The Seesaw Mechanism and Group Effects

M. Lindner Technical University Munich

Based on collaborations with: S. Antusch M. Drees C. Hagedorn J. Kersten M. Ratz Mixing Parameters

U =

surprise!

how small?

spectrum?

Dirac and Majorana CP phases?

M. Lindner See Saw 25 2 Guessing the Mass Spectrum

Quarks  hierarchical masses  ?  large mixings!

Quarks and charged :

n  mD ~ H ; n = 0,1,2 H > 20 ... 200

n Neutrinos: mν ~ H  H ~ 10

See-saw:

T -1 mν = -mD MR mD

~10 >20 ? >20

• correlated hierarchy in MR ? • non-hierarchical?  RG effects very important

M. Lindner See Saw 25 3 Neutrino Mass Models & Renormalization

High energies: low energies: renormalization group running • mass models • small masses • flavour-symmetries • large mixings • GUT-models, ... atmospheric   bi-maximal

solar 

reactor   small

M. Lindner See Saw 25 4 d=5 Effective Neutrino Mass Operators

M. Lindner See Saw 25 5 βκ in the

M. Lindner See Saw 25 6 βκ in 2Higgs Models x

M. Lindner See Saw 25 7 βκ in the MSSM

M. Lindner See Saw 25 8 Analytic Formulae

M. Lindner See Saw 25 9 Implications for

M. Lindner See Saw 25 10 Implications for Leptogenesis

M. Lindner See Saw 25 11 Implications for Leptogenesis

M. Lindner See Saw 25 12 θ RG Evolution of 13

M. Lindner See Saw 25 13 θ RG Evolution of 23

M. Lindner See Saw 25 14 θ RG Evolution of 12

MSSM tan β=50 m1=0.1eV dark: θ 13€[0°,9°] CP phases=0 medium: phases θ 13€[0°,9°] δ=0,π/2,π,3π/2 light: remaining CP phases

M. Lindner See Saw 25 15 θ θ Evolution of 13 and 23

MSSM tan β=50 m1=0.1eV dark: θ 13€[0°,9°] CP phases=0 light: arbitrary CP phases

M. Lindner See Saw 25 16 Radiative Generation of Dirac Phase δ

δ=0 φ 1=16° φ 2=140°

M. Lindner See Saw 25 17 Evolution of Majorana Phases

MSSM tan β=50

m1=0.15eV φ 1=75° φ 2=70°

M. Lindner See Saw 25 18 Extreme Examples normal hierarchy, m =0.19eV min inverted hierarchy , mmin=0.19eV

normal

M. Lindner See Saw 25 19 RG Running above lowest Threshold

Non-degenrate heavy Majorana thresholds:  above all thresholds: running Y, MR  sucessively integrate out heavy Majorana fields

M. Lindner See Saw 25 20 RG Running & Flavour Textures - neutrino masses & mixings  flavour textures at high energies - only certain texture-zero mass matrices are allowed P.H. Frampton, S.L. Glashow, D. Marfatia W.-I. Guo, Z.-z. Xing

-RG running  previously forbidden textures 

 class F becomes allowed

 class E remains forbidden

- even some 3 zero textures become allowed! ...other textures C. Hagedorn, ML, J. Kersten, hep-ph/0406103 M. Lindner See Saw 25 21 Summary

 RG effects connect measurements and high energy models  are important – especially for non-hierarchical masses  simple analytic expressions (including CP phases)  important effects from integrating out MR thresholds  RG effects have interesting phenomenological consequences: • leptogenesis  smaller mass window • textures vs. data  more solutions θ θ  • evolution of 13 and 23 future precision • interesting evolution effects for CP phases • ... • neutrino-less double β-decay • WMAP • ...

M. Lindner See Saw 25 22