Transcript No Slide Title

A. Yu. Smirnov
International Centre for Theoretical Physics, Trieste, Italy
Institute for Nuclear Research, RAS, Moscow, Russia
Summarizing achievements and highlights
Pattern of lepton mixings: New theoretical puzzle?
Towards the underlying physics
New symmetry of Nature?
Quarks - Lepton symmetry
Flavor symmetry or family symmetry?
Mass spectrum: Degenerate or hierarchical?
Flavor states:
ne
nm
Mixing:
Flavor
states
nt
=
Mass
eigenstate
Eigenstates of the CC weak
interactions
Sterile neutrinos
no weak interactions
?
Mass eigenstates:
n1
n2
n3
m1
m2
m3
n3
m2
m1
n2
n1
mass
ns
m3
Neutrino mass and
flavor spectrum
A Yu Smirnov
n2 = sinq ne + cosq nm
n1 = cosq ne - sinq nm
vacuum mixing angle
ne = cosq n1 + sinq n2
ne
n1
n2
coherent mixture
of mass eigenstates
wave
packets
Interference of the parts of wave packets
with the same flavor depends on the
phase difference Df between n1 and n2
Dm2
Df = ---- l
2E
Dm2 = m22 - m12
Solar
neutrinos
Supernova
neutrinos,
SN 1987A
Atmospheric
neutrinos
Reactor experiments
CHOOZ, PaloVerde
KamLAND
Masses, mixing
Dmij2, qi j
Oscillations
Conversion in matter
Direct kinematic
measurements
of neutrino masses
Accelerator
experiments
Cosmology
Neutrinoless
double beta
decay
A Yu Smirnov
Flavors of mass eigenstates do not change
Admixtures of mass eigenstates
do not change: no n1 <-> n2 transitions
ne
Determined by q
n2
n1
Df = 0
Df = Dvphase t
Dm2
Dvphase =
2E
Due to difference of masses n1 and n2
have different phase velocities:
Oscillation length:
Dm2 = m22 - m12
ln = 2p/Dvphase = 4pE/Dm2
effects of the phase difference
increase which changes
the interference pattern
Amplitude (depth) of oscillations:
A = sin22q
A. Yu. Smirnov
n1m <--> n2m
n0 >> nR
Non-oscillatory transition
P = sin2 q
n2m
n1m
n2
n1
Mixing suppressed
n0 > nR
Resonance
interference suppressed
Adiabatic conversion + oscillations
n2m
n1m
n2
n1
n0 < nR
Small matter corrections
n2m
n1m
A. Yu. Smirnov
n2
n1
ne
p
N
p
m
nm
ne
nm - nt
vacuum
oscillations
nm
e
n
core
cosmic rays
nm - ne
oscillations
in matter
At low energies:
r = Fm /Fe = 2
atmosphere
Parametric effects in
nm - ne oscillations for
core crossing trajectories
mantle
n
detector
SuperKamiokande
Preliminary
1.9x10-3 < Dm2 < 3.0x10-3 eV2
0.90 < sin22q
at 90% C.L.
Dm2=2.4x10-3,sin22q=1.00
2min=37.8/40 d.o.f
(sin22q=1.02,
2min=37.7/40 d.o.f)
L/E analysis
Zenith angle analysis
90% allowed regions
4p + 2eAdiabatic conversion
in matter of the Sun
r : (150
4He
+ 2ne + 26.73 MeV
electron neutrinos are produced
F = 6 1010 cm-2 c-1
0) g/cc
Oscillations
in vacuum
n
J.N. Bahcall
total flux at the Earth
Oscillations
in matter
of the Earth
P. de Holanda, A.S.
solar data
solar data + KamLAND
sin2q13 = 0.0
KL
Dm2 = 6.3 10-5 eV2
tan2q = 0.39
Dm2 = 7.1 10-5eV2
tan2q = 0.40
Kamioka
Large Anti-Neutrino Detector
Reactor long baseline experiment
150 - 210 km
Liquid scintillation detector
ne + p ---> e+ + n
Epr > 2.6 MeV
Total rate
energy spectrum of events
LMA
precise determination of
the oscillation parameters
10% accuracy
Detection of the Geo-neutrinos
Epr > 1.3 MeV
1 kton of LS
Ue3 = sin q13 e-id
= <ne | n3 >
CHOOZ
Has important implications for
phenomenology and theory:
supernova neutrinos: can lead to
O(1) effect;
atmospheric neutrinos (resonance
enhancement, parametric effects);
allows to establish mass hierarchy;
LBL experiments;
CP-violations requires Ue3 = 0;
key test of models of large
lepton mixing
atmospheric
CHOOZ+atmospheric
sin22q13
tan q13
ne
nm nt
|2
|Ue3
?
n2
n1
Dm2atm
n2
n1
Dm2sun
Normal mass hierarchy
(ordering)
mass
mass
n3
Dm2sun
Dm2atm
|Ue3|2
n3
Inverted mass hierarchy
(ordering)
Type of mass spectrum: with Hierarchy, Ordering, Degeneracy
absolute mass scale
Type of the mass hierarchy: Normal, Inverted
Ue3 = ?
