Flavour scenarios from 5D SO(10): order and anarchy interplay Denise Vicino, University of Padova in collaboration with: F. Feruglio and K. Patel Based on: arXiv: 1507.00669 and JHEP 1409(2014)095 - arXiv: 1407.2913 Nu@Fermilab 2015 21-25 Jul 2015
Grand Unification and the Flavour puzzle Unification of Forces: String 10 18 TOE? theory? Energy (GeV) Grand Unification GUT? 10 16 k BSM a e w SUSY? o r t Strong c e l E 100 Gravity SM EM Weak SU (3) C × SU (2) L × U (1) Y Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 2
Grand Unification and the Flavour puzzle Unification of Forces: String 10 18 TOE? theory? Energy (GeV) Grand Unification GUT? 10 16 SU(5) ? k BSM a e w SUSY? o r t Strong c e l E 100 Gravity SM EM Weak SU (3) C × SU (2) L × U (1) Y Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 2
Grand Unification and the Flavour puzzle Unification of Forces: String 10 18 TOE? theory? Energy (GeV) Grand Unification GUT? 10 16 SU(5) ? ⊂ SO(10)? k BSM a e w SUSY? o r t Strong c e l E 100 Gravity SM EM Weak SU (3) C × SU (2) L × U (1) Y Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 2
Grand Unification and the Flavour puzzle Unification of Forces: } • Explain the origin of SM gauge structure: but which symmetry String breaking down to the SM? 10 18 TOE? theory? • Unified description of SM fermions: Energy (GeV) Grand Unification a single SO(10) SM fermions representation: GUT? 10 16 + SU(5) ? ⊂ SO(10)? RH neutrinos 16 i =1 , 2 , 3 k BSM a e w SUSY? o r t Strong c e l E 100 Gravity SM EM Weak SU (3) C × SU (2) L × U (1) Y Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 2
Grand Unification and the Flavour puzzle Why this peculiar structure of the Yukawa couplings? • Charged Fermions • Neutrinos Masses m u : m c : m t ≈ λ 8 : λ 4 : 1 ∆ S m ν ≤ O (eV) ≈ λ 2 ∆ A m d : m s : m b ≈ λ 5 : λ 3 : 1 m 2 ν 2 − m 2 ∆ S ≡ ν 1 m e : m µ : m τ ≈ λ 6 : λ 2 : 1 � � m 2 ν 3 − m 2 � ∆ A ≡ � ν 2 • Quark sector • Lepton sector Mixing λ 3 λ 0 . 8 0 . 5 0 . 2 1 λ 2 | U PMNS | ≈ 0 . 5 0 . 6 0 . 6 | V CKM | ≈ λ 1 λ 3 λ 2 0 . 3 0 . 6 0 . 7 1 SO(10) GUT: which advantages? • RH neutrinos, natural implementation of (type I) [Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] • Embedding SU(5) SO(10): explain similar hierarchy in down quarks ⊂ and charged leptons [Georgi-Glashow (1974)] Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 3
Grand Unification and the Flavour puzzle Why this peculiar structure of the Yukawa couplings? • Charged Fermions • Neutrinos Masses m u : m c : m t ≈ λ 8 : λ 4 : 1 ∆ S m ν ≤ O (eV) ≈ λ 2 ∆ A m d : m s : m b ≈ λ 5 : λ 3 : 1 m 2 ν 2 − m 2 ∆ S ≡ ν 1 m e : m µ : m τ ≈ λ 6 : λ 2 : 1 � � m 2 ν 3 − m 2 � ∆ A ≡ � ν 2 • Quark sector • Lepton sector Mixing λ 3 λ 0 . 8 0 . 5 0 . 2 1 λ 2 | U PMNS | ≈ 0 . 5 0 . 6 0 . 6 | V CKM | ≈ λ 1 λ 3 λ 2 0 . 3 0 . 6 0 . 7 1 SO(10) GUT: which advantages? • RH neutrinos, natural implementation of (type I) See-Saw mechanism • RH neutrinos, natural implementation of (type I) [Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] • Embedding SU(5) SO(10): explain similar hierarchy in down quarks ⊂ and charged leptons [Georgi-Glashow (1974)] Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 3
Grand Unification and the Flavour puzzle Why this peculiar structure of the Yukawa couplings? • Charged Fermions • Neutrinos Masses m u : m c : m t ≈ λ 8 : λ 4 : 1 ∆ S m ν ≤ O (eV) ≈ λ 2 ∆ A m d : m s : m b ≈ λ 5 : λ 3 : 1 m 2 ν 2 − m 2 ∆ S ≡ ν 1 m e : m µ : m τ ≈ λ 6 : λ 2 : 1 � � m 2 ν 3 − m 2 � ∆ A ≡ � ν 2 • Quark sector • Lepton sector Mixing λ 3 λ 0 . 8 0 . 5 0 . 2 1 λ 2 | U PMNS | ≈ 0 . 5 0 . 6 0 . 6 | V CKM | ≈ λ 1 λ 3 λ 2 0 . 3 0 . 6 0 . 7 1 SO(10) GUT: which advantages? • RH neutrinos, natural implementation of (type I) See-Saw mechanism • RH neutrinos, natural implementation of (type I) [Minkowski (1977), Yanagida (1979), Gell-Mann,Ramond, Slansky (1979), Mohapatra and Senjanovic (1980)] • Embedding SU(5) SO(10): explain similar hierarchy in down quarks • Embedding SU(5) SO(10): explain similar hierarchy in down quarks ⊂ ⊂ and charged leptons and charged leptons [Georgi-Glashow (1974)] Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 3
