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Models of Neutrino Mass

Models of Neutrino Mass. Introduction (neutrino masses,mixings) Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices) Natural hierarchy (sequential right-handed neutrino dominance) Relation between neutrino factory CP violation and leptogenesis?

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Models of Neutrino Mass

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  1. Models of Neutrino Mass • Introduction (neutrino masses,mixings) • Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices) • Natural hierarchy (sequential right-handed neutrino dominance) • Relation between neutrino factory CP violation and leptogenesis? • SUSY and lepton flavour violation: see-saw vs. SUGRA • GUTs and Family Symmetry Steve King, Coseners House

  2. Possible three neutrino mass patterns with LMA and . “Normal” “Inverted” Steve King, Coseners House

  3. Large Mixing Angles solar LMA MSW atmospheric CHOOZ Steve King, Coseners House

  4. The Neutrino Mixing Matrix U Majorana matrix Constructing Parametrising Steve King, Coseners House

  5. Origin of neutrino mass In the Standard Model neutrinos are massless, and a neutrino and anti-neutrino are distinguished by a (total) conserved lepton number L. CP conjugate of left-handed neutrino Majorana or Dirac? Majorana mass (violates L) Right-handed neutrinos Dirac mass from Yukawa couplings (conserves L) Steve King, Coseners House

  6. See-saw mechanism Diracmatrix Heavy Majorana matrix Diagonalise Light Majorana matrix Steve King, Coseners House

  7. Leading order consistent with LMA MSW Barbieri,Hall,Smith,Strumia,Weiner;Altarelli,Feruglio;… Natural cases: SFK hep-ph/0204360 Type A (zero in 11) Type B (non-zero 11) Hierarchy Large neutrinoless double beta decay (Petcov,…) Inverted hierarchy Pseudo-Dirac Degenerate Steve King, Coseners House

  8. Natural Neutrino Hierarchy? Natural eigenvalues are why ? Technically need a small 23 sub-determinant: • But why should the sub-determinant be small ? • How can we get this from the see-saw mechanism? Steve King, Coseners House

  9. See-saw with diagonal heavy Majorana matrix Columns can be re-ordered without loss of generality If one right-handed neutrino of mass Y dominates then sub-determinant is naturally small: single right-handed neutrino dominance (SFK PLB 98, NPB 99) Sequential dominance(SFK NPB2000) Steve King, Coseners House

  10. Analytic estimates for neutrino masses and mixing angles (valid for sequential dominance) SFK hep-ph/0204360 Sequential dominance (set d=0 below) Mass hierarchy and large mixing angles naturally! Phases fixed by real 12 angle condition where and is fixed by the real 13 angle condition Steve King, Coseners House

  11. Light or Heavy Sequential Dominance? Heavy Sequential Dominance (HSD) “Lop-sided” (large 23 element) Light Sequential Dominance (LSD) “Quark-like” (no large off-diagonal entries) Note that X’ is irrelevent for neutrino masses, mixings (and leptogenesis-see later), and the model reduces to an effective 2 right-handed neutrino modelSFK 2000;Frampton,Glashow,Yanagida 2002; Raidal,Strumia 2002. Steve King, Coseners House

  12. Fukugita,Yanagida; Buchmuller,Plumacher; Di Bari, Davidson… Leptogenesis • Right-handed neutrinos are produced in early universe and decay out of equilibrium giving net lepton number L • CP violation from complex Yukawa couplings • L is processed into B via B-L conserving sphalerons Steve King, Coseners House

  13. Relation between CP violation at a neutrino factory and in leptogenesis? SFK hep-ph/0211228 LSD Assume 11 texture zero (see later) Di Bari,Buchmuller,Plumacher Heavy RH neutrino of mass X’ is irrelevant for both leptogenesis and neutrino masses, mixings Neutrino factory phase and leptogenesis phase are linked in terms of two invariant see-saw phases Remarkably the leptogenesis phase is equal to the phase which enters neutrinoless double beta decay ! In HSD (Hirsch,SFK) and gravitino bound may be respected (but no leptogenesis-MNS link since X’ couplings are relevant for leptogenesis but not neutrino masses, mixings)

  14. Borzumati, Masiero; Hisano, Moroi, Tobe, Yamaguchi; SFK, Oliveira; Casas, Ibarra; Lavignac, Masina, Savoy;Blazek,SFK SUSY and Lepton Flavour Violation If SUSY is present then neutrino masses inevitably lead to lepton flavour violation due to radiatively generated off-diagonal slepton masses HSD/lopsided will lead to large due to large 23 Yukawa. Blazek, SFK Steve King, Coseners House

  15. Steve King, Coseners House

  16. Lepton Flavour Violation in Constrained Minimal Supersymmetric Standard Model Blazek,SFK hep-ph/0211368 HSD parametrisation with dominant heaviest RH neutrino in 33 position LSD parametrisation with dominant lightest RH neutrino in 11 position Large 23 element (lop-sided) Steve King, Coseners House

  17. Blazek,SFK hep-ph/0211368 13 angle depends on a ratio of Yukawa couplings HSD Steve King, Coseners House

  18. HSD predictions for constrained MSSM Blazek,SFK hep-ph/0211368 Steve King, Coseners House

  19. LSD predictions for constrained MSSM Blazek,SFK hep-ph/0211368 Steve King, Coseners House

  20. Iain Peddie, SFK (preliminary) Supergravity LFV can mimic see-saw LFV Steve King, Coseners House

  21. The goal is to describe the quark and lepton mass hierarchies t Charge +2/3 quarks Charge –1/3 quarks u d c Charged leptons e s b A neutrino hierarchy Steve King, Coseners House

  22. GUTs Steve King, Coseners House

  23. Family Symmetry Democracy, Fritzsch,… Hierarchy Froggatt,Nielsen,Ross… Nothing Harrison, Scott Steve King, Coseners House

  24. G.Ross, SFK G.Ross, Velasco-Sevilla Flavour Unification Leads to approximately symmetric mass matrices • Allows a universal form for mass matrices • Example of Light Sequential Dominance (LSD) • Texture zero in 11 position  leptogenesis-neutrino factory link Steve King, Coseners House

  25. Conclusion • Small neutrino masses can be elegantly explained by see-saw mechanism • Sequential dominance then provides a natural explanation of a neutrino mass hierarchy and large mixing angles • The dominant right-handed neutrino may be either the heaviest (HSD) or the lightest one (LSD) • LSD with 11 zero links leptogenesis phase and the CP phase which is measurable at a neutrino factory, but is inconsistent with SUSY models • HSD has no such link, but may be consistent with SUSY models • SUSY leads to lepton flavour violating processes, which can discriminate HSD from LSD • SUGRA LFV can mimic see-saw LFV • GUTs and family symmetry can solve flavour problem G.Ross talk Steve King, Coseners House

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