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Flavour structure from the seesaw Michael A. Schmidt University of Melbourne 28th Jun 2012 Alexei Smirnov Fest Whats nu? Invisibles 12 M. Lindner, MS, A. Y. .Smirnov, JHEP 0507 (2005) 048 C. Hagedorn, MS, A. Y. .Smirnov, Phys. Rev. D 79

  1. Flavour structure from the seesaw Michael A. Schmidt University of Melbourne 28th Jun 2012 Alexei Smirnov Fest What’s nu? – Invisibles 12 M. Lindner, MS, A. Y. .Smirnov, JHEP 0507 (2005) 048 C. Hagedorn, MS, A. Y. .Smirnov, Phys. Rev. D 79 , 036002 (2009) MS, A. Y. .Smirnov, Nucl.Phys. B857 (2012) 1-27 1

  2. Outline Introduction 1 Implementations of Double Seesaw Structure 2 Stability with respect to Quantum Corrections 3 Conclusions 4 2

  3. Outline Introduction 1 Implementations of Double Seesaw Structure 2 Stability with respect to Quantum Corrections 3 Conclusions 4 3

  4. ★ ★ ✒ ✍ ✿ ✍ ✍ ✿ ✒ ✒ ✒ ✍ ✍ ✿ ✍ ✍ ✍ ✿ ✍ Fermion Masses Huge hierarchy of charged fermions: m t : m c : m u ✘ 1 : 7 ✁ 10 � 3 : 10 � 5 m b : m s : m d ✘ 1 : 2 ✁ 10 � 2 : 10 � 3 m ✜ : m ✖ : m e ✘ 1 : 6 ✁ 10 � 2 : 3 ✁ 10 � 4 Neutral fermions have smaller masses and a weaker hierarchy inverted ordering normal ordering ✗ 2 ∆ m 2 ✗ 3 ∆ m 2 21 31 ✗ 1 ∆ m 2 31 ✗ 2 ∆ m 2 21 ✗ 3 ✗ 1 4

  5. Fermion Masses Huge hierarchy of charged fermions: m t : m c : m u ✘ 1 : 7 ✁ 10 � 3 : 10 � 5 m b : m s : m d ✘ 1 : 2 ✁ 10 � 2 : 10 � 3 m ✜ : m ✖ : m e ✘ 1 : 6 ✁ 10 � 2 : 3 ✁ 10 � 4 Neutral fermions have smaller masses and a weaker hierarchy Small mixing angles in CKM matrix: ★ 12 ★ 23 ✒ 13 13 ✍ 2 ✿ 4 ✍ 0 ✿ 23 ✍ Large mixing angles in PMNS matrix: inverted ordering normal ordering ✗ 2 ∆ m 2 ✗ 3 ∆ m 2 21 ✒ 12 ✒ 23 ✒ 13 31 ✗ 1 ∆ m 2 31 ✗ 2 ∆ m 2 34 ✍ 44 ✍ 9 ✿ 3 ✍ 21 ✗ 3 ✗ 1 [Forero et. al (2012)] 34 ✍ 39 ✍ 9 ✿ 0 ✍ [Fogli et. al (2012)] 4

  6. Fermion Masses Huge hierarchy of charged fermions: m t : m c : m u ✘ 1 : 7 ✁ 10 � 3 : 10 � 5 m b : m s : m d ✘ 1 : 2 ✁ 10 � 2 : 10 � 3 m ✜ : m ✖ : m e ✘ 1 : 6 ✁ 10 � 2 : 3 ✁ 10 � 4 Neutral fermions have smaller masses and a weaker hierarchy Small mixing angles in CKM matrix: ★ 12 ★ 23 ✒ 13 13 ✍ 2 ✿ 4 ✍ 0 ✿ 23 ✍ Large mixing angles in PMNS matrix: inverted ordering normal ordering ✗ 2 ∆ m 2 ✗ 3 ∆ m 2 21 ✒ 12 ✒ 23 ✒ 13 31 ✗ 1 ∆ m 2 31 ✗ 2 ∆ m 2 34 ✍ 44 ✍ 9 ✿ 3 ✍ 21 ✗ 3 ✗ 1 [Forero et. al (2012)] 34 ✍ 39 ✍ 9 ✿ 0 ✍ [Fogli et. al (2012)] Explanation of different structures? Compatibility with GUTs? 4

  7. ❤ ✐ ❤ ✐ ☛ ☞ � ✮ ✗ ✙ � � ✁ ✘ ❖ ❀ ✘ ❖ ❁ ✮ ❖ ✿ ✗ ✮ ✘ ✮ ✮ Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ✒ m T ✓ 0 D ▼ = ✁ M NN 5

