Models of Neutrino Mass G.G.Ross, IPPP December 2005 Origin of mass and mass hierarchy What do we learn from the mixing angles?

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Models of Neutrino Mass G.G.Ross, IPPP December 2005 Origin of mass and mass hierarchy What do we learn from the mixing angles?

Origin of Neutrino masses Dirac or Majorana?

Origin of Neutrino masses Dirac or Majorana? Weinberg 1979

Minkowski mechanism Origin of Neutrino masses Dirac or Majorana?

Weinberg 1979 Origin of Neutrino masses Dirac or Majorana?

New space dimensions Closed string 11D propagation Graviton, Modulini Open string SM states } Flux spreading Arkani Hamed, Dimopoulos, March Russell Dienes,Farragi In 4D small Dirac masses can arise through higher dimension operators Abel, Dedes, Tamvakis Dirac or Majorana?

Neutrino mass and dark energy Quintessence field Symmetry needed to keep it light CP violating field of neutrino mass matrix? Barbieri, Hall, Oliver, Strumia Mass varying neutrinos energy in A At finite density : Fardon, Nelson, Weiner

… dimension of operator … order of radiative corrections Hierarchy Structure Can get normal, inverted or degenerate structures (NB Radiative corrections can split precise degeneracies unless protected by symmetry)

Unravelling the origin of mass….. …difficult (impossible) unless we are lucky! eV Mixing Bi-Tri Maximal Mixing … Harrison, Perkins, Scott ansatz Non Abelian Structure? Many possibilities, many parameters… Small in quark sector, large in lepton sector?

Tri-Bi-Maximal mixing

Discrete non Abelian family symmetry Bi-maximal But what about the charged lepton sector Need complete theory…

“ See-saw ” with sequential domination SRHD King Two ingredients : (Discrete) Non-Abelian family symmetry small Vacuum alignment King, GGR, Varzielas

Vacuum alignment Altarelli,Feruglio King,GGR,Varzielas

Summary Origin of mass and mass hierarchy - Many possibilities for both Majorana and Dirac masses : Heavy see-saw, light see-saw, bare Dirac, radiative generation, radiative running, running masses…dark energy - All patterns of mass possible : normal, inverted, degenerate What do we learn from the mixing angles? -Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)? Unified theory of quark, charged lepton and neutrino masses with related textures

Spontaneous symmetry breaking c.f. Georgi-Jarskog only terms allowed by G I de Medeiros, GGR King, Vives, Velasco Sevilla… Common texture zero

Summary Origin of mass and mass hierarchy - Many possibilities for both Majorana and Dirac masses : Heavy see-saw, light see-saw, bare Dirac, radiative generation, radiative running, running masses…dark energy - All patterns of mass possible : normal, inverted, degenerate What do we learn from the mixing angles? -Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)? Unified theory of quark, charged lepton and neutrino masses with related textures - A discrete non-Abelian subgroup can give vacuum alignment needed for bi-tri-maximal mixing