# Presentation: 325735

- Open Theoretical Questions

- Neutrino Physics:

- What we have learned?

- Bottom-up

- Open theoretical questions

- How we might go...

- A. Yu. Smirnov

- International Centre for Theoretical Physics, Trieste, Italy
-   Institute for Nuclear Research,  RAS, Moscow, Russia

- 1. What we have learned?

- Neutrino masses and lepton mixing:

- Summary

- A Yu Smirnov

- CC
- NC

- AND %

- Lines of constant  CC/NC ratio and
- Day-Night  asymmetry at SNO

- P.de Holanda, A.S.

- Solar Neutrinos

- Best fit point:

- m122 = 7  10-5  eV2

- tan 212  =  0.4

- 3

- 1

- sin 213  ~  0

*LM MSW*

*Any problem?*

- ~ 2  higher Ar-production
- rate than Homestake result

- Absence of the upturn
- of the spectrum

- Survival

- probability

- P. de Holanda, A.S.

- R =  m012 / m212

- Motivation for the
- low energy solar neutrino
- experiments
-   BOREXINO, KamLAND
-   MOON, LENS ...

- Be

- pep

- B (SK, SNO)

- pp

- Dip in the survival probability:
-    - reduces the Ar-production
-       rate
-    - suppresses the upturn
-      of spectrum

- - mixing angle of sterile
-       neutrino

- Light sterile neutrino

- Atmospheric Neutrinos

- sin2 223 = 1.0

- m322  = 2.0  10-3 eV2

-  sin2 223 > 0.9

- SuperKamiokande:

-  m322  = (1.3 - 3.0) 10-3 eV2

- (90 % C.L.)

- sin2 213  <  0.067  (3)

- Confirmed by
- MACRO,
- SOUDAN
- K2K

- Combined analysis of CHOOZ,
- atmospheric (SK) and solar data:

- G.L. Fogli et al, hep-ph/p0308055

- Best fit point:

- In the sub-GeV sample

- Fe
- Fe0

- - 1  =  P2 ( r c232  - 1)

- r =  F / Fe0  ~  2

- ``screening factor’’

- Zenith angle and energy dependences
- of the e-like events

- The excess is zero for
- maximal 23- mixing

- Excess of the e-like events in sub-GeV

- P2 = P(m21212)   is the  2 transition
- probability

- LMA oscillations of atmospheric

- 0.Peres,  A.S.

- Searches of the excess can be used
- to restrict deviation of the 2-3 mixing
- from maximal

- neutrinos

## Conversion of neutrinos from SN1987A

- F(e) =  F0(e)  + p F0

- F0 = F0()  - F0(e)

- p  is the permutation factor

- p

- The earth matter effect can partially explain
- the difference of  Kamiokande and IMB:
- spectra of events

- p  depends on distance traveled
- by neutrinos inside the earth to a given
- detector:

-              4363 km    Kamioka
- d =        8535 km    IMB
-             10449 km   Baksan

- C.Lunardini,  A.S.

- After KamLAND: one must take into
- account conversion effects of supernova
- neutrinos

- Conversion in the star

- Earth matter effect

- Normal hierarchy is preferable

- H. Minakata, H. Nunokawa,
- J Bahcall, D Spergel, A.S.

- Absolute scale of mass

- F. Feruglio,  A. Strumia, F. Vissani

- Neutrinoless double beta decay

- Kinematic searches, cosmology

- Sensitivity limit

- Both  cosmology and
- double beta decay
- have similar sensitivities

- mee =  k Uek mk ei

- A Yu Smirnov

- 

- 

- e

- 2

- 1

- mass

- 1

- 2

- 3

- 3

- mass

- m2atm

- m2atm

- m2sun

- m2sun

- Inverted mass hierarchy
- (ordering)

- Normal mass hierarchy
- (ordering)

- |Ue3|2

- |Ue3|2

- Type of the mass hierarchy: Normal, Inverted

- Type of mass spectrum: with Hierarchy, Ordering, Degeneracy      absolute mass scale

- Ue3 = ?