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling quarks and leptons); • Large representations; • Lots of parameters, Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling is possible (more then one Higgs, necessary to distinguish • No minimal coupling quarks and leptons); quarks and leptons); • Large representations; • Lots of parameters, Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling • No minimal coupling is possible (more then one Higgs, necessary to distinguish quarks and leptons); quarks and leptons); • Large representations; Doublet-Triplet splitting problem; • Large representations; • Lots of parameters, Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling • No minimal coupling is possible (more then one Higgs, necessary to distinguish quarks and leptons); quarks and leptons); • Large representations; Doublet-Triplet splitting problem; • Large representations; • Lots of parameters, hierarchical and fine-tuned (as much as in the SM) • Lots of parameters, Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling • No minimal coupling is possible (more then one Higgs, necessary to distinguish quarks and leptons); quarks and leptons); • Large representations; Doublet-Triplet splitting problem; • Large representations; • Lots of parameters, hierarchical and fine-tuned (as much as in the SM) • Lots of parameters, Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Grand Unification and the Flavour puzzle SO(10) GUT: which disadvantages? Y ij Structure of the Yukawa couplings: + ... 10 16 i 16 j 10 H + 3 possible Higgs representations 16 × 16 = 10 + 120 + 126 • No minimal coupling • No minimal coupling is possible (more then one Higgs, necessary to distinguish quarks and leptons); quarks and leptons); • Large representations; Doublet-Triplet splitting problem; • Large representations; • Lots of parameters, hierarchical and fine-tuned (as much as in the SM) • Lots of parameters, Are ANARCHICAL O (1) Yukawas allowed? Can any mechanism ORDER the parameters and create the hierarchies? Is this compatible with unified description of fermions in SO(10)? Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 4
Anarchy and order interplay: the basic idea Hierarchical Anarchical O (1) F Q 1 ⌧ F Q 2 ⌧ F Q 3 } Y u = F Q Y u F u c F u 1 < F u 2 < F u 3 Y d = F Q Y d F d c F d 1 . F d 2 . F d 3 } F L 1 ≈ F L 2 ≈ F L 3 Y e = F L Y e F e c F e 1 ⌧ F e 2 ⌧ F e 3 [Kawamura, (2001 Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5
Anarchy and order interplay: the basic idea Hierarchical Anarchical “Ordering” Which mechanism O (1) can generate these hierarchies ? F Q 1 ⌧ F Q 2 ⌧ F Q 3 } Y u = F Q Y u F u c F u 1 < F u 2 < F u 3 Y d = F Q Y d F d c F d 1 . F d 2 . F d 3 } F L 1 ≈ F L 2 ≈ F L 3 Y e = F L Y e F e c F e 1 ⌧ F e 2 ⌧ F e 3 [Kawamura, (2001 Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5
Anarchy and order interplay: the basic idea Hierarchical Anarchical “Ordering” Which mechanism O (1) can generate these hierarchies ? F Q 1 ⌧ F Q 2 ⌧ F Q 3 } Y u = F Q Y u F u c F u 1 < F u 2 < F u 3 Froggatt-Nielsen charges: Y d = F Q Y d F d c G f = U (1) F N F d 1 . F d 2 . F d 3 } F L 1 ≈ F L 2 ≈ F L 3 Y e = F L Y e F e c F e 1 ⌧ F e 2 ⌧ F e 3 [Kawamura, (2001 Denise Vicino Flavour scenarios from 5D SO(10): order and anarchy interplay 5
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