A' Yu' Smirnov

1
Status interpretation

of neutrino mixing
A. Yu. Smirnov
International Centre for Theoretical Physics,
Trieste, Italy Institute for Nuclear
Research, RAS, Moscow, Russia
Launch
Heidelberg, March-07
2

1. Status
3
50 years ago...

B. Pontecorvo
Mesonium and antimesonium
Zh. Eksp.Teor. Fiz. 33, 549 (1957) Sov. Phys.
JETP 6, 429 (1957) translation
First mentioning of a possibility of neutrino
mixing and oscillations
Another line Wu experiment, 1957 Parity
violation ? V-A theory, two-component massless
neutrino
4
The first phase
of studies of neutrino mass and mixing is
essentially over

The main results
Discovery of non-zero neutrino masses
Determination of the dominant structure of the
lepton mixing discovery of two large mixing
angles
Establishing strong difference of the quark and
lepton mass spectra and mixing patterns
New phase starts in 2008 2010 the main
objectives - determination of the
absolute scale of neutrino mass
- subdominant structures of mixing matrix
- identification of the mass hierarchy,
etc.
5
Mixing summary
M.C. Gonzalez-Garcia, M. Maltoni, Moriond,
March 2007 (Phys. Rep.)

The angles
1s (3 s)
very good agreement with other fits
4.3 - 3.5
q12o 33.7 /- 1.3
small shift from maximal mixing
4.3 - 3.8
9.8 - 8.8
q23o 43.3
b.f. value is zero stronger upper bound
11.5 - 0.0
5.3 - 0.0
q13o 0.0
Mixing matrix (moduli of matrix elements)
0.81 0.85 0.53 0.58 0.00
0.12 0.32 0.49 0.52 0.69 0.60 -
0.76 0.27 0.46 0.47 0.64 0.65
0.80
UPMNS
90 C.L.
6
1-2 mixing

Give the almost same 12 mixing
Utbm Utm Um13
UQLC1 UC Ubm
QLCl
QLCn
p/4 - qC
tbm
3s
SNO (2n)
2s
1s
Strumia-Vissani
99
90
Fogli et al
3s
Gonzalez-Garcia, Maltoni
1s
q12
29 31 33 35 37 39
q12 qC p/4
7
1-3 mixing

T2K
Double CHOOZ
qC
Dm212/Dm322
QLCn
QLCl
Gonzalez-Garcia, Maltoni
3s
1s
Strumia-Vissani
99
90
Fogli et al
3s
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
MINOS lead to stronger the bound on 1-3 mixing
(G-G, M.)
8

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

maximal mixing
T2K
QLCn
QLCl
Gonzalez-Garcia, Maltoni, 2007
3s
1s
SK (3n, one mass scale)
90
3s
Gonzalez-Garcia, Maltoni, A.S.
2s
1s
Fogli et al
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
9
Masses summary

0.44 - 0.26
Dm312 2.74 x 10-3 eV2
MINOS
(1 s)
1.27 1020 p.o.t.
in future tension with SK? new physics?
Dm312 2.6 /- 0.2 (0.6) x 10-3 eV2
Global fit
1.10 - 0.89
0.27 - 0.28
M. Gonzalez-Garcia, M. Maltoni, 2007
Dm212 7.90 x 10-5 eV2
m2 /m3 gt 0.18
the weakest mass hierarchy
Cosmology
Si mi lt 0.42 eV (95 C.L. )
S. Hannestadt
U. Seljak et al
Si mi lt 0.17 eV (95 C.L. )
lt 0.6 eV
m 0.05 0.10 eV
At least for one neutrino
if confirmed, other than light neutrino Mass
mechanism?
mee 0.24 0.58 eV
Heidelberg-Moscow
10
Forthcoming results

MINOS results 2 years data
taking (double statistics)
Dm2 (2.5 - 3.1) x 10-3 eV2
Improvements of the 1-2 mixing determination Ue2
SNO results of the third phase
He counters
Improvement of sensitivity to 1-2 mixing
comparable to solar neutrino sensitivity
KAMLAND update calibration
MiniBooNE oscillation results
Tests of LSND, overall picture of mass and
mixing
BOREXINO CNGS
11

Standard'' neutrino model
1. There are only 3 types of light neutrinos
2. Interactions are described by the
Standard (electroweak) model
3. Masses and mixing have pure vacuum origin
they are generated at the EW and probably
higher mass scales
Hard masses
Tests of these statements Search for physics
beyond
12
More light neutrinos?

LSND not clear that light neutrinos are
relevant
Gallium calibration
C. Giunti, M. Laveder
Cosmology effective number of light neutrino
species in the epoch when
structures start to form
Warm dark matter very small mixing, produced in
EU by some mechanism which differs from mixing
with light neutrinos.
M. Shaposhnikov
Small perturbations
How inclusion of these neutrinos affect
standard neutrino model?
Strong changes?
13
Bounds on active - sterile mixing

R. Zukanovic-Funchal, A.S.
Contours of constant induced mass and bounds
bb0n
thermalization line above if S are in
equilibrium
CMB
For benchmark parameters S were thermalized
X-rays
Bounds - in non-equilibrium
region
LSS
reactors
atmospheric
14
New interactions

Short range
Long range
interactions
interactions
Heavy particle exchange
Light particles
New scalars
New scalars exchange
Majorons, Accelerons Cosmons
With some cosmological motivations
SUSY with R-parity breaking
Phenomenology T. Ota
Restrictions see talk S. Hannestadt
15
Soft'' neutrino mass?

Are neutrino masses usual?
in the context of MaVaN scenario
ln
Exchange by very light scalar
D B Kalplan, E. Nelson, N. Weiner , K. M.
Zurek M. Cirelli, M.C. Gonzalez-Garcia, C.
Pena-Garay V. Barger, P Huber, D. Marfatia
nR
nL
f
mf 10-8 - 10-6 eV
f e, u, d, n
lf
fL
fR
chirality flip true mass
lf f/M Pl
msoft ln lf nf /mf
mvac ? mvac msoft
In the evolution equation
medium and energy dependent mass
generated by some short range physics
(interactions) EW scale VEV
16
to

2. Interpretation
of lepton mixing results
17
High vs. Low mass scales

Grand
Low scale
unification
mechanisms
Planck
M3 MGUT
Intermediate
EW scale?
scale
scale
kev-scale mechanisms?
With many O(100) RH neutrinos
R. Mohapatra
M. Shaposhnikov
W. Buchmuller, M. Ratz et al
Problem of unification difference of mass and
mixing patterns
Origin of difference seesaw?
FUT flavor symmetry even more complicated
18
Analyzing data

mass-mixing
tri-bimaximal
GST-approach
mixing
Quark-lepton
No-symmetry
Complementarity
Large mixing is related to weak mass hierarchy
of neutrinos
Have different implications
19
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
In flavor basis relation to masses? No analogy
in the Quark sector? Implies non-abelian
symmetry
Clebsch-Gordan coefficients
immediate relation to group matrices?
20
Possible implications

Utbm Umag U13(p/4)
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
T , D4 , S4 , D(3n2 )
C.Hadedorn
Extended higgs sector, Auxiliary symmetries,
Flavor alignment, Extra dimensions?
Relation to masses? No analogy in the quark
sector? Unification?
21
Quark-Lepton Complementarity

A.S. M. Raidal H. Minakata
QLC- relations
ql12 qq12 p/4
q12 qC 46.5o /- 1.3o
ql23 qq23 p/4
1s
q23 V cb 43.9o 5.1/-3.6o
H. Minakata, A.S. Phys. Rev. D70 073009 (2004)
hep-ph/0405088
Qualitatively correlation
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
22
Possible implications

Lepton mixing bi-maximal mixing quark
mixing
Quark-lepton symmetry
Existence of structure which produces bi-maximal
mixing
Mixing matrix weakly depends on mass eigenvalues
Appears in different places of theory
Vquarks I, Vleptons Vbm m1 m2 0
In the lowest approximation
23
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
24
QLC_nu V_bm from neutrinos

In the symmetry basis
Quarks
Leptons
Seesaw?
Vu I
Vn Vbm
Vd VCKM
Vl VCKM
q-l symmetry
Vquarks Vu Vd VCKM
VPMNS Vl Vn VCKM Vbm
(or both rotations from neutrinos)
Predictions
sinq12 sin(p/4 - qC) 0.5sinqC ( 2 - 1- Vcb)
sin2q12 0.330
large !
sinq13 sinq23 sinqC 0.16
D23 0.5 sin2qC cos2qC Vcbcos a 0.02 /-
0.04
H. Minakata, A.S.
25
QLC_l V_bm from charged leptons

M. Raidal
Leptons
Quarks
Vn VCKM
Vu VCKM
q-l symmetry
Vl Vbm
Vd I
Lopsided
Vleptons Vbm VCKM
Vquarks Vu Vd VCKM
Predictions
sinqsun sin (p/4 - qC )
sinq13 - sin qsun Vcb 0.03
H. Minakata, A.S.
D23 cos qsun Vcb cos d lt 0.03
26
tbm vs. QLC

Physical parameter
Ue2 cos q13 sin q12
Global fit 0.53 0.58 (90 C.L.)
tbm 0.577
(depending on Majorana CP phases)
QLC 0.576 0.584
QLC
RGE
tbm
RGE for tbm A. Dighe, S. Goswami, W. Rodejohann
hep-ph/0512328
data
Ue2
0.53 0.55 0.57 0.59
tbm RGE q13 lt 10-3 for hierarchical nu
? 0.1 for degenerate nu
27
QLC RGE effects
M. A. Schmidt, A.S. hep-ph/0607232

D q12
D q12
MSSM
SM
positive
f2 - f1
tan b
m1/eV
m1/eV
seesaw-I ? bi-maximal mixing,
mD mu
ml md
28
Real or accidental?

