, 2): MSSM-Higgs F = (6, 1, 1): possibly light triplets } 10 full E 6 multiplets when including matter Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

5 Higgs Superpotential construct renormalizable Higgs sector superpotential calculate tree-level Higgs masses Results see-saw-like mass terms in Higgs fields new intermediate mass-scale: M F m F + H R 2 light colour triplets (down to TeV-scale) useful for unification additionally Z 2 -symmetry above L-R-scale two light doublets from H L (at MSSM-scale) makes h optional Σ W. Kilian, J.Reuter: arxiv:hep-ph/ SU(2) R and SU(2) L breaking form same SO(10) representation Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

6 Gauge coupling Unification Requirements for Unification (1) PS hypercharge condition Y = T3 R + B L 2 rescaling of U(1) Y unification-condition at the L-R-scale αy -1 = α-1 R α-1 B L ; αr -1 = α-1 L (2) unification condition at the PS-scale αb L -1 = α-1 3 ; α3-1 = α-1 4 (3) complete unification of couplings near the Planck-scale Inputs: MSSM-scale: 250 GeV 3 unification-requirements but 3 (4) mass-scales + normalization of U(1) B L scales are constrained but not fixed Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

7 Minimal model Higgs field content H R u/d = (4, 1, 2) ; HL u/d = (4, 2, 1) ; Σ = (15, 1, 1) green band: 4.7 log [M L-R ] red band: 12.6 log [M PS ] blue band: 16.4 log [M GUT ] Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

8 Full model Higgs field content Full SO(10) representations : 10 ; 16 ; 16 ; green band: 2.8 log [M L-R ] red band: 11.6 log [M PS ] 16.4 blue band: 14.4 log [M GUT ] Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

9 E 6 inspired Flavour triplet model Higgs and matter field content Full E 6 SU(3) F representations : (27, 3) ; (78, 1) green band: 5.4 log [M L-R ] red band: 9.6 log [M PS ] 16.7 blue band: 11.8 log [M GUT ] Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

10 Outline 1 Running couplings in PS Multi-step breaking of Pati-Salam Gauge coupling Unification Unification Plots 2 Flavour Models Aim of Flavour Models Model of triplet Flavons Model with decuplet flavons 3 Conclusions Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

11 Aim of Flavour Models Flavour symmetry L Yuk = c M Φ n ij h Ψ L i Ψ cr j c M Φ n ij h Ψ L i Ψ cr j > M M Planck < M with the SM-Yukawa-coupling y ij = c M n Φ ij and Φ ij = n k φ k (1) following form fits quark-data quite well ( 0 O(ɛ3 ) ) O(ɛ 3 ) Y u/d O(ɛ 3 ) O(ɛ 2 ) O(ɛ 2 ) O(ɛ 3 ) O(ɛ 2 ) O(1) with ɛ u 0.05 and ɛ d 0.15 m t Roberts, Romanino, Ross, Velasco-Sevilla: arxiv:hep-ph/ (2) neutrino-data also described in case of Sequential Right-Handed Neutrino Dominance (SRHND) King: arxiv:hep-ph/ Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

12 Three Higgs Generations consider Flavour-SU(3) F Pati-Salam GUT take Higgs as Flavour-triplet consistent with matter-higgs-unification: Ψ = (27, 3) (E 6 -unification) Caution: new trivial invariant ε ijk Ψ L i Ψ R j h k large off-diagonal Yukawa matrix entries Additional discrete symmetry needed Considered flavon representations Case 1: φ i 3 / 3 Case 2: φ i 10 = (3 3 3) s Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

13 Model of triplet Flavons Ansatz consider SU(3) PS-model with Flavour triplet Higgs (for singlet Higgs equivalent to existing models) King, Ross: arxiv:hep-ph/ flavons are Flavour triplets φ 3 = φ 3 = (0, 0, 1) M ; φ 23 = φ 23 = (0, ɛ, ±ɛ) M discrete symmetries (U(1) Z 2 ) set new quantum numbers Results: leading order in flavon insertion generates Yukawa 2-3 block NLO leads to large corrections to Yukawa matrix only possible to forbid field-configurations (not invariants) fine tuning possible, but fine-tuning or more flavons needed work in progress Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

14 Model with decuplet flavons Field SU(3) F PS U(1) Ψ 3 (4, 2, 1) 1 Ψ c 3 ( 4, 1, 2) 1 h 3 (1, 2, 2) 1 φ 1 10 (1, 1, 1) 3 φ 2 10 (1, 1, 1) 3 φ 3 10 (1, 1, 1) 3 H u 3 ( 4, 1, 2) 2 H d 3 (4, 1, 2) 2 0 ɛ 3 ɛ 3 Ylead f ɛ 3 ɛ 2 ɛ 2 ɛ 3 ɛ 2 1 no next to leading order contributions φ M φ ɛ 2 M φ ɛ 2 M φ ɛ 3 M φ ɛ 3 M W lead = 3 i=1 y i M ΨΨc h φ i Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

15 Potential and vacuum alignment introduce P i to align vevs D-term leads to φ 1 φ 2 φ 3 10 i to guarantee D-term flatness assign same vev to 10 additional sub-leading terms Field SU(3) F PS U(1) φ 1 10 (1, 1, 1) 5 φ 2 10 (1, 1, 1) 1 φ 3 10 (1, 1, 1) 6 P 1 1 (1, 1, 1) 9 P 2 1 (1, 1, 1) 2 P 3 1 (1, 1, 1) 2 P 4 1 (1, 1, 1) 3 W 10 = c M P 1 φ 1 φ 2 φ 3 W Ren = 3 ( ) P i+1 φi φ j µ i i,j F 10 not sufficient vevs can be chosen diagonal φ i φ j = 0, i k F Pi+1 φ i φ i µ i = 0 hierarchy of the vevs Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

16 Majorana mass matrix W Maj = 1 ( M 3 Ψc 2 Hd 2 C 1 φ 1 φ 1 + C 2 φ 1 φ 2 + C 3 φ 1 φ 3 + C ) 4 φ 2 φ 2 M Maj c 8 ɛ 4 ν c 3 ɛ 3 ν (c 3 c 7 ) ɛ 3 ν c 3 ɛ 3 ν c 2 ɛ 2 ν (c 2 c 6 ) ɛ 2 ν (c 3 c 7 ) ɛ 3 ν (c 2 c 6 ) ɛ 2 ν (c 1 + c 4 c 5 ) Eigenvalues of order: ( 1, ɛ 2 ν, ɛ 4 ) ν sequential dominance Eigenvectors: unit vectors up to corrections of order ɛ 2 near tri-bimaximal lepton mixing H d 2 M Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

17 Conclusions Multi-step breaking of SUSY-Pati-Salam unification of gauge-couplings possible introduction of intermediate L-R-scale explanation for the low scale of light triplets M LR and M PS can vary over quite large mass-ranges Flavour triplet Higgs models models with SU(3) F and Flavour triplet Higgs are possible model with triplet flavons are challenging but possible decuplet flavons reproduce Flavour structure only single U(1) needed Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15

18 Conclusions Multi-step breaking of SUSY-Pati-Salam unification of gauge-couplings possible introduction of intermediate L-R-scale explanation for the low scale of light triplets M LR and M PS can vary over quite large mass-ranges Flavour triplet Higgs models models with SU(3) F and Flavour triplet Higgs are possible model with triplet flavons are challenging but possible decuplet flavons reproduce Flavour structure only single U(1) needed Thanks for your attention! Florian Hartmann (Universität Siegen) SU(3)-Flavons and Pati-Salam-GUTs Dortmund / 15