1. Modeles Theoriques
Andrea Romanino
CERN

2. Plan of the talk Interpretation of ATM and SUN data
Expectations for and
Precise predictions for and

3. Experimental constraints
(ATM, K2K)
(SUN, KamLAND)
(CHOOZ, Palo Verde)
(Heidelberg-Moscow)
(Mainz, Troitsk)
(Cosmology)
68% C.L.
90% C.L.
99% C.L.
FC + PC + up-going m
1489 days
(Hayato, SK, HEP 2003)
(SNO, nucl-ex/ )
Guidelines for model building:

4. Smallness of neutrino masses
Natural scale of fermion masses: v = 174 GeV
Why
(must have a different origin than

6. Right-handed neutrinos÷ ø ö ç è æ ç è æ ÷ ø ö ç è æ ÷ ø ö ç è æ ÷ ø ö ç è æ ÷ ø ö
SO(10)

7. See-saw X

8. Origin of large mixings
The large angles can in principle originate from either or
(the distinction is physical in terms of the physics giving rise to the masses)

9. (from in the case of degenerate neutrinos)
from in the case of normal hierarchy
from in the case of inverse hierarchy
from
(anarchy)

10. Large angles?
: Dirac and Majorana mass terms trasform differently under symmetries
E.g.: In the symmetric limit:
However, it only works
with degenerate ν’s:
E.g.:
Requires a non abelian symmetry acting on the three families
Often unstable

11. However A, B are not fundamental parameters see-saw: Natural solution:
and
[King]
det ≠ 0
det = 0

13. not incompatible even in SU(5), where (up to GJ factors)
[e.g. Altarelli Feruglio and refs]

14. Inverse Hierarchy: barring tunings or cancellations, must be close to the experimental limit
In fact:
an inverse hierarchy requires, barring tunings, a correction to from
a correction to from contributes to

15. an inverse hierarchy requires, barring tunings, a correction to from
Correction from :

16. a correction to from contributes to

17. In all cases, contributes to
is also model-dependent, but involves the charged fermions
Implementing the same pattern in (e.g. SU(5))
Central value observable with suberbeams (but > O(1) uncertainty)
[Gatto Sartori]

18. Feruglio Strumia Vissani

19. Minimal models
Use the minimal number of “effective” parameters needed to account for the data: 4+1
Produce 2 correlations among
i.e. a prediction for

20. Reducing the number of parameters
Simplest possibility: assume the presence of (2) zeros in the neutrino mass matrix written in the flavor basis,
However, the parameters in are only combinations of the parameters in the basic lagrangian
Our approach:
assume the relative smallness (vanishing) of some parameters in the basic lagrangian
assume there are no correlations among those parameters (non-abelian symmetries could give rise to further possibilities)
We find only 5 possible predictions
[Frampton, Glashow, Marfatia]
[Barbieri, Hambye, AR]
[e.g. Ibarra, Ross]

21. Barbieri, Hambye, AR

22. E is the only case which corresponds to IH and in which the predictions depend on δ (hence the lower limit and the constraint cos δ > 0.8)
In case D, (hence the upper limit)
Cases A, B, E are within the sensitivity of superbeams; case C requires SB + BB; case D has chances with a nu-factory.
Cases A, B, C, D assume no “12” rotation in the charged lepton sector
There are good prospects for 0ν2β decay only in the IH case (E), but as long as δ is not known, there is no special prediction.
Case A has been first studied by Frampton, Glashow, Yanagida.

23. Summary
The present data can be comfortably accommodated in the standard framework for the origin of neutrino masses and provides valuable information on the structure of the basic lagrangian
Based on the interpretation of present data, on our understanding of the charged fermion sector, and on naturalness considerations, there are good prospects of measuring with superbeams
Despite the large number of model building possibilities, there is a relatively small number of possible predictions for compatible with not having correlations among the parameters in the basic lagrangian