- ?

- Mass spectrum and mixing

- A Yu Smirnov

- Ue1        Ue2      U e3
- UUU
- UUU

- UPMNS =

- |Ue3U*|

-   |Ue3 | = 0.16

- Leptonic Unitarity Triangle

- 0.79 - 0.86       0.50 - 0. 61      0.0   - 0.16
- 0.24 - 0.52       0.44 - 0.69       0.63 - 0.79
- 0.26 - 0.52       0.47 - 0.71       0.60 - 0.77

- Global fit of the oscillation data 1

- =

- M.C. Gonzalez-Garcia ,
-  C. Pena-Garay

- |Ue2 U*|

- |Ue1 U*|

- nearly best
- fit values of
- other angles

- Can we reconstruct the triangle?
- Can we use it to determine the CP-violating phase?

- Y. Farsan,  A.S.

- Problem: coherence (we deal with coherent states and
-                not mass eigenstates of neutrinos)

- A Yu Smirnov

*LSND*

*(3 + 1)-scheme*

*Non-standard*

*Interactions*

*Sterile neutrino*

*CPT-violation*

- Ultimate oscillation
-  anomaly?

*(3 + 2)  ?*

- K.Babu, S Pakvasa

- Disfavored by a
- new analysis of
- KARMEN
- collaboration

- Disfavored by
- atmospheric
- neutrino data,
- no compatibility
- of LSND and
- all-but LSND data
- below  3-level

- O. Peres, A.S.
- M. Sorel, J. Conrad, M. Shaevitz

- M.C. Gonzalez-Garcia,
- M. Maltoni, T. Schwetz

- G. Barenboim,
- L. Borissov, J. Lykken

- After KamLAND:

- 

- 

- e

- 2

- 1

- 4

- mass

- m2atm

- m2sun

- 3

- m2LSND

- s

*(3 + 1)*

- Generic possibility  of interest even
- independently of the LSND result

- Generation of large mixing of
- active neutrinos due to small
- mixing with  sterile state

- Produces uncertainty in interpretation
- of results

- The  problem is

- P   ~  |Ue4 |2  |U|2

- Restricted by short baseline
- experiments  CHOOZ, CDHS, NOMAD

- 2 - 3  below the observed probability

- 

- 

- e

- 2

- 1

- 4

- mass

- m2atm

- m2sun

- 3

- m2LSND’

- s

- 5

- s’

*3 + 2  scheme*

- m2LSND

- FINeSE

- M. Sorel, J. Conrad, M. Shaevitz

- x

- x

- Main features

- Smallness of masses:

- m  << ml ,  mq

- m  < (1 - 2) eV

- Hierarchy of mass
- squared differences:

- m122  m232 | =  0.01 - 0.15

- m  >  m232  > 0.04  eV

- (at least for one mass)

- |m2 m3| >  |m122  m232 | = 0.18

- No strong hierarchy
- of masses:

- + 0.22
- -  0.08

- |sin |

- Bi-large or large-maximal
- mixing between neighboring
- families (1- 2)  (2- 3):

- Small  mixing between
- remote families (1- 3):

- 0             0.2           0.4           0.6           0.8

- 1-3

- 1-2

- 2-3

- 1

- ...and unknown

- Several key elements
- are unknown yet
- which leads to variety
- of possible interpretations

- Absolute mass
- scale,  m1
- type of spectrum

- Type of mass  hierarchy
- ordering of states
- (sign of                            )