  8. ✮ ✘ ✮ ✮ Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ❤ H ✐ ❤ H ✐ ✒ m T ✓ 0 L ☛ L ☞ ✮ m ✗ ✙ � m T D M � 1 D ▼ = NN m D N ✁ M NN 10 14 GeV � ✁ m D ✘ ❖ (Λ ew ) ❀ M NN ✘ ❖ ❁ Λ GUT ✮ effective light neutrino mass: m ✗ � ❖ ( 0 ✿ 1 eV ) 5

  9. ✮ ✘ ✮ ✮ Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ❤ H ✐ ❤ H ✐ ✒ m T ✓ 0 L ☛ L ☞ ✮ m ✗ ✙ � m T D M � 1 D ▼ = NN m D N ✁ M NN 10 14 GeV � ✁ m D ✘ ❖ (Λ ew ) ❀ M NN ✘ ❖ ❁ Λ GUT ✮ effective light neutrino mass: m ✗ � ❖ ( 0 ✿ 1 eV ) Different flavour structure possible 5

  10. ✮ Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ❤ H ✐ ❤ H ✐ ✒ m T ✓ 0 L ☛ L ☞ ✮ m ✗ ✙ � m T D M � 1 D ▼ = NN m D N ✁ M NN 10 14 GeV � ✁ m D ✘ ❖ (Λ ew ) ❀ M NN ✘ ❖ ❁ Λ GUT ✮ effective light neutrino mass: m ✗ � ❖ ( 0 ✿ 1 eV ) Different flavour structure possible If SO(10): RH neutrinos as well as all SM fermions in 16 ✮ m D ✘ m u ✮ Large (quadratic) hierarchy in neutrino masses 5

  11. Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ❤ H ✐ ❤ H ✐ ✒ m T ✓ 0 L ☛ L ☞ ✮ m ✗ ✙ � m T D M � 1 D ▼ = NN m D N ✁ M NN 10 14 GeV � ✁ m D ✘ ❖ (Λ ew ) ❀ M NN ✘ ❖ ❁ Λ GUT ✮ effective light neutrino mass: m ✗ � ❖ ( 0 ✿ 1 eV ) Different flavour structure possible If SO(10): RH neutrinos as well as all SM fermions in 16 ✮ m D ✘ m u ✮ Large (quadratic) hierarchy in neutrino masses ✮ Cancellation of hierarchies needed in neutrino mass matrix 5

  12. Seesaw Mechanism Standard Seesaw [Minkowski;Yanagida;Glashow;Gell-Mann,Ramond,Slansky;Mohapatra,Senjanovic] Introduction of right-handed (RH) neutrinos N ❤ H ✐ ❤ H ✐ ✒ m T ✓ 0 L ☛ L ☞ ✮ m ✗ ✙ � m T D M � 1 D ▼ = NN m D N ✁ M NN 10 14 GeV � ✁ m D ✘ ❖ (Λ ew ) ❀ M NN ✘ ❖ ❁ Λ GUT ✮ effective light neutrino mass: m ✗ � ❖ ( 0 ✿ 1 eV ) Different flavour structure possible If SO(10): RH neutrinos as well as all SM fermions in 16 ✮ m D ✘ m u ✮ Large (quadratic) hierarchy in neutrino masses ✮ Cancellation of hierarchies needed in neutrino mass matrix New scale below Λ GUT needed 5

  13. ❤ ✐ ❤ ✐ ❤ ✐ ❤ ✐ ☞ ☛ ☞ ☛ Solutions to Large Hierarchy from Seesaw Forget about SO(10), use e.g. SU(5) 6

  14. Solutions to Large Hierarchy from Seesaw Forget about SO(10), use e.g. SU(5) Use an alternative seesaw mechanism Alternative Seesaw Type II (scalar triplet) seesaw Type III (fermionic triplet) seesaw ❤ H ✐ ❤ H ✐ ❤ H ✐ ❤ H ✐ L ☞ ∆ L ☛ Σ L ☛ L ☞ 6

  15. Solutions to Large Hierarchy from Seesaw Forget about SO(10), use e.g. SU(5) Use an alternative seesaw mechanism Cancel hierarchy through structure in RH Majorana mass matrix M NN . . . Alternative Seesaw Type II (scalar triplet) seesaw Type III (fermionic triplet) seesaw ❤ H ✐ ❤ H ✐ ❤ H ✐ ❤ H ✐ L ☞ ∆ L ☛ Σ L ☛ L ☞ 6

  16. � � ✮ ✗ ✢ ✢ ✮ ✘ ❖ ❀ ✘ ❖ ❀ ✘ ❖ ✿ ✢ ✢ ✮ ✘ ❖ ❀ ✘ ❖ ❀ ✘ ❖ ✘ ❂ ✘ ❂ ✘ Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S m T ✵ 0 0 ✶ D M T ✿ 0 ▼ = ❇ ❈ SN ❅ ❆ ✿ ✿ M SS Mainly two different limits studied: 7

