Smirnov (op.) - ICTP

Workshop on theoretical aspects
of neutrino masses and mixing
ICTP, Trieste, Italy
September 17 – 23, 2012

Ongoing progress

eaking
T2K 90%
Fogli et al, 1
Daya Bay, 1
Double Chooz, 1
QLC
RENO, 1
0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
sin 2 13
mass ratio

d 23 = ½ - sin 2 23
the key to ( probe)
understand the
underlying physics
NH
MINOS, 1
symmetry
violation
Connection to
1-3 mixing
Quark -Lepton
Complementarity
Fogli et al, 1
SK, 90%
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
23 ~ /2 - V cb
sin 2 23

SK (NH), 90%
SK (IH), 90%
Fogli et al, 1
MINOS,
1
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
sin 2 23
QLC

sin 2 13 ~ 0.022
sin 2 13 =
O(1)
m 21 2
m 32 2
``Naturalness’’ of mass matrix
~ ½ sin 2 C Quark Lepton Complementarity
~ ½cos 2 2 23 - symmetry violation
12
Mixing anarchy
Self-complementarity
The same 1-3 mixing with completely different implications

sin 2 13~ ½sin 2 C
Follows from
permutation of
matrices
From charged
leptons
13~ ½ c
First obtained in the context of
Quark-Lepton Complementarity
U 12 ( c) U 23( /2)
Permutation - to reduce the lepton
mixing matrix to the standard form
Maximal from
neutrinos
H. Minakata, A Y S
Related to smallness
of mass

m 2 31 - m 2 31
Resonance in the antineutrino
channel> V -V

MASS
3
2
1
Normal mass hierarchy
m 2 32
m 2 21
?
FLAVOR FLAVOR
Two large mixings
m 2 32 = 2.3 x 10 -3 eV 2
m 2 21 = 8 x 10 -5 eV 2
MASS
2
1
3
e
Inverted mass hierarchy
m 2 21
m 2 23

Precision IceCube Next Generation Upgrade
Denser array
20 new strings (~60 DOMs each)
in 30 MTon DeepCore volume
Few GeV threshold in inner
10 Mton volume
Energy resolution ~ 3 GeV
Existing IceCube strings
Existing DeepCore strings
New PINGU-I strings
125 m
PINGU v2

~ 1/E0.5 = 0.2E Degeneracy

G. L. Fogli
First glimpses?
T . Yanagida
Neutrinoantineutrino
asymmery
CP ~ /2 +/- 0.02
Third way
Key measurement:
amplitudes of the
- oscillations
due to solar and
atmospheric mass
splittings
Do we have predictions for the phase in quark sector?
Why do we think that we can predict leptonic mixing?
Again because of neutrinos are special ? Symmetries?

In the first
approximation
U tbm =
- maximal 2-3 mixing
- zero 1-3 mixing
- no CP-violation
- sin 2 12 = 1/3
Symmetry from mixing matrix
2/3 1/3 0
- 1/6 1/3 - 1/2
- 1/6 1/3 1/2
U tbm = U 23( /4) U 12
L. Wolfenstein
P. F. Harrison
D. H. Perkins
W. G. Scott
3 is bi-maximally mixed
2 is tri-maximally mixed
Uncertainty related
to sign of 2-3 mixing:
23 =

Mixing appears as a result of different ways of the flavor
symmetry breaking in neutrino and charged lepton sectors
Residual
symmetries
G l
M l
diagonal
G f
G
M
TBM-type
the splitting originates from different flavor assignments of
the RH components of N c and l c and different higgs multiplets
?
1
A4 T7 T’
S 4

Deviations from BM due to high order corrections
Complementarity:
implies quark-lepton
symmetry or GUT,
or horizontal symmetry
sin C =
m
m
Self-complementarity relations
Xinyi Zhang Bo-Qian Ma, arXiv:1202.4258
Weak complementarity or
Cabibbo haze
P. Ramond
Altarelli et al
Corrections from high order
flavon interactions generate
Cabibbo mixing and deviation from BM,
GUT is not necessary
sin C = 0.22
as ``quantum’’ of
flavor physics

