A' Yu' Smirnov

1
Neutrino mass

and
New physics
A. Yu. Smirnov
International Centre for Theoretical Physics,
Trieste, Italy Institute for Nuclear
Research, RAS, Moscow, Russia
Blois, June 2009
2
Proposed new physics
covers enormous range of possibilities

and not yet excluded
From eV and EW scales of the underlying
physics
to Planck mass scale (27 orders of magnitude !)
The only what we really know that all known
proposals can not be correct simultaneously and
can conclude that physics behind neutrino mass
has not yet been identified
to anarchy and randomness
from exact symmetry
to fundamental difference of quarks and leptons

from quarklepton unification
To idea that nothing can be explained and the
observed features are results of complicated
evolution from Planck /string scale to low
energies
From attempts to explain the observed features
in single QFT context
Like creation and evolution of planetary system
3
Plan

1. What do we really know?
2. New physics old and new
3. Do ends meet?
4

What do we really know?
some observations
5
Absolute mass scale

106 105 104 103 102 101 100 10-1 10 -2
MINOS, atmospheric neutrinos
me
Pauli
m gt Dm312 gt 0.045 eV
Fermi
COSMOLOGY bound on the sum of neutrino masses
mn , eV
Bergkvist
m lt S/3 lt 0.2 0.3 eV
ITEP
Zurich
Los Alamos
Troitzk, Mainz
The heaviest neutrino has mass is in the range
(0.045 0.20) eV
KATRIN
2010
6
l
Mass hierarchies

Solar, KamLAND
at mZ
up down charged
neutrinos quarks quarks leptons
1
m2 m3
Dm212 Dm322
gt
10-1
0.18
10-2
Neutrinos have the weakest mass hierarchy (if
any) among fermions
mass ratios
10-3
10-4
Related to the large lepton mixing?
Koide relation
10-5
sinqC md/ms
mu mt mc2
GattoSartori-Tonin relation
7
Nature of neutrino mass

Smallness may indicate that nature of the
neutrino mass (or at least what we observe in
oscillations) differs from masses of other
fermions
Is it the same as the mass of electron or top
quark?
?
mn(oscillations) mn(kinematics)
mn mstandard msoft(E,n)
medium (environment ) dependent (soft)
component
In general
Can msoft dominate?
mi m0 tanh (li r(g/cm3))
P. De Holanda
dependence on density with saturations
li ( 0, 0.06, 3)
m0 5 10-2 eV
Dirac versus Majorana?
8
Neutrino mixing
ne
nm
nt

Ue32
Um32
Ut32
tan2q12 Ue22 / Ue12
n3
sin2q13 Ue32
tan2q23 Um32 / Ut32
Dm2atm
mass
Ue22
n2
n1
Dm2sun
Ue12
nf UPMNS nmass
Normal mass hierarchy
UPMNS U23 Id U13 I-d U12
Dm2atm Dm232 m23 - m22
Dm2sun Dm221 m22 - m21
9
Spectrum
ne
nm
nt

zero 1-3 mixing?
n2
n3
Dm221
n1
?
bi-maximal
mass
mass
Dm223
tri-maximal
Dm232
n2
Dm221
n1
n3
Inverted mass hierarchy
Normal mass hierarchy
Tri-bimaximal mixing if 1-3 mixing is zero
nf UPMNS nmass
UPMNS U23 Id U13 I-d U12
10
12- and 13- mixings

T. Schwetz et al., 0808..2016
G.L. Fogli, et al 0805.2517, v3
sin2q13 0.016 /- 0.010
MINOS (2009)
sin2q13 0.05 /- 0.03
All data MINOS
x
sin2q13 0.02 /- 0.01
x
x
QLCl
TBM
All errors 1s
11
Leptons versus quarks

n3
t
mass
mass
n2
c
n1
u
QLC
Quarks
Leptons
small mixing
nf UPMNS nmass
Ud UCKM U
U (u, c, t)
combination of down-quarks produced with a given
up quark
12

New physics
Old New
13
New physics

L-R symmetric models
Grand
Neutrino
Unification
Supersymmetry
Mass
Flavor
symmetry
Extra
Extensions of
Dimensions
Superstrings
Electroweak
theory
Physics related to violation of fundamental
symmetries
14
Comments