A Yu Smirnov
Heaviest mass:
m h ~ (0.04 - 0.4) eV
m h > Dm232 > 0.04 eV
Hierarchy of mass
squared differences:
| Dm122 / Dm232 | = 0.01 - 0.15
No strong hierarchy
of masses:
|m2 /m3| > |Dm122 / Dm232 | = 0.18
Bi-large or large-maximal
mixing between neighboring
families (1- 2) (2- 3):
1s
2-3
1-2
q12 + qC = q23 ~ 45o
bi-maximal + corrections?
+ 0.22
- 0.08
1-3
0
0.2
0.4
0.6
|sin q|
0.8
Mixing
Quarks
Leptons
1-2, q12
13o
32o
2-3, q23
2.3o
45o
1-3, q13
~ 0.5o
<13o
q12 + qC = q23 ~ 45o
Hierarchy of mass:
Neutrinos |m2 /m3| > 0.18
Charged
leptons
Down
quarks
Upquarks
1s
2-3
|m m/mt| = 0.06
1-2
|ms /mb| ~ 0.02 - 0.03
|mc /mt| ~ 0.005
1-3
0
0.2
0.4
0.6
|sin q|
0.8
Neutrino masses and mixing - important message
which we can not understand yet
In which terms, at which level
theory (principles) should be formulated?
masses mixing angles are
fundamental parameters
which show certain symmetry
Schemes with bi-maximal mixing,
or broken bi-maximal mixing;
Tri-bimaximal mixing
their properties, symmetries
at certain energy scale
observables are outcome,
can be to some extend accidental
numbers which do not reflect
the underlying symmetry
No regularities - ``anarchy’’
Smallness of neutrino masses
and pattern of lepton mixing
are related?
ne nm nt
Mass matrix for the flavor states
nf = ( ne, nm , nt )T, mf is not diagonal
nf = Un nmass
nmass = ( n1, n2, n3 )T
mf = UnT mdiag Un *
ne
nm
nt
(Majorana)
mdiag = diag ( m1, m2, m3)
In general (symmetry) basis the mass matrix of
the charged leptons is also non-diagonal
lS L = UlL l mass L
UP-MNS = UlL+ Un
l = (e, m, t)T
Lepton mixing --> the mismatch
of rotations of the neutrinos
and the charge leptons which
diagonalize the corresponding
mass matrices
Smallness of
neutrino
masses
NT Y L H + 1 NT MR N + h.c.
2
L = (n, l)T
N = ( n R) c
n
N
0
mD m = Y<H>
D
mDT MR
If MR >> mD
T. Yanagida
M. Gell-Mann, P. Ramond, R. Slansky
S. L. Glashow
R.N. Mohapatra, G. Senjanovic
mn
mD
MR
mn = - mDT MR-1 mD
Neutrality
QEM = 0,
QC = 0
Smallness
of neutrino
mass
Zero charges
-> can have Majorana mass
Right handed components:
singlets of the SM symmetry group
-> mass is unprotected by symmetry
can be large -- at the scale of
lepton number violation
What can testify ?
Maximal
or close to
maximal
2-3 mixing
|0.5 - sin2q23| << sin2q23
2n data fit:
Best fit value:
sin2 2q23 = 1.0
sin2 2q23 > 0.91, 90% CL
Degenerate
or partially
degenerate
spectrum
Very small
1 -3 mixing
Dm << m
q13 << q12 x q23
m1 = m 2 = m 3
m3 = m2 << m1
( inverted
hierarchy) ?
Dm/m0 ~ Dmatm2/2m02
Degenerate: m0 > (0.08 - 0.10) eV
Large or
maximal
mixing
Cosmology:
Mass
degeneracy
m0 = 0.20 +/- 10 eV
Heidelberg-Moscow
result
77.7 kg y
4.2s effect
mi > mee
Large scale structure analysis
including X-ray galaxy clusters
S.W Allen, R.W. Schmidt, S. L. Bridle
at least for one mass eigenstate
mee = (0.29 - 0. 60 ) eV (3s )
mee(b.f.) = 0.44 eV
H. Klapdor-Kleingrothaus,
et al.