Similar Ansatz for
structure of mass matrices
Relations between
masses and mixing
The same coupling
strength between
generations
sin 13 ~ ½ sin 12 sin 23
Fritzsch Anzatz
similar to quark sector
3 RH neutrinos with equal
masses
Normal mass hierarhy,
Right value of 13 mixing
Flavor ordering in
mass matrix

Values of elements gradually decrease from m to m ee
corrections wash out sharp
difference of elements of the
dominant -block and
the subdominant e-line
This can originate from power dependence of elements
on large expansion parameter ~ 0.7 – 0.8 .
Another complementarity: = 1 - C
Froggatt-Nielsen?

After many speculations back to good old picture?
High scale seesaw
The same mechanism which explains
smallness of neutrino mass is responsible
for large lepton mixing
Something is
still missed
Difference of quarks and leptons
is related to smallness of neutrino mass

u r , u b , u j ,
d r , d b , d j , e
- Enhance mixing
- Produce zero order mixing
- Screen Dirac mass hierarchies
- Produce randomness (anarchy)
- Seesaw symmetries
- Increase seesaw scale
u r c , ub c , uj c , c
d r c , db c , dj c , e c
S
S S
S
S
S
S
S
S
S
S
S
S
S
S S
S S
RH-neutrino
S
S
S
S
S
S
S
S
S
S
S
Hidden sector

L R
BAU
WDM
Normal
Mass
hierarchy
M. Shaposhnikov et al
Everything below EW scale
small Yukawa couplings
Few 100 MeV
split ~ few kev
- generate light
mass of neutrinos
- generate via oscillations
lepton asymmetry
in the Universe
- can beproduced in
B-decays (BR ~ 10 -10 )
3- 10 kev - warm dark
matter
- radiative decays
X-rays
EW seesaw

cosmology
BUGEY+MINOS
In assumption of
no-oscillations in ND
|U 4| 2 < 0.019 (90% CL) 13 = 11.5 o
LSND/MiniBooNE require:
|U 4| 2 > 0.025
- s mixing
m 41 2 > 0.5 eV 2
or modification of Cosmology:
N = 1.23 (add massless)
= - 1.11
BBN: chemical potential for e
J Hamann et al 1108.4136

T. Schwetz
Hints from νe disappearance
(reactor and gallium anomalies)
Strong tension between disappearance
data and νμ → νe LSND-MiniB signals
(non-observation of νμ disappearance)

m = m a + m
Original active mass
matrix e.g. from see-saw
Induced mass matrix
due to mixing with nu sterile
m can change structure (symmetries) of the original
mass matrix completely (not a perturbation)
Enhance lepton mixing
Be origin of difference of
and

mass
2
3
0
1
sin 2 2 ~ 10 -3
sin 2 2 ~ 10 -1
m 2 31
m 2 21
m 2 dip
s
Very light sterile neutrino
m 0 ~ 0.003 eV
M 2
M Planck
e
- solar neutrino data
DE scale?
M ~ 2 - 3 TeV

pp 7 Be CNO 8 B
e - survival probability from solar
neutrino data vs LMA-MSW solution
HOMESTAKE
low rate
pep
.
SNO
SNO+

No distortion of the energy spectrum
at low energies : the upturn is disfavored
at (1.1 – 1.9) level
This is how new physics may show up
M. Smy
Increasing tension between m 2 21
measured by KamLAND and in
solar neutrinos 1.3 level

BBN:
N = 3.0 +/-0.5
Pettini and Cooke
2012
A. Melchiori
et al 2012
L. Verde

HDM
Direct
connection
New
neutrino
states
Warm DM
Light active
neutrinos
indirect
connection
Mixing pattern
Flavor symmetries
Mechanism of
neutrino mass
generation
ensure stability
of DM particles
new particles
of the Universe
Z 2
right handed
neutrinos
play the role of DM
Neutrinos
and gravitino
as DM
W. Buchmueller
Everything from one