Data show both order, regularities and
some degree of randomness
Different pieces of data testify for different
underlying physics
No simple relation between masses and mixing
parameters which could testify for certain simple
scenario
No simple explanation is expected?
15
Hints from data

Grand Unification
? quark-lepton correspondence
See-saw
Scale of neutrino mass
Extra dimensions
? for Dirac masses
Symmetry
accidental absence of RH neutrinos
? Mass hierarchy
Pattern of lepton mixing
Flavor symmetries
? Koide mass relation for charged leptons
Anarchy
16
Scale of neutrino mass

Two issues
Suppression of the natural (EW) scale
Generation of small mass measured in
oscillations
Seesaw mechanism do these two things
simultaneously
No new symmetry is needed
Seesaw - only suppression, e.g. if the RH masses
are at Planck scale. The dominant contribution
- from another mechanism

• - No right handed neutrinos
• - Seesaw
• symmetry (unnatural to introduce for RH
  neutrinos)
• multi-singlet mechanisms

Suppression
17
P. Minkowski T. Yanagida M. Gell-Mann, P. Ramond,
R. Slansky S. L. Glashow R.N. Mohapatra, G.
Senjanovic
See-saw

Type 1
H
x
H
x
mn
n
MR
x
gt
lt
Y
Y
mD YltHgt
mD
S T
S T
n
n
N
MR
Type 3 (triplet)
Type 2
n N
H
H
n N
0 mD mDT MR
D

If MR gtgt mD
n
n
mn - mDT MR-1 mD
18
Extra dimensions

New mechanism of generation of small Dirac
masses overlap suppression
Mass term m fL fR h. c.
If left and right components are localized
differently in extra dimensions ? suppression
Related to the fact that the right-handed
components of neutrinos have no SM
interactions
m e fL fR h. c.
amount of overlap in extra D
As in strings
19
In extra dimensions

Grossman Neubert Huber, Shafi...
In warped extra D
Flat extra D
Hidden brane
Visible brane
3D brane
fR0
fL0
fL
wave functions
overlap
overlap
fR
p
0
f
In Randall -Sundrum (non-factorizable metric)
Arkani-Hamed, Dvali, Dimopoulos
20
Small effective couplings

effective coupling produced by
non-renormalizable operators
S M
aij liLniL H
(renormalizable coupling is suppressed by
symmetry)
ltHgt
ltSgt
x
x
niL
njR
For aij O(1)
ltSgt M
hij aij
ltSgt M
aij/M
10 -13
SUSY / GUT scales?
ltS1gt
ltHgt
ltSngt
Small VEV L. Hall...
In general
m3/2/MPlanck
x
x
x
...
Difficult to test directly --gt test
context/models
niL
njR
21
Supersymmetry

Genuine SUSY mechanisms/features
New mass
SUSY breaking scale, m3/2
scales
m - mass term for 2 higgses
mn m vEW MGUT-1
New interactions New phenomenology
Neutralinos (higgsinos, wino, bino)
New particles
Neutral fermions with Majorana masses
Neutrinos are not unique
? can mix with neutralinos if R-parity is broken
? new mechanism of neutrino mass generation
22
Mixing pattern
With different implications

Quark-lepton
Quark-Lepton
Tri-bimaximal
universality
complementarity
mixing
bi-maximal - CKM''
Flavor symmetry
The same principle as in quark sector
Quark-lepton symmetry, GUT
Extension to quarks ?
no relation between masses and mixing
Large mixing is related to weak mass hierarchy
of neutrinos,
Some relations between mases and mixing
23
Tri/bimaximal mixing

L. Wolfenstein
P. F. Harrison D. H. Perkins W. G. Scott
2/3 1/3 0 - 1/6 1/3 1/2
1/6 - 1/3 1/2
Utbm
n3 is bi-maximally mixed
n2 is tri-maximally mixed
- maximal 2-3 mixing - zero 1-3 mixing - no
CP-violation
Utbm U23(p/4)U12
sin2q12 1/3
Something fundamental? Accidental and
misleading? Just organizing principle
Broken tri-bimaximal mixing
sin2q13 0.14
TBM corrections
sin2q23 0.45
sin2q12 0.31
24
Discrete flavor symmetry

