Neutrinos and the Universe

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Neutrino Mass Models

• Neutrino oscillations and cosmological limit
• Theory of neutrino mass Majorana, Dirac,
  see-saw, Majorana matrices
• Hierarchical models right-handed neutrino
  dominance
• Neutrinoless double beta decay
• Partially degenerate models (Antusch, SFK)

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Neutrino oscillation summary ( Murayama)
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Cosmological limits on neutrino mass
Animations due to Tegmark
CMB power spectrum
2dF Galaxy Redshift survey astro-ph/0204152 and
WMAP implies
Galaxy power spectrum
Neutrino oscillations then imply
per neutrino species
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We focus on three family neutrino oscillations
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Possible three neutrino mass patterns with LMA
.


Normal
Inverted
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Neutrino masses as a function of m_1 (normal
ordering)
Stefan Antusch
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Lepton Mixing (no phases)
solar LMA MSW
atmospheric
CHOOZ
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The leptonic mixing matrix U
Neutrino mass matrix (Majorana)
Constructing
Parametrising
Three physical phases give CP violation
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Types 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)
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Types of see-saw mechanism
Type II see-saw mechanism
Type I see-saw mechanism
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Complete See-Saw Mechanism
Dirac matrix
Type II contribution
Heavy Majorana matrix
Diagonalise to give effective mass
Light Majorana matrix
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Leading order consistent with LMA MSW
Type A (zero in 11)
Type B (non-zero 11)
Hierarchy
Large neutrinoless double beta decay
Inverted hierarchy
Pseudo-Dirac
Degenerate
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Focus on Neutrino Hierarchy
Need to understand
Technically need a small 23 sub-determinant

• Why is the sub-determinant small?
• Why is the solar angle large?

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Right-handed neutrino dominance (SFK)

• If one right-handed neutrino dominates in the
  type I see-saw mechanism and couples equally to
  the second and third family left-handed neutrinos
  then (SRHND
  SFK 98,99)
• If a second right-handed neutrino gives the
  leading sub-dominant contributions and couples
  with approximately equal strength to all three
  families of left-handed neutrinos then have
  large solar angles such as
  (sequential dominance SFK 00)
• 
  
  
• Corollary if the dominant right-handed neutrino
  is the lightest then there is a link between the
  neutrino oscillation phase and the phases of
  leptogenesis and neutrinoless double beta decay
  ( SFK 02)

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A two by two example (2nd and 3rd family only)
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)
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Three family generalisation
(Columns can be re-ordered without loss of
generality)
Sequential dominance (SFK NPB2000, JHEP03)
Neutrino hierarchy, bilarge mixing
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Klapdor-Kleingrothaus et al (2001) have claimed a
neutrinoless double beta decay signal based on
re-analysis of Heidelberg-Moscow data
Strongly criticised by Aalseth et al, Feruglio et
al, but if confirmed it would rule out a neutrino
mass hierarchy
Hierarchy and Inverted A
Pascoli, Petcov
Inverted B
Degenerate B
c.f. KATRIN tritium decay sensitivity
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From neutrino mass hierarchy to partial
degeneracy (Stefan Antusch, SFK in progress)
So far we have shown that a neutrino mass
hierarchy can arise from the type I see-saw
mechanism with sequential dominance Now we add a
type II see-saw contribution proportional to unit
matrix
Leads to bilarge mixing angles similar to the
sequential dominance, but with enhanced neutrino
masses and neutrinoless double beta decay
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Neutrinoless double beta decay effective mass as
a function of the type II neutrino mass
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Conclusion

• Neutrino oscillation data require neutrino masses
  and mixings (three family only)
• Small neutrino masses can be elegantly explained
  by the see-saw mechanism
• Type I see-saw mechanism with sequential
  dominance then provides a natural explanation of
  a neutrino mass hierarchy and large mixing angles
• Hierarchical models predict small (unobservable)
  neutrinoless double beta decay
• But hierarchical models can be upgraded to
  partially degenerate models via a type II see-saw
  part proportional to unit matrix
• Such upgraded models can predict large
  (observable) neutrinoless double beta decay