On September 21

Discovery of relatively large 1-3 mixing – important
implications for theory, phenomenology and
experiment. Strong impact on further developments.
Mass hierarchy: with NOvA, atmospheric neutrinos
ICAL INO, DeepCore IC, PINGU-I,
supernova neutrinos
Measurements of the deviation of 23 mixing
from maximal, CP- phase, absolute mass scale

NH IH
nu antinu
Earth matter
effect
NOvA Energy spectrs
Neutrino beam
Fermilab-PINGU(W. Winter)
Sterile neutrinos
may help?

MASS
3
2
1
Oscillations
D 31 ~ 2D 32
Matter
effect
Normal hierarchy
32 ij = m 2 ij /2E
31
Mass states can
be marked by
e - admixtures
Inverted hierarchy
31 > 32 31 < 32
Fourier
analysis
makes the e-flavor heavier
changes two spectra differently
2
1
3
31
32
e
S. Petcov
M. Piai

e
E, GeV
100
10
1
0.1
IceCube
IC Deep Core
PINGU-1
0.005
0.03
0.10
contours of constant oscillation
probability in energy- nadir
(or zenith) angle plane
NuFac 2800
LENF
T2KK
CNGS
MINOS
NOvA
T2K
HyperK
OK for CP

Oscillation physics with Huge
atmospheric neutrino detectors
ANTARES
DeepCore
Ice Cube
Oscillations 2.7
Oscillations at high energies 10 –
100 GeV in agreement with
low energy data
no oscillation effect
at E > 100 GeV
Bounds on non-standard
interaction,
Lorentz violation etc
P. Coyle
G. Sullivan

Next step: determination of neutrino mass hierarchy and
CP-violating phase
Establishing the absolute neutrino mass scale, and
Majorana nature among main goals

mass
3
2
1
Leptons
f = U PMNS mass
mass
t
c
u
Quarks
U d = U CKM + U
U = (u, c, t)
combination of down-quarks
produced with a given up quark

symmetry

Daya Bay:
RENO:
QLC
Double CHOOZ
0 0.1 0.2 0.3
0.04
0.092 +/- 0.012
0.116 +/- 0.024
Daya Bay
RENO
sin 2 13
> 7 from 0
Important: Daya Bay, RENO and T2K
(different energies, setups..) give the same value of the angle

GERmanium
Detector
Array
Phase I: 15 kg y: 0.3 – 0.9 eV
Phase II: 37.5 kg y: 0.09 – 0.29 eV
Phase III: 1 ton 0.01 eV
Xe- Observatory
130 Te
Cryogenic Underground
Observatory for Rare Events
CUORE-0

G. L. Fogli
Serious implications
for theory
Non-zero, relatively
Large 1-3 mixing
Substantial deviation
of the 2-3 mixing
from maximal
CP ~
Robust ?

1. Two mass scales in the mass matrix
m 21 2
2. Two large mixing angles
3. Normal mass hierarchy
sin 13 ~
m 31 2
m 21 2 / m31 2 = 0.17 - 0.20
sin 2 13 ~
4. No fine tuning - no equalities of matrix elements
- no particular (for leptons) flavor symmetries,
- normal mass hierarchy
m 21 2
m 32 2
E. Akhmedov,
G. Branco et al 2002
M Frigerio E. Ma, 2006
W. Rodejohann et al,
arXiv 1201.4936

1. - – symmetry of m
sin 2 13 ~ ½cos 2 2 23
- maximal 2-3 mixing
- zero 1-3 mixing
2. breaking of - symmetry by corrections to matrix elements:
|m e - m e | ~ |m - m | = m
3. Normal mass hierarchy
sin 13 ~
m
2m 3
D = ½ - sin 2 23 ~
also: the - symmetry is broken by charged leptons
m
2m 3
D - deviation from
maximal 23 mixing
m ~ m 2

Asymmetry, statistical significance
S tot ~ s n 1/2
Quick estimation
of significance
Effective average
significance in individual bin
Number of bins in
resolution domains
E. Kh Akhmedov,
S Razzaque,
A. Y. S.