  17. ✢ ✢ ✮ ✘ ❖ ❀ ✘ ❖ ❀ ✘ ❖ ✘ ❂ ✘ ❂ ✘ Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S m T ✵ 0 0 ✶ D M T D M � 1 SN M SS M � 1 T ❆ ✮ m ✗ = m T ✿ 0 ▼ = m D ❇ ❈ SN SN ❅ ✿ ✿ M SS Mainly two different limits studied: Inverse seesaw: M SN ✢ m D ✢ M SS ✮ e.g. m D ✘ ❖ ( 100 GeV ) ❀ M SN ✘ ❖ ( TeV ) ❀ M SS ✘ ❖ ( 0 ✿ 01 keV ) 7

  18. ✘ ❂ ✘ ❂ ✘ Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S m T ✵ 0 0 ✶ D M T D M � 1 SN M SS M � 1 T ❆ ✮ m ✗ = m T ✿ 0 ▼ = m D ❇ ❈ SN SN ❅ ✿ ✿ M SS Mainly two different limits studied: Inverse seesaw: M SN ✢ m D ✢ M SS ✮ e.g. m D ✘ ❖ ( 100 GeV ) ❀ M SN ✘ ❖ ( TeV ) ❀ M SS ✘ ❖ ( 0 ✿ 01 keV ) Double seesaw: M SS ✢ M SN ✢ m D ✮ m D ✘ ❖ (Λ ew ) ❀ M SN ✘ ❖ (Λ GUT ) ❀ M SS ✘ ❖ ( M Pl ) 7

  19. Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S m T ✵ 0 0 ✶ D M T D M � 1 SN M SS M � 1 T ❆ ✮ m ✗ = m T ✿ 0 ▼ = m D ❇ ❈ SN SN ❅ ✿ ✿ M SS Mainly two different limits studied: Inverse seesaw: M SN ✢ m D ✢ M SS ✮ e.g. m D ✘ ❖ ( 100 GeV ) ❀ M SN ✘ ❖ ( TeV ) ❀ M SS ✘ ❖ ( 0 ✿ 01 keV ) Double seesaw: M SS ✢ M SN ✢ m D ✮ m D ✘ ❖ (Λ ew ) ❀ M SN ✘ ❖ (Λ GUT ) ❀ M SS ✘ ❖ ( M Pl ) Naturally leads to correct scale of RH neutrinos GUT ❂ M Pl ✘ 10 13 GeV M NN ✘ M 2 SN ❂ M SS ✘ Λ 2 7

  20. Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S ✵ m T m T ✶ 0 S ✗ D M T D M � 1 SN M SS M � 1 T ❆ ✮ m ✗ = m T ❇ ✿ M NN ❈ ▼ = m D SN ❇ ❈ SN ❅ ✿ ✿ M SS Mainly two different limits studied: Inverse seesaw: M SN ✢ m D ✢ M SS ✮ e.g. m D ✘ ❖ ( 100 GeV ) ❀ M SN ✘ ❖ ( TeV ) ❀ M SS ✘ ❖ ( 0 ✿ 01 keV ) Double seesaw: M SS ✢ M SN ✢ m D ✮ m D ✘ ❖ (Λ ew ) ❀ M SN ✘ ❖ (Λ GUT ) ❀ M SS ✘ ❖ ( M Pl ) Naturally leads to correct scale of RH neutrinos GUT ❂ M Pl ✘ 10 13 GeV M NN ✘ M 2 SN ❂ M SS ✘ Λ 2 7

  21. Double Seesaw Double Seesaw [Mohapatra,Valle;Barr] Introduce additional singlets S ✵ m T m T ✶ 0 S ✗ D M T D M � 1 SN M SS M � 1 T ❆ ✮ m ✗ = m T ❇ ✿ M NN ❈ ▼ = m D SN ❇ ❈ SN ❅ ✿ ✿ M SS Mainly two different limits studied: Inverse seesaw: M SN ✢ m D ✢ M SS ✮ e.g. m D ✘ ❖ ( 100 GeV ) ❀ M SN ✘ ❖ ( TeV ) ❀ M SS ✘ ❖ ( 0 ✿ 01 keV ) Double seesaw: M SS ✢ M SN ✢ m D ✮ m D ✘ ❖ (Λ ew ) ❀ M SN ✘ ❖ (Λ GUT ) ❀ M SS ✘ ❖ ( M Pl ) Naturally leads to correct scale of RH neutrinos GUT ❂ M Pl ✘ 10 13 GeV M NN ✘ M 2 SN ❂ M SS ✘ Λ 2 If M SS singular, there are massless neutrinos. 7

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