Tri-bimaximal mixing
Small 1-3 mixing
Q-L-complementarity
Maximal 2-3 mixing
Koide relation
29
Perturbative approach

Fermion mass matrices
Mf M0 dMf
f u, d, l, n
Determined by symmetry?
corrections due to new interactions Planck scale
effects
What is zero order structure? What it should
explain?

• - third generation masses
• 2-3 mixing
• - 1-3 mixing

The rest from perturbations?
30
...but

Koide relation
Y. Koide, Lett. Nuov. Cim. 34
(1982), 201
me mm mt
2/3
( me mm mt )2
with accuracy 10-5
mm - me
all three families are substantially involved!
tanqC 3
2 m t - mm - me
Both relations can be reproduced if
mi m0(zi z0)2
C A Brannen
Si zi 0
Neutrinos, hierarchical spectrum
z0 Si zi2 /3
31
From the bottom
from the top

Data
String theory
Existence of a number O(100) of singlets of
SM and GUT symmetry group
GUT
no simple relations between masses and mixing ?
can not be described in terms of a few
parameters
Several U(1) gauge factors
Discrete symmetries
Heavy vector-like families
Non-renormalizable interaction
Selection rules for interactions
Explicit violation of symmetry
Incomplete GUT multiplets
No simple one-step explanations
How one can get from this complicated
structure simple pattern we observed at low
energies?
? data look complicated
? data look too simple
32
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
33
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
34
Neutrinos LHC

The EW-scale mechanisms of neutrino mass
generation
HE scale seesaw
New Higgs bosons at the EW scale
?
Zee, Babu-Zee radiative mechanisms
R-parity violation
Double charged bosons
New fermions?
35
Seesaw at LHC

W. Buchmuller, D. Wyler
Can RH neutrinos be detected at LHC?
Type-I RH neutrinos- singlets of the SM symmetry
group
RH neutrinos can be produced/decay
Via mixing with light neutrinos
Additional interactions
Negligible unless strong cancellation occurs
- RH gauge bosons in LR models - New higgs bosons
Type-III seesaw
36
RH neutrinos at LHC

Type III seesaw
B. Bajc G. Senjanovic M. Nemevsek P.
Filiviez-Perez
SU(2) triplet
H
H
T T T0 T-
y 10-6
x
y
n
n
T0
MT 100 GeV
S
In SU(5)
24F T, S
Type I Type III one usual neutrino is mass less
y 5F 24F 5H y/M 5F 24F 24H 5H
EW production
W ? T T0,
Z ? T0 T0
LHC
T0 ? W l ,
Decay
T0 ? Z n ,
t 10-16 - 10-13 sec
T0 ? T l - n
G (mixing) 2
37
Mixing and cancellation

Single RH neutrino generate a contribution to
neutrino mass matrix
W. Buchmuller C. Greub, G. Ingelman, J.
Rathsman A. Pilaftsis
1 Mi
(mi)ab - m ai x mbiT
Define mixing
sin qai m ai / M i
(mi)ab - sinqai sin qbi M i
J. Kersten, A.S.
Neutrino data
s (qai)2
qai lt 10-6 ( 10 GeV / M i)1/2
(mi)ab lt 0.1 eV
negligible effect at HE colliders
qai 10-1
If
M 1 GeV
Bound from m ? e g
Cancellation at the level 10-10
38
Cancellation and symmetry

For 2 and 3 RH neutrinos exact cancellation
occurs if and only if
y1 ay1 by1 mD m y2
ay2 by2 y3 ay3 by3
1. the Dirac mass matrix is singular
J. Kersten, A.S.
J. Gluza
2. the Yukawa couplings and RH neutrino
masses are related as
y12/M1 y22/M2 y32/M3 0
Imply conservation of the lepton number and one
decoupled heavy neutrino
1 1 1 m D hv w
w w w2 w2 w2

An example motivated by A4
M M0 diag (1, 1, 1)
39
Cancellation and perturbations

Perturbations of the symmetric structure
J. Kersten, A.S. in progress
T. Underwood
non-zero usual neutrino mass
negligible consequences for HE (LHC) physics
Neutrino mass generation and HE physics
decouple
Indirect relation
imprinted
Simple perturbations ?
correlation of light neutrino properties and
heavy leptons
Pattern of neutrino mass and mixing
reflects features that lead to cancellation, ?
maximal 2-3 mixing and zero 1-3 mixing
40
Summary

Status standard model of neutrino mass and
mixing further confirmations/checks.
Deviations?
?
ti-bimaximal mixing possible presence of special
leptonic (neutrino) symmetries
Q-L complementarity bi-maximal mixing and Q-L
symmetry/unification
Real or accidental?
GUT flavor (ultimate unification?) string
inspired framework with extended singlet sector,
non-renormalizable interactions ?
Can LHC help?
41

Launch
with non-stop flight
to great success!