Sensitivity
limit
Neutrinoless double beta decay
F. Feruglio, A. Strumia, F. Vissani
p
n
H-M
e
n x
e
n
p
mee = Sk Uek2 mk eif(k)
m1
Kinematic searches, cosmology
Both cosmology and
double beta decay
have similar sensitivities
Naively
excluded which implies
dominant structures
or/and degeneracy
in the mass matrix
sinq13 ~ sinq12 x sinq23
~ 0.3 - 0.5
A bit seriously
solar
sector
Mass scales:
Dmsun2
sinq13
Atmospheric
sector
Dmatm2
sinq13 ~ Dmsun2/ Dmatm2
~ 0.15 - 0.20
With comparable contribution from the charge leptons
If there is no cancellation:
sin2q13 ~ 0.01 - 0.05
?
Symmetry which leads to
maximal 2-3 mixing e.g.
Permutations, Z2
can give sin q13 = 0
Violation of
the symmetry
D23 = 0
sin q13 = 0
New symmetry
SO(3), A4, Z2 , ...
S Barshay,
M. Fukugita,
T. Yanagida
...
Quark -lepton
symmetry?
No particular symmetry
Deviation from
maximal mixing
Quark-lepton
analogy/symmetry
In the flavor
basis:
Features:
ne
nm
nt
mn = m0
1 0 0
0 0 1
0 1 0
+ dm
dm << m0
Degenerate spectrum: m1 = m2 = - m3
Maximal or near maximal 2-3 mixing
Opposite CP parities of n2 and n3
n2 and n3 form pseudo-Dirac pair
Neutrinoless double beta decay: mee~ m0
Most of the oscillation parameters are not imprinted
in to the dominant structure: all Dm2 the as well as
1-2 and 1-3 mixings are determined by dm.
dm is due to the radiative corrections?
E. Ma,
G. Rajasekaran
K.S. Babu,
J. Valle
A4
Symmetry group of even permutations of 4 elements
Symmetry of tetrahedron: (4 faces, 4 vertices)
Plato’s fire
Irreducible representations: 3, 1, 1’, 1’’
Transformations
under A4
(ni , ei ) ~ 3
u1c, d1c, e1c ~ 1
New heavy quarks leptons
and Higgs are introduced
(ui , di ) ~ 3
(i = 1, 2, 3)
u2c, d2c, e2c ~ 1’
H1,2 ~ 1
u3c, d3c, e3c ~ 1’’
Ui, U1c, Di, D1c, Ei, E1c, Nic , i ~ 3
Explicit asymmetry of charged fermions and neutrino sector:
no nic and Ni
Leads to different mixing
of quarks and leptons
Problem to include leptons and quarks in unique model
Symmetry between leptons and quarks is explicitly broken
Neutral and charge lepton sectors are different:
H1
ei
e1c
|
| < i >
Eic ----- Ei
ME
H2
A4 is broken
ni
|
Nic
MN
Extra symmetries
required (e.g. Z3)
i = 1, 2, 3
Majorana mass
Seesaw
Mixing - from the charged leptons in the symmetry basis
Mixing of quarks: UL+ UL = I
Mixing of leptons: ULT UL = M 0
Oscillation parameters are determined by dm
- an additional theory independent on A4 required
Masses and mixing angles are unrelated
1 1 1
UL = 1 w w2
1 w2 w
w = exp (-2ip/3)
No symmetry
Symmetry
- New leptons and quarks;
- Extended non-trivial Higgs sector to break symmetry;
- Additional symmetries to suppress unwanted interactions
of new particles
Often - difficult to embed into Grand Unified schemes
Profound implications
or
Misleading approach
??
??
1). The only serious indication is nearly maximal 2-3 mixing:
sin2 2q23 > 0.91, 90 % CL
2). sin2 2q23 is a ``bad’’ parameter from theoretical point of view
sin2q23 is better, but for this parameter:
sin2q23 = (0.35 - 0.65) 90 % CL
Relative deviation from maximal mixing (1/2) can be large
Dsin2q23 /sin2q23 ~ 0.7
3). The atmospheric neutrino results may provide some hint
that the mixing is not maximal
Excess of the
e-like events (?)
Three neutrino analysis
of data is needed
Best fit
sin22q=1.0, Dm2=2.0x10-3 eV2
Null oscillation
nm  nt
Sub-GeV e-like
Sub-GeV Multi-R
m-like
Up stop m
Multi-GeV Multi-R
m-like
Up thru m
Sub-GeV m-like
Multi-GeV m-like
+ PC
Multi-GeV e-like
~13000km ~500km
~15km
SuperKamiokande
Excess of the e-like events in sub-GeV
Fe
- 1 = P2 ( r c232 - 1)
0
Fe
``screening factor’’
P2 = P(Dm212 , q12) is the 2n transition
probability
In the sub-GeV sample
r = Fm0 / Fe0 ~ 2
The excess is zero for
maximal 23- mixing
Searches of the excess can be used
to restrict deviation of the 2-3 mixing
from maximal
Zenith angle dependences
of the e-like events
0.Peres, A.S.
Dm2 = 0
Dm2 = 0
sin2q23= 0.45 - 0.47
M. C. Gonzalez-Garcia
M. Maltoni, A.S.
2-3 mixing differs
from maximal one
No special symmetry
for neutrinos or leptons
I. Dorsner, A. S
Approximate quark-lepton
symmetry (analogy, correspondence)
Family structure, weak interfamily connections
no large mixing in the original mass matrices
All quark and lepton mass matrices have
similar structure with ``flavor alignment’’
Seesaw mechanism of
neutrino mass generation
qij ~ mi/mj
qatm = 36 - 380
Large lepton mixing is
the artifact of seesaw
Quarks-Lepton symmetry is realized in terms of the mass matrices
(matrices of the Yukawa couplings).
For the Dirac mass matrices of all quarks and leptons:
YU ~ YD ~ YnD ~ YL ~ Y0
Specifically:
Yf = Y0 + DYf
( Y0)ij << (DYf)ij
(implies large tan b)
f = U, D, L, nD
Y0 is ``unstable’’: det (Y0) ~ 0 (as well as determinants of sub-matrices)
small perturbations produce significant change of masses and and mixings
Assume:
Y=
a11 e4
a21 e3
a31 e2
a12 e3 a13 e2
a22 e2 a23 e
a32 e
1
e ~ 0.2 - 0.3
|aij|= 1 + O(e)
Observables (masses and mixings) appear as small perturbations
of the dominant structure given by Y0 .
Enhances (by factor
~ 2) the mixing
which comes from
diagonalization of
the neutrino mass
matrix
For the RH neutrino
mass matrix we take
for simplicity the same
form
Leads to smallness
of neutrino masses
MR ~ Y0
Changes the relative
sign of ``rotations’’
which diagonalize
mass matrices of the
charge leptons and
neutrinos
quark mixing:
lepton mixing:
VCKM = U (up)+ U(down)
VP-MNS = U(l)+ U(n)
For quarks the up and down rotations cancel each other
leading to small mixing whereas for leptons they sum up
producing large mixing
U
D
qCKM
It is the see-saw leads to flip of
the sign of rotation which
diagonalizes the neutrino mass matrix
Enhances 22 and 23 elements
n
S. Barshay
L
qPMNS
changes the sign
of the 23-elements
leads to m(22) > m(33)
e is determined by inequality of masses of the s-quark and the muon
(one would expect mm = ms in the case of exact q-l symmetry )
ms/mb = kq e3
mm /mt = kL e3
kf e ~ a22 - a23 2
These mass ratios can be reproduces for aij = 1 + O(e) if
e > 0.25
e ~ 0.26
|aij(l)| =
1.00
...
...
0.91 1.01
1.26 0.74
. . . 1.00
1.0000
|aij(M)| = . . .
...
1.0026
1.0005
...
m1 = 0.0017 eV
|sin2q13| = 0.005
1.00
|aij(D )| = . . .
...
1.0000
1.0007
1.0000
1.26 1.00
1.09 1.05
. . . 1.00
For quarks deviations of |aij|
from 1 are smaller than 15%
mee = 0.001 - 0.005 eV
Generically |sinq13| ~ (1 - 3)e 2
Masses of the RH neutrinos:
M1 = 1.2 1010 GeV
M2 = 5.8 1010 GeV
M3 = 8.8 1014 GeV
Strong hierarchy: seesaw
enhancement of 23-mixing
No special symmetry for neutrinos of
for lepton sector
Y0 can be reproduced with U(1) family symmetry
and charges q, q + 1, q + 2 charges,
if unut charge is associated with
one degree of e ( a la Froggatt-Nielsen)
Violation of the symmetry appears
at the level e2 - e3 ~ (1 - 3) 10-2
If the flavor symmetry is at GU scale its
violation can come e.g. from the string scale
One of the main results is an amazing
pattern of the lepton mixing which
differs strongly from the quark mixing
The key question to the underlying physics is
if there is a new (different from quark) symmetry
behind neutrino mass spectrum and mixing
- maximal (near) maximal 2-3 mixing
- degenerate spectrum
- probably, small 1-3 mixing
New symmetry of Nature,
which is realized (manifest
itself) in the properties
of neutrinos or lepton sector.
Nothing special: weakly broken
quark-lepton symmetry;
family structure, small interfamily
mixing. Large lepton mixing artifact of the seesaw mechanism
Neutrinos can shed some light on the
fermion mass problem in general.
Hint: flavor alignment, e ~ 0.25 ,
``unstable’’ mass matrices, U(1)
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