- sin 

- m132   =  m12  - m32

- test of  mechanisms
- of  the lepton mixing
- enhancement

- - normal
- - inverted

- - hierarchical
- - partially degenerate
- - quasi  degenerate

- CP-violating
- phases, especially
- Majorana phases

- Deviation of
- 2-3 and 1-2 mixings
- from maximal

- Phenomenological
- and experimental
- problems

- Existence of
- new neutrino
- states

- 2. Open theoretical questions

*What does all this mean?*

*(results on neutrino *

*masses and mixing)*

*What is the origin of neutrino mass?*

- - we do not know yet the origin of quark and charged lepton
-    masses where  information is more complete
- - for neutrinos the problem can be even more  complex
- - the hope is that neutrinos can shed some light on  whole
-    problem of fermion masses

*Why neutrino masses are small?*

- - small in comparison with charged leptons and quarks masses
- - what are relations with other mass scales in nature?
-   e.g., dark energy scale?

- Old...

- and New:

*Why the lepton mixing is large?*

*Why it is so different from quark mixing?*

- - may be correct question is why the quark mixing is so small?
-   In quark sector the smallness of mixing can be related to strong
-   mass hierarchy

*How the observed pattern of the lepton *

*mixing is generated?*

- - two large mixings and one small (zero)?
- - one maximal mixing?
- - what are relations between mixing angles?

*Do neutrinos show certain flavor *

*or horizontal  symmetry?*

- - if so, is this symmetry consistent with quark masses and mixing?
- - ad hoc introduced symmetries for neutrinos only do not look appealing

*Are results on neutrino masses and*

*mixing consistent with *

*- quark-lepton symmetry?*

*- Grand Unification?*

*If new light (sterile) neutrino(s) exist*

*- what is their nature?*

*- why they are light?*

- Experimental and
- phenomenological
- problem

*What are implications of the neutrino *

*results for*

*- GUT*

*- SUSY*

*- Extra Dimensions?*

*vice versa*

*What these theories can tell us about *

*neutrinos?*

*- Strings*

- 3. Bottom-Up

- Bottom -Up and Top-Down

- Experimental
- results on

- mij2

- ij

- mee

- Theory of
- neutrino mass
- and mixing

- Reconstruct
- the neutrino
- mass matrix
- in the flavor
- basis

- m = U* mdiag U+

- Identify symmetry scale
- and symmetry basis
- Renormalization group
- effects

- Identify symmetry
- and underlying
- dynamics

- mdiag = diag(m1e-2i, m2, m3e-2i)

- U = U(ij )

- m2 =  m12 +m212

- m3 =  m12 +m312

- Mass matrix unifies
- information contained
- in masses and mixing

- Normal hierarchy

- m1 = 0.006 eV

- m3 /m2 = 5

- 0    0    
- 0    1    1
-  1    1

- 0        0
-     1    1
-  1    1

- q4   q3  q2
- q3   q2   q
- q2   q    1

-    ~ 0.2

- 2    
-     1    1
-  1    1

-  = 0

- sin2223 = 1

- q ~ 0.7

- sin13 = 0.1

- M. Frigerio, A.S.

- a

- b

- c

- a).

- b).

- c).

- Normal ordering

- m1 = 0.027 eV

- m3 /m2 = 2

- q4   q3  q2
- q3   q2   q
- q2   q    1

-  = 0

- sin2223 = 1

- q ~ 0.7

- sin13 = 0.1

- Flavor alignment

- Quasi-degeneracy

- m1 = 0.35 eV

- m3 /m2 = 1.01

-  = 0

- sin2223 = 1

- sin13 = 0.1

- 1    0    0
- 0    1    0
- 0    0    1

- 1    0    0
- 0    0    1
- 0    1    0

- 1    1    1
- 1    1    1
- 1    1    1

- a).

- a

- b

- c

- b).

- c).

- M. Frigerio, A.S

- Inverted ordering

- m3 = 0.029 eV

- m3 /m2 = 0.5

-  = 0

- sin2223 = 1

- sin13 = 0.1

- Inverted hierarchy

- m3 = 0.005 eV

- m3 /m2 = 0.1

-  = 0

- sin2223 = 1

- sin13 = 0.1

- 0.7     1      1
-  1      0.1   0.1
-  1      0.1   0.1

- 1       < 0.1   < 0.1
- < 0.1     0.5     0.5
- < 0.1     0.5     0.5

- a).

