Transcript No Slide Title

A. Yu. Smirnov
International Centre for Theoretical Physics, Trieste, Italy
Institute for Nuclear Research, RAS, Moscow, Russia
NO-VE 2006: ``Ultimate Goals’’
Two fundamental issues
Mixing
Quarks
Leptons
1-2, q12
13o
34o
2-3, q23
2.3o
45o
1-3, q13
~ 0.5o
<10o
Hierarchy of masses:
Neutrinos |m2 /m3| ~ 0.2
Charged |m m/mt| = 0.06
leptons
Down
|ms /mb| ~ 0.02 - 0.03
quarks
Up-quarks |mc /mt| ~ 0.005
2-3
1-2
1s
1-3
0
0.2
0.4
0.6
|sin q|
0.8
1
up
quarks
10-1
down
quarks
charged
leptons
neutrinos
Regularities?
mu mt = mc2
10-2
Vus Vcb ~ Vub
10-3
Koide relation
10-4
10-5
at mZ
Can both
features be
accidental?
Neutrino mass matrix
in the flavor basis:
For charged
leptons: D = 0
A
B
B
B B
C D
D C
nm - nt
permutation
symmetry
Often related to equality
of neutrino masses
Discrete symmetries S3, D4
Can this symmetry be extended
to quark sector?
Are quarks and leptons
fundamentally different?
A. Joshipura,
hep-ph/0512252
2-3 symmetry
Maximal (large)
2-3 leptonic mixing
Smallness of Vcb
Universal mass
matrices
2-3 symmetry
Does not contradict
mass hierarchy
X AA
A B C
A C B
+ dm
Quarks, charged leptons: B ~ C, