1. Natural expectations for…
Neutrino oscillations, masses and mixings, MNS
Majorana mass and the see-saw mechanisms
Hierarchical neutrinos, sequential dominance, expectations for theta13
Partially degenerate neutrinos, expectations for theta13
Conclusions
Steve King
19/02/2019
Steve King, Oxford

2. Neutrino oscillation summary (2003)
19/02/2019
Steve King, Oxford

3. Neutrino Mass and Mixing Patterns
19/02/2019
Steve King, Oxford

4. Lepton Mixing Unmeasured! This meeting solar LMA MSW atmospheric CHOOZ
19/02/2019
Steve King, Oxford

5. The lepton mixing matrix U a.k.a. MNS, PMNS, MNSP,…
Neutrino mass matrix (Majorana)
Constructing
Parametrising
Three physical phases give CP violation
19/02/2019
Steve King, Oxford

6. Types of neutrino mass (violates L) (conserves L) Majorana or Dirac?
CP conjugate of left-handed neutrino
Majorana mass
(violates L)
Right-handed neutrinos
Dirac mass
from Yukawa couplings
(conserves L)
19/02/2019
Steve King, Oxford

7. The see-saw mechanisms
Type I see-saw mechanism
Type II see-saw mechanism
Heavy triplet
19/02/2019
Steve King, Oxford

8. The See-Saw Matrix Dirac matrix Heavy Majorana matrix
Type II contribution (frequently ignored)
Heavy Majorana matrix
Diagonalise to give effective mass
Light Majorana matrix
19/02/2019
Steve King, Oxford

9. 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
19/02/2019
Steve King, Oxford

10. Technically need a small 23 sub-determinant:
Neutrino Hierarchy
Need to understand:
Technically need a small 23 sub-determinant:
Why is the sub-determinant small?
Why is the solar angle large?
What is the natural expectation for ?
19/02/2019
Steve King, Oxford

11. Single Right-Handed Neutrino Dominance (SFK 98,99)
If one right-handed neutrino of mass Y dominates then sub-determinant is naturally small
Natural explanation of m_2<<m_3 and large atmospheric angle if e~f
19/02/2019
Steve King, Oxford

12. Sequential dominance SFK 00
(Columns can be re-ordered without loss of generality)
Same features as SRHND plus natural explanation of large solar angle if a~b-c
19/02/2019
Steve King, Oxford

13. What about ? For small d  0 expect
However the coefficient of can be arbitrarily small, e.g. neglecting complex phases and assuming maximal atmospheric mixing as b/c-1
19/02/2019
Steve King, Oxford

14. Blazek,SFK 00
19/02/2019
Steve King, Oxford

15. Partially degenerate neutrinos in the type II see-saw mechanism
Antusch, SFK 03
Consider a type II see-saw contribution proportional to unit matrix [enforced by SO(3)] which governs the degenerate neutrino mass scale
Type I contribution controls the neutrino mass splittings
Type I part determines the neutrino mixing angles due to unit matrix and type I phase structure
19/02/2019
Steve King, Oxford

16. For partially degenerate neutrinos the type I splittings must be very hierarchical
19/02/2019
Steve King, Oxford

17. Such strong hierarchies require a natural origin sequential dominance where is now smaller:
19/02/2019
Steve King, Oxford

18. Summary of natural expectations
Generically expect
19/02/2019
Steve King, Oxford

19. The above predictions apply to a large class of natural models with sequential dominance
Effective two right-handed neutrino models
SFK 00, Frampton, Glashow, Yanagida 02, Raidal, Strumia 03, SFK 03, Ibarra and Ross 03
GUT and Family Symmetry Models with neutrino hierarchy
SU(5)xU(1) Altarelli and Feruglio 98
SO(10)xU(1) SFK, Oliveira 01, Blazek, Parry, SFK 03
SO(10)xU(2) Barbieri, Creminelli, Romanino 99, Raby 03
SO(10)xSU(3) SFK, Ross 01,03, Ross, Velasco-Sevilla 03
Sneutrino Inflation Models Ellis, Raidal, Yanagida 04
Partially degenerate models SO(3) Antusch, SFK 03,04
Graham talk
19/02/2019
Steve King, Oxford

20. SO(3) Type II Upgrade Model
Antusch,SFK 03
Real vacuum alignment (a,b,c,e,f,h real)
Red=dominant, Blue=subdominant, Black=decoupled
19/02/2019
Steve King, Oxford