Origins: KK states of extra dimensions
Statistical distribution of Yukawa couplings y
(y) ~
1
Y 1+
Y = 10 -6 - 1
M = 10 14 - 10 16 GeV Linear scale
Random simulations, random phases
Anarchical spectrum
B. Feldstein, W. Klemm
arXiv: 1111.6690
reasonable fit
for charged leptons
Seesaw type I

Mass matrix in
the flavor basis
If there is no fine tuning
of 12 and 13 elements
1 1
1 1
sin 13 = ½ sin2 12 cot 23
sin 13 = ½ sin2 12 tan 23

Leptons
U = U bm
U l = U CKM
seesaw
U PMNS = U l + U = U CKM + U bm
q-l symmetry
1-3 mixing is generated by permutation of U 12 and U 23
sin 13 = sin 23 sin C ~ 0.16
sin 12 = sin( C) + 0.5sin C ( 2 - 1- V cbcos )
D 23 = 0.5 sin 2 C + cos 2 C V cbcos = 0.02 +/- 0.04
Quarks
V u = I
V d = VCKM
H. Minakata, A.S.
V quarks = V u + V d = V CKM
sin 2 12 = 0.3345
RGE -> can reduce
M. Schmidt, A.S.

sin 2 13~ sin 2 23 sin 2 C
Bi-maximal mixing?
RGE effect
D. Hernandez,
A.S.
Improves also
predictions
for 1-2 mixing
sin 2 13~ sin 2 23 sin 2 C

If G is von Dyck group D(2, m, p)
For column of the
mixing matrix:
|U i| 2 = |U i| 2
|U i| 2 =
1 – a
4 sin 2 ( k/m)
A is determined from
condition
3 + a 2 - a* - 1 = 0
i p = 1
k, m, p integers which
determine symmetry group
S 4
= 103 0
S 4
D. Hernandez, A.S.
A 4
Also S. F. Ge, D. A. Dicus,
W. W. Repko, PRL 108 (2012) 041801

Based on relation
Bi-maximal mixing
12
Octahedral group
Geometric violation of residual symmetry in the charged
lepton sector (additional rotation from charged leptons)
12
H. J. He, X. J. Xu
1203.2908 [hep-ph]

RH neutrino components have large
Majorana mass
M R ~
M GUT
M GUT 2
M Pl
in the presence
of mixing
1
m = - m D T m D
M GUT ~ 10 16 GeV - possible scale of unification of
EM , strong and weak interactions
Neutrino mass as an evidence of Grand Unification ?
Leptogenesis:
the CP-violating out of
equilibrium decay
N l + H
M R
lepton asymmetry
baryon asymmetry
of the Universe

Mass matrix e mee me me meS … m m
… … m
For m SS ~ 1 eV
S
… … …
tan jS = m jS/m SS
~ 0.2
m ij ~ - tan iStan jS m SS ~ 0.04 m SS
m S
m S
m SS
In general can not be considered as small perturbation!
Effect on mixing is small if
Active neutrino spectrum
is quasi degenerate mSS ~ mab m eS m S m S have
certain symmetry
m SS >> m ab , m aS
J. Barry,
W. Rodejohann,
He Zhang
arXiv: 1105.3911

m 0 ~ 0.003 eV
m 0 =
M 2
M Planck
M ~ 2 - 3 TeV
P. de Holanda,
AYS

m 0 ~ 0.003 eV
mixing
sin 2 2 ~ 10 -3
sin 2 2 ~ 10 -1
M2 m0 =
M M ~ 2 - 3 TeV
Planck
~
~
h v EW
M
v EW
M
h = 0.1