- b).

- a

- b

- Observations

- 1). Large variety of different structures is still possible,
-      depending strongly on unknown m1, type of mass hierarchy,
-      Majorana phases   and , weaker dependence is on sin13 and .

- 2). Generically  the hierarchy of elements is not strong:
-      within 1 order  of magnitude.
-      Although, matrices with one or two zeros are possible.

- 3).  Structures (in the flavor basis):
-       - with dominant  diagonal elements (~ I ) ,  or dominant  -block,
-       - with dominant e-row elements, (ee-, - , -) elements, etc.,
-       - democratic structures,
-       - with flavor alignment,
-       - non-hierarchical structures with all elements of the same order
-       - with flavor disordering,
-       - with zeros and various equalities of matrix elements.

- 4). Typically hierarchical structures appear for  and  near 0, /2, 

- 5). The structures can be parameterized in terms of power of small
- parameter  = 0.2 - 0.3 consistent with Cabibbo mixing

*Anarchy?*

- L.Hall,
- H. Murayama,
-  A.de Gouvea,
- F.Vissani,
- G. Altarelli,
-  F. Feruglio,
- J.R. Espinosa

- Neutrino mass and horizontal symmetry

- Do neutrino results on masses and mixing or
- the neutrino mass matrix show some symmetry?

- Is the neutrino mass matrix consistent with symmetries suggested for quarks?

- Le - L - L

- U(1)

- SU(2)

- SU(3)

- Discrete
- symmetries
- A4    S3   Z4   D4

- can describe mass matrices both quarks
- and leptons.
- U(1) charges: discrete free parameters,
- also  coefficients  ~O(1) in front of

- Complicated higgs sector to break symmetry
- too restrictive...

-  in  the Froggatt-Nielsen context

- Treat quarks and
- leptons differently

- 4. How we might go ...

- Neutrality and mass

- Relate  features of the neutrino masses and mixing
- with already known difference  of neutrino
- and  quarks and charged leptons.

- possibility to be
- a Majorana particle
- (Majorana mass term)

- Right handed components,
-  if exists,  are singlet of
- SU(3) x SU(2) xU(1)

- Can propagate
- in extra dimensions

- Unprotected by
- this symmetry

-  Q = 0
-  Qc = 0

- Can have large
- Majorana  masses
- M R >> VEW

- Properties of
- mass spectrum
- and mixing

- Can mix with
- singlets of the SM
- symmetry group

- Minimalistic approach:

- Neutrality

- Minimal
- number
- of new
- concepts

*Is this enough?*

- q - l,  SU(2)LxU(2)R xU(1)B-L

- Seesaw

- T. Yanagida
- M. Gell-Mann, P. Ramond,  R. Slansky
- S. L. Glashow
- R.N. Mohapatra, G. Senjanovic

- 0   mD
- mD   MR

- m  = - mDT  MR-1 mD

- (type I)

- If  the SU(2) triplet, L , exists with interaction   f lT l  L  + h.c.,  then f lT l  L   +  h.c.

- m  =   mL  - mDT  MR-1 mD

- In SO(10):  L and S are in the samef = fS  = f

- If L is  heavy,   induced VEV due to the interaction with doublet  <L <H>2 / M

- MR =  fS <S> = fS v R

- m =  f         - mDT  f -1 mD       (f  - YT  f -1 Y)

- vEW2
-  vR

- vEW2
-  vR

- (type II)

-    Flavor structure
- of two contributions
-       correlates

- mD = Y v EW

- Variations on the theme

- 0   mD
- mD    0     M
-  0     M      

- m  = - mDT  MD-1T   MD-1 mD

- The number of the RH neutrinos can differ from 3

*Less than 3 ...*

*3x2-seesaw*

- limit when one of  R  is very heavy   M ~ MPl

- motivated  by horizontal SU(2)H

- (two RH neutrinos)

- one massless neutrino
- less number of  parameters

*More than 3 ...*

*Double seesaw*

- Beyond SM: many heavy singlets
- ...string theory

- R.N. Mohapatra
- J. Valle

- Three additional singlets S
- which  couple with RH neutrinos

- 
- c
- S

- allows to lower the scales

-     << MD

-     >> M

- explains intermediate scale

-     ~ MGU, M ~ MPl

- Grand Unification and neutrino Mixing

- GUT provide large scale comparable  to the scale of  RH neutrino masses

- One can argue that  GUT (+ seesaw) can naturally lead to large lepton mixing,
- or inversely, that large lepton mixing  testifies for GUT

- 1. Suppose that all quarks and
-     leptons of a given family are
-     in a single multiplet  Fi
-    (as 16 of SO(10))

- 2.  Suppose that all yukawa couplings
-      are of the same  order thus
-      producing  matrices with large mixing

- 3. If  Dirac masses are generated by
-    a unique higgs multiplet, (10 of SO(10)),
-    the mass matrices of the up- and
-    down- components  of the weak doublets
-    have identical structure,  and so
-    will be diagonalized by the same rotation.

- As a result,
-     -  no mixing appears for quarks
-     -  masses of up and down components
-         will be proportional each other

- 4.  In contrast to other fermions RH
-      neutrinos have additional yukawa
-      interactions (with 126) which
-     generate the  Majorana  mass terms

- 5. Since those (Majorana type) Yukawa
-    couplings are also of  generic form they
-     produce M  with large mixing which
-    leads  then to large lepton  mixing

- Need to be
- slightly
- corrected

- Problem:

- m  =   mL  - mDT  MR-1 mD

- Strong hierarchy of the quark and charged lepton masses

- In this  scenario

- mD  = diag(mu, mc, mt )

- Then for generic MR the seesaw of the type I  produces strongly
- hierarchical  matrix with small mixing

- Possible solutions:

- Type II seesaw:
- no dependence on mD

- Special structure  of
- MR which compensate
- strong hierarchy in  mD

- Substantial difference
- of  Dirac matrices of
- quarks and leptons
-  mD(q)  ==   mD(l)

- Seesaw enhancement of mixing

- Can the same mechanism (seesaw) which explains
- a smallness of neutrino mass also explain large lepton mixing?
- Large lepton mixing is an artifact of seesaw?

- A.S.
- M. Tanimoto
- M.Bando,
- T.Kugo
- P. Ramond

*Two  possibilities:*

- Large
- lepton
- mixing

- Special
- structure
- of   MR

- Quark-lepton symmetry
- mD   ~  mup ,   ml   ~  md  ,
- small mixing in Dirac sector

- Strong  (``quadratic’’) hierarchy of
- the right handed neutrino masses:

-    MiR ~  (mi up )2

- Strong interfamily  connection
- (pseudo Dirac structures)

- a   0  0
- 0   0  b
- 0   b   0

- MR =

- Masses of RH neutrinos

- Leptogenesis
- gives strong
- restrictions

- E. Kh. Akhmedov,
- M.Frigerio, A.S.

- In the hierarchical
- case the  lower
- bound on the
- lightest  mass

- M1 > 4 108 GeV

- W. Buchmuller
- P. di Bari M. Plumacher,
- S. Davidson, A. Ibarra

- Only in particular
-  cases with strong
- degeneracy: M1  =  M2
- required asymmetry
- can be produced

- Large mixing and type II Seesaw

- K. Babu, R. Mohapatra, Matsuda,
- B.Bajc, G. Senjanovic, F.Vissani
- R. Mohapatra,  Goh,  Ng

- Structure of the mass matrix generated
- by  the type II (triplet) seesaw  can be
- related to quark and lepton masses

- gives  contribution to quark
- and lepton masses
- (Georgi-Jarlskog relation)

- mL  ~  Y126

- mb  -  m~ Y126

- (subtraction of
- 10 -contribution)

- 126 of  SO(10)

- generates
- neutrino
- masses mL

- Large 2-3 mixing needs  b -   unification

-  b -   unification:    element (Y126 )33  ~ (Y126 )23  << 1
-                                --> large 2-3 lepton mixing

- Successful leptogenesis is possible with participation
- of the scalar triplet

- T. Hambye, G. Senjanovic

- Single RH neutrino dominance

- Large mixing from the Dirac neutrino mass matrix

- S. F. King,
- R. Barbieri, Creminelli,
- A. Romanino,
- G. Altarelli, F.Feruglio,
- I. Masina

- In another version it may coincide with seesaw enhancement:
- Single RH neutrino dominance is realized when other RH neutrinos
- are heavy = strong hierarchy

- *    *    
- *    *    1
- *    *    1

- mD = m

- MR-1 = M

- 0   0   0
- 0   0   0
- 0   0   1

- Seesaw gives:

- 2   
-  1   1
-  1   1

- m  =

- (*  <<  

- ``Lopsided'' Models

- K. Babu, S.M. Barr,
- C.H. Albright,
- J.Sato, T. Yanagida,
- N. Igres, S. Lavignac,
- P.Ramond

- Large mixing follows from  charged lepton mass matrix
- Non-symmetric mass matrices
- No contradiction with GUT:
- in SU(5):   LH  components of leptons are  unified
- with RH components  of  quarks:   5 =  (dc, dc, dc,  l,  )

- mD  = m_u_

- ml  = m d

-     0    0
- 0     0    
- 0    -    1

- 0           d’
-      0   
-  ’ -      1

-   <<  ’  << 

-   ~  1

- Also possible in SO(10) if it is broken via SU(5)

-  
- 

- Single
- lopsided

- Double lopsided (for both large mixings)

- K. Babu,  S. Barr

- Hybrid possibilities: large 2-3 mixing from charged lepton mass matrix
-                                 large 1-2 mixing  from neutrino mass matrices

- Radiative enhancement of mixing

- Mixing is small at the Unification scale (similar to quark mixing)
- running to low energies       enhancement of mixing.

- Generation of small elements ratiatively: m122,  sin 13

- Requirement:

- Large
- mixing

- Quasi-degenerate
- spectrum

- K. Babu,
- C.N. Leung
- J. Pantaleone
- P. Chankowski
- M. Pluciniek,
- J. Ellis, S. Lola,
- J. Casas,
- M.Lindner. .....

- d sin23
-  dt

- ~  ( sin12 U1 D31   - cos12 U2 D32 )

- t  = 1/82 log q/M

- Dij  =  (mi  + mj)/(mi   -  mj )

- e.g.

- S. Petcov, A.S. A. Joshipura
- M. Lindner

- Enhancement
- when neutrinos
- become  more
- degenerate

- Requires fine tuning of the initial mass splitting and
- radiative corrections

- In MSSM both 1-2 and 2-3 mixings can be enhanced.

- In SM ?

- If masses from Kahler potential:  large mixing infrared fixed point

- J.A.Casas,
- J.R. Espinosa
- I. Navarro

- How to test Seesaw?

*Leptogenesis*

- For hierarchical RH neutrino
- spectrum gives bound  on

- - Mass of the lightest RH neutrino  M1R

- - Effective parameter  m1
-   which determines  the washout effect

- ~

- How to test existence of the heavy  Majorana RH neutrinos?

- M1R > 4 108 GeV

- m  <  0.1 eV

- for  type II seesaw: still possible

- W. Buchmuller
- P. di Bari
- M. Plumacher

- M. Fukugita, T. Yanagida

- excluding degenerate
- spectrum (?)