The simplest with irreducible representation 3
Utbm Umag U13(p/4)
3
E. Ma
w 1
1 1 1 Umag 1 w w2
1 w2 w
w exp (-2ip/3)
tetrahedron
Symmetry
symmetry group of even permutations of 4
elements
A4
representations 3, 1, 1, 1
Other possibilities
Deviation from TBM?
T7 , D4 , S4 , D(3n2 )
25
Origins of mixing

Mixing appears as a result of different ways of
the flavor symmetry breaking in neutrino and Cl
sectors
Symmetry is not broken completely residual
symmetries in the neutrino and Cl sectors are
different
Gf
accidental symmetry due to particular
selection of flavon representations and
configuration of VEVs
Residual symmetries determine structure of the
mass matrices
Gl
Gn
Amt
Ml diagonal
Mn TBM-type
In turn, this split originates from different
flavor assignments of the RH components of Nc
and lc and different higgs multiplets
Strings support?
26
The simplest model?
G. Altarelli D. Melone

Yukawa sectors
A4
Z4
Charged lepton
Neutrinos
1 i -1 -i
3
L
L
1
n
k
i
i
hd
x
hu
fT
1
i
Nc
i
1
lc
i
-1
at multiplets
1, i, -1
1
fS
M
lt fT gt v S (0, 1, 0)
x
1
n 1,
k 0,
1
lt fS gt v S (1, 1, 1)
Flavon sector
U(1)R
Particular selection of representations
x
x
fT
fS
0 2
x0
fS0
fT0
Driving fields
-1
1
1
GUT-scale or higher?
27
Quark-Lepton Complementarity

Lepton mixing bi-maximal mixing quark
mixing
A.S. M. Raidal H. Minakata
ql12 k qq12 p/4
ql23 qq23 p/4
k 2-1/2 or 1
qualitatively
2-3 leptonic mixing is close to maximal because
2-3 quark mixing is small
1-2 leptonic mixing deviates from maximal
substantially because 1-2 quark mixing is
relatively large
28
Possible implications

Lepton mixing bi-maximal mixing quark
mixing
Quark-lepton symmetry
unification
Existence of structure which produces bi-maximal
mixing
See-saw? Properties of the RH neutrinos
Vquarks I, Vleptons Vbm m1 m2 0
In the lowest approximation
29
Bi-maximal mixing
F. Vissani V. Barger et al

Ubm U23mU12m
½ ½ -½ ½ ½ ½ -½ ½
0
Two maximal rotations
Ubm
as dominant structure? Zero order?
UPMNS Ubm

• - maximal 2-3 mixing
• - zero 1-3 mixing
• maximal 1-2 mixing
• - no CP-violation

contradicts data at (5-6)s level
Seesaw Structure of Majorana mass matrix of RH
neutrinos
Bi-maximal mixing
Deviation
Dirac matrix GUT or/and horizontal symmetry
30
Complementarity or Cabibbo hassle ''

P. Ramond
Deviations from BM due to high order corrections
Altarelli et al
Complementarity implies quark lepton symmetry
or GUT
Weak complementarity or Cabibbo hassle
Corrections of from high order flavon
interactions which generate simultaneously
Cabibbo mixing and deviation from BM, GUT is
not necessary
mm sinqC mt
or
sin qC 0.22 as quantum of flavor physics
31
Quark-Lepton symmetry

ur , ub , uj lt-gt n dr , db , dj lt-gt e
Correspondence
color
Symmetry
Pati-Salam
Leptons as 4th color
form multiplet of the extended gauge group, in
particular, 16-plet of SO(10)
Unification
Can it be accidental?
GUT
- unification leptons and quarks - unification
of forces
32
SO(10) GUT

16-spinorial representation which can accommodate
all known fermionic components including RH
neutrinos
RH-neutrino
ur , ub , uj , n dr , db , dj , e
urc, ubc, ujc, nc drc, dbc, djc, ec
16
- charge quantization - correct quantum numbers
for all components
SUSY without intermediate scales Non-SUSY with
intermediate scale
Gauge coupling unification
Proton decay?
Notice q-l unification may not imply q-l
correspondence and symmetry SU(5)
33
Grand unification?

RH neutrino components have large Majorana mass
1 MR
mn - mDT mD
in the presence of mixing
MGUT
MR
MGUT2 MPl
MGUT 1016 GeV - possible scale of
unification of EM
, strong and weak interactions
Neutrino mass as an evidence of Grand
Unification ?

• ? lepton asymmetry
• baryon asymmetry
• of the Universe

Leptogenesis the CP-violating out of
equilibrium decay
N ? l H
34
GUT's
generically

Give relations between masses of leptons and
quarks
Provide with all the ingredients necessary for
seesaw mechanism
mb mt
In general sum rules
RH neutrino components
large 2-3 leptonic mixing
Large mass scale
b - t unification
Lepton number violation
Some flavor features can be generated
But - no real explanation of the flavor structure
35
SO(10) GUT ...

Hagedorn Schmidt AS
Something is missed?
RH-neutrino
ur , ub , uj , n dr , db , dj , e
urc, ubc, ujc, nc drc, dbc, djc, ec
16
S
S
S
S
S
S
S
S
S
S
S
S
S

• - Decrease effective scale
• Enhance mixing
• Produce zero order mixing
• - Screen Dirac mass hierarchies
• Produce randomness (anarchy)
• Seesaw symmetries

S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
36
Real or accidental?

Tri-bimaximal mixing
Q-L-complementarity
Maximal 2-3 mixing
Very small 1-3 mixing
Koide relation
Accidental interplay of different independent
factors / contributions
Real immediate one step
Discovery of degenerate neutrino mass spectrum
would be convincing evidence of existence of
symmetry
KATRIN
Heidelberg-Moscow
Degenerate spectrum and TBM are not related ?
37

Something important
is missed?
38
Top - down
String theory

GUT
Existence of a number O(100) of singlets of SM
and GUT symmetry group
Several U(1) gauge factors
Top-down
Discrete symmetries
Heavy vector-like families
Non-renormalizable interaction
Explicit violation of symmetry
Incomplete GUT multiplets
Bottom up
Do the ends meet?
39
String engineering

Playing with geometry of internal space
Generic elements of the F-theory
V .Bouchard, J J Heckman J Seo, C. Vafa
1. In the lowest order Yukawa couplings appear
from overlap of the 6D fields localized
on matter curves at intersection of
three matter curves which correspond to
matter and Higgs fields. This leads to
singular Yukawa matrices
SU(5)
10M
5H
Yij zi zj
5M
Only one eigenvalue (mass) is non-zero
2. Masses of lighter quarks and leptons appear
as result of corrections due to
interactions with the background gauge fields.
6D
Corrections are determined by the gauge coupling
Ri MGUT -1
e aGUT
(M Ri) -2
M4 aGUT -1 MGUT4
Mass matrices appear then as powers of these
parameters
40
String engineering

versus model building
Expansion parameters and powers for different
fermions are different
3. GUT symmetry is broken in the
hypercharge direction
Origin of Yukawa structures is in the gauge
sector!
4. Large lepton mixing is related to weak mass
hierarchy of neutrinos and originates with
properties of RH neutrinos or objects which
play role of the RH neutrinos
- Kaluza-Klein seesaw
1 LUV
M L Hu L Hu
From integration of the KK modes

• e1/2 e
• e1/2 1 e1/2
• e e1/2 1

up to coefficients of the order 1
sin qC aGUT
UPMNS
Froggatt-Nielsen is back?
41
Connections

B-physics
Rare LNV
decays
Leptogenesis
MEG, etc
Proton
Neutrino
Decays
LHC
Mass
Leptonic EDM
HE accelerator
experiments
Cosmology
Further studies of neutrinos may reveal some
new features
42

Conclusions
43
New underlying physics No quick and simple
answer, no unique and convincing scenario.
Neutrinos did not help to resolve flavor
problem, added new puzzle

Approximate tri-bimaximal mixing or
quark-lepton complementarity - appealing
phenomenological schemes. Still can be
accidental and misleading, without any
fundamental implications
Plausible scenario of underlying physics could
include - see-saw with high mass scales -
(broken) flavor symmetry (effective) -
quark-lepton symmetry , unification
Identification of the correct scenario will
require further phenomenological and
experimental developments Long way of exclusion
of different possibilities.
LHC and other HE experiments may clarify the
situation
44
Blois, France, June 25, 2009
It is about 11 years since the discovery of
neutrino mass

Still, in spite of enormous efforts of many
theoreticians and experimentalists Physics
behind Neutrino mass has not been identified
It should be some New physics physics
beyond the Standard Model.
It may be old new physics invented many
years ago and studied in details theoretically.
It may be new New physics proposed recently
or something we have not though about.
45
Neutrino mass without new physics

M. Shaposhnikov et al
L
R

• - generate light
• mass of neutrinos
• generate via oscillations
• lepton asymmetry
• in the Universe
• Produced in B-decays
• (BR 10-10 )

Few 100 MeV
split few kev
3- 10 kev
- warm dark matter - radiative decays ?
X-rays
Normal Mass hierarchy
Phenomenology of sterile neutrinos
46
Mixing matrix

nf UPMNS nmass
ne nm nt
n1 n2 n3
the matrix is unitary
nmass
nf
where
UPMNS UPMNS I
Pontecorvo-Maki-Nakagawa-Sakata mixing matrix
Ue1 Ue2 U e3 Um1 Um2
Um3 Ut1 Ut2 Ut3
UPMNS
ifai
Uai Uai e
Due to unitarity and possibility to
renormalize wave functions of neutrinos and
charge leptons only one phase is physical
47
Neutrino symmetry?

Can both features be accidental?
Zero
Maximal
1-3 mixing
2-3 mixing
nm - nt permutation symmetry
Often related to equality of neutrino masses
Neutrino mass matrix in the flavor basis
Discrete symmetries S3, D4
For charged leptons D 0
A B B B C D B D C
Are quarks and leptons fundamentally different?
48
Neutrinos LHC

Expectations range from
Identification of the mechanism of neutrino mass
generation
e.g. if the Higgs triplet with terascale mass and
small VEV generates neutrino mass and mixing
to
Practically nothing
with conclusion that some EW scale mechanisms
with certain values of parameters are excluded
49
and ugly realisation

Ad hoc introduced - representations
- assignment of transformation properties
in particular Z4 - not all simplest
representations used (why not others?)
All this is just residuals of some broken
symmetry remnants of exploded star, debries
with some nice pieces Broken vase with buitiful
paintings on
50
Explaining via anti-Unification?

Usually explanation is achieved on the way of
unification joint description of different
facts. This leads to reducing number of free
parameters and principles
Here mixing ( mismatch of neutrino and charge
lepton rotations) is explained by separation of
the neutrino and charged lepton sectors
Different flavons are introduced, Different
flavors assigned to N and l (RH components)
Mixing appears as consequence of different charge
assignments and VEV configurations. Symmetry is
broken differently in neutrino and CL sectors.
Additional symmetries are introduced to prevent
interaction (communications) between two
sectors (at least in the lowest order).
Separation of masses and mixing even within
single sector (neutrino or charged leptons)
masses and mixing are unrelated. Some other
physics is responsible for values of masses scale
and hierarchy.
This in turn creates problems for grand
unification
51
... and moreover

Even mass generation of different charge leptons
is essentially independent separate sector for
each charged lepton. Often the Froggatt-Nielsen
sector introduced to explain mass hierarchy
Still precise values of masses are unpredicted
They depend on VEVs and arbitrary coupling
constants of the order 1 y O(1) (even this is
not justified)
- selection of basis for representation of the
group generators?
Tools
- selection of additional group (s)
- assignment of transformation properties
- selection of particular representations (among
all possible)
- fixing constants of the order one
Discretise arbitrarines

• Still TBM is achieved in the lowest order only
• corrections from HD operators and RGE will
  modify prediction

Proof of existence a possibility to express
observed features in term of broken symmetries
52
Interpretation

Tri-bimaximal mixing is accidental nothing
fundamental behind
Interpretation as tri-bimaximal mixing is not
correct
Alternative QLC gives equally good description
Tri-bimaximal mixing has fundamental
implications However realizations are not
correct
Flavor symmetry ? Wrong realization different
symmetries Accidental symmetry underlying
theory has different symmetry
Approach is correct but some elements are missed
So that behind neutrino mass is very reach
structure with other possible consequences
Approach is correct what we see is
All this is just residuals of some broken
symmetry remnants of exploded star, debries
with some nice pieces Broken vase with
beautiful paintings on
53
Classification

Majorana
Dirac
x
x
ltHgt
x
x
x
ltDgt
ltHgt
ltHgt
nL
nR
nL
nL
nL
nL
Small overlap (of wave functions In extra
dimensions)
Small coupling (effective)
Small VEV
Tree level
Radiative
A Yu Smirnov
54
Small Yukawa couplings

Unnatural untestable can be excluded if
bb0n-decay is discovered
ltHgt
x
niL
njR
hij 10 -13
hij
Dirac mass term is formed by LH neutrino and new
singlet which may have some particular symmetry
properties or come from the hidden sector of
theory
Usual Dirac term is suppressed by seesaw or
multi-singlet couplings
ltHgt
x
niL
Sj
Suppressed by symmetry or seesaw
hij
A Yu Smirnov
55
Hidden sector

56
Multisinglet suppression

Where are the right handed neutrinos?
If exist, why the Dirac mass terms are small or
absent?
Forbidden by symmetry
Suppressed by couplings with heavy degrees of
freedom
Unnatural? Why the RH neutrinos but not other
RH fermions?
See-saw as the mechanism of suppression of the
Dirac mass term (but not main contribution to
the mass)
n nR N
0 mD 0 mD 0 M 0 M 0
J. Valle, R. Mohapatra
m(n) 0
A Yu Smirnov
57
Road map in

jungles of neutrino
mass models
A. Yu. Smirnov
International Centre for Theoretical Physics,
Trieste, Italy Institute for Nuclear
Research, RAS, Moscow, Russia

Blois, June 2009
58
Model for BM-mixing
G. Altarelli F. Feruglio, L. Merlo


Yukawa sectors
S4
Z4
Charged lepton
Neutrinos
1 i -1 -i
3

L
L
3
n
k
1
i
cl
hd
hu
fl
2
i
Nc
i
1
i
ec
1
mc
1
at multiplets
tc
-1, -i, -i
1
fn
M
lt fl gt vl (0, 1, 0)
x
1
lt cl gt vl (0, 0, 1)
1

lt fngt vn (0, 1, -1)
Flavon sector
U(1)R
Froggatt-Nielsen sector
cl
fl
x
0 2
fn
ec, mc, t c q
i
i
fn0
x0
cl0
yl0
2, 1, 0 -1
U(1)FN
Driving fields
-1
1
-1
59
Mass scale mass spectrum

1. Absolute mass scale
m gt Dm312 gt 0.04 eV
m lt S/3 lt 0.2 0.3 eV
MINOS Atmospheric neutrinos
COSMOLOGY bound on the sum of neutrino masses
The heaviest neutrino has mass is in the range
(0.045 0.20) eV
2. Mass hierarchy
Neutrinos have the weakest mass hierarchy (if
any) among fermions
m2 m3
Dm212 Dm322

gt
0.18
Related to the large lepton mixing?
60
Disentangling possibilities

q12 , q13
QLC
n
TBM
q13
35.40, 9o
35.2o, 0
q12 , q13
q12
QLC
TBM 23-mixing should be zero or very small
l
32.2o, 1.5o
61
New physics

Two aspects
with m
behind m
n
n
Physics behind scale of neutrino mass, mass
spectrum, and pattern of lepton mixing
Collective effects mass plus nn -scattering
Old new new physics or undiscovered yet
Neutrino structures of the Universe Neutrinos
and dark energy, MaVaN Mass new interactions
New new physics
theoreticians
New for
experimentalists
62
New conundrum?

The observables are affected by many factors,
physics effects at different mass scales
including certain selection of string vacuum,
various threshold effects and corrections RGE
running, etc. etc.
63
1-2 mixing
Precision benchmarks

QLCl
p/4 - qC
tbm
QLCn
2s
SK, 2008
KamLADN SNO, 2008
1s
3s
Schwetz et al., 2008
2s
1s
3s
SNO (2008)
2s
1s
Strumia-Vissani
99
90
Fogli et al 2008
3s
Gonzalez-Garcia, Maltoni 2008
1s
q12
29 31 33 35 37 39
q12 qC p/4
Utbm Utm Um13
UQLC1 UC Ubm
give almost the same 12 mixing
64
1-3 mixing

T2K
Double CHOOZ
QLCn
qC
Dm212/Dm322
QLCl
Schwetz et al., 2008
3s
2s
1s
Gonzalez-Garcia, Maltoni 2008
3s
1s
Fogli et al 2009
All MINOS
1s
Fogli et al 2008
2s
1s
sin2q13
0 0.01 0.02 0.03 0.04 0.05
Non-zero central value (Fogli, et al)
Atmospheric neutrinos, SK spectrum of
multi-GeV e-like events
65

2-3 mixing
SK sin22q23 gt 0.93, 90 C.L.

T2K
maximal mixing
QLCn
QLCl
Schwetz et al., 2008 (without 1-2 split)
1s
Gonzalez-Garcia, Maltoni, 2008
3s
1s
SK (3n, one mass scale)
90
3s
Gonzalez-Garcia, Maltoni, A.S.
2s
1s
Fogli et al 2008
0.2 0.3 0.4 0.5 0.6 0.7
sin2q23
in agreement with maximal, though all complete
3n - analyses show shift shift of the bfp
from maximal is small still large deviation is
allowed
(0.5 - sin2q23)/sin q23 40
2s
66
Framework
String inspired

Non-abelian flavor (family symmetry) G with
irreducible representation 3
SO(10) 3 fermionic families in complete
representations 16F, 10H , 16H
16F 3
Singlet sector several (many ?) singlets
(fermionic and bosonic) of SO(10), S,
additional symmetries
No higher representations no 126H
Heavy vector-like families of 10F, 16F
their mixing corrects masses of charged
fermions
C. Hagedorn M. Schmidt A.S.
Non-renormalizable interactions
67
Singlet sector

Singlet sector
C. Hagedorn M. Schmidt, A.S. in progress
16F
16H
- several (many ?) singlets
(fermionic and bosonic) of SO(10), -
additional symmetries (U(1), discrete) ?
hierarchy of masses and couplings with
neutrinos from 16 - some singlets
can be light sterile neutrinos
Due to symmetries only certain restricted subset
is relevant for neutrino mass and mixing
Mixing of singlets with neutrinos (neutral
components of 16). responsible for neutrino
mass and mixing and strong difference of quark
and lepton patterns
Easier realizations of symmetries
68
Flavor physics flavons

Physics

• - existence of 3 fermionic generations
  (families)
• mass spectra of fermions (mass hierarchies)
• pattern of quark and lepton mixing
• other phenomena which lead to flavor transitions

responsible
for
Based on existence of some new symmetry
of nature flavor symmetry Related to some
new sector of theory beyond the
standard model
Flavor symmetry
In general product of several factors
Gf G1 x G2 x G n
SU(3) or SO(3) or/and some their subgroups (in
particular discrete) U(1) factors
Gi
Symmetry is in general broken and still some
residual (unbroken) symmetries
exist may
69
Two scenarios

The Higgs multiplets (doublets) which break EW
symmetry can carry flavor charge
1. Flavor and EW symmetry breakings can be
entangled
They break both EW symmetry and flavor symmetry
Flavor physics is at EW scale can be tested
New particles flavored bosons should (?) exist
at the EW scale
Models must be tuned to avoid FCNC
2. Flavor and EW symmetry breakings are
disentangled
EW Higgses have no flavor charge

• - scalar bosons
• carry flavor charge
• singlets of the SM symmetry group
• get VEVs, thus violating flavor symmetry

Flavons
ltlt MGUT
intermediate
Scale
MGUT
Lf
GUT-scale
gtgt MGUT
MPl
70
Reconciling

Neutrino
Generic problem
Data
Data Flavor symmetry
Flavor
- quarks and leptons, - RH components of
charge leptons and neutrinos have different
flavor properties
seesaw
Symmetries
Grand
Unification
prevents from GU