The Seesaw Mechanism and Renormalization 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 Neutrino Mass Spectrum
Quarks hierarchical masses neutrinos? large mixings!
Quarks and charged leptons:
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 Standard Model
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 Leptogenesis
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