- G.Senjanovic
- T. Hambye

*Renormalization effects of RH neutrinos*

- Renormalization effects between the scale MiR   and GUT

- e.g.,  on  mb  - m  mass relation

- F. Vissani, A.S.,
- H. Murayama, R. Rattazzi
- A. Brignole

- Probe of   (Y Y+ )ij

- SUSY Seesaw

- 1
- 2

- Wlep =  ec T Ye l H1  +  c T Y l H2  +     cT  MR c

-  (mS2)ab  =   ma2 ab -        (3 m02 +A02 )Y+ )ai Y)ib log(M X /M iR )

- Superpotential

- structure of SUSY
- (slepton) sector

- Structures relevant
- for seesaw (Y, MR)

- Imprinted
- into

- 1). Universal soft masses
-      (m02 , A0 ) at  high  scale MX

- Contribution to the low energy left handed slepton mass matrices:

- 2). No new particles apart
-      from those in MSSM

- Assumptions:

- 
- 2

- A.Masiero,
- F.Borzumatti
- L.J. Hall,
- V.A.Kostelecky,
- S. Raby
- F. Gabbiani,
- E Gabrielli,
- L. Silvestrini

- diagonal part

- SUSY

- Seesaw

- Rare decays
-  -> e  
-  -> e  
-  -> 

- Sneutrino-
- antisneutrino
- oscillations

- Slepton
- decays

- Sneutrino flavor
- oscillations

- Y. Grossman
- H.E. Haber

- A. Masiero
- F.Borzumati

- N. Arkani-Hamed
- H. Cheng, J. L. Feng,
- L.J. Hall

- A. Hinchliffe
- F.E. Paige

- Testing SUSY seesaw

- (Y+ Y)

- Reconstruction of

- S. Davidson
- A. Ibarra

- Electric
- dipole
- moments

- J.Ellis,
- S.Ferrara,
- DNanopoulos
- .............

- Rare decays

-      (mS2)e  =        (3 m02 +A02 )Y+ )i Y)ie log(M X /M iR )

- 
- 2

- A.Masiero,
- F.Borzumatti
- F. Gabbiani,
- E Gabrielli,
- L. Silvestrini

- gaugino

- 

- e

- 

- x

-  mS2e

- l

- le

- If large lepton mixing originates from the Dirac matrix
- (lopsided models, versions of  SRHN dominance)
- Y)i Y)ie  are large

- B(   e ) =

- B(   e ) ~ 10-11 - 10-12

- At the level of present bound

- 3   |(mS2)e|2   tan2
-   GF2 ms8

- ms    = ms (m0 , m1/2)
- effective SUSY
- mass parameter

- Beyond
-  leading log:
-  S. Petcov,
- S.Profumo,
- Y. Takanishi,
- C.E. Yaguna

- Other mechanisms

*Radiative mechanims*

-  Zee (one loop, generalized)

- Zee-Babu (two loops)

*Bi-linear R-parity violation*

- Trilinear R- violating couplings

*Extra Dimensions*

- Large extra D (ADD)
- Warped extra D (RS)
- Infinite extra D (Dvali-Poratti)
- ...

*Dynamical symmetry breaking*

*Technicolor*

*Little Higgs*

*Deconstruction*

- Can accommodate
- neutrino masses
- produce some interesting
- features

- Conclusions

- Enormous progress in determination
- of the neutrino masses  and mixings,
- studies of properties of mass matrix.
- Still large freedom in possible
- structures  exists  which leads
- to very different  interpretations.

- Main open question:
- what is behind obtained results?
- Preference? Probably  seesaw,
- and probably associated
- with Grand Unification.
- Although other mechanisms
- are not excluded and can
- give important or sub-leading
- contributions.

- How to check our  ideas about neutrinos?
- Future experiments will  perform precision
- measurements  of neutrino parameters.
- Apart from that we  will need results
- from non-neutrino  experiments:
-   - from astrophysics  and cosmology
-   - from searches for proton decay
-      and rare decays
-   - from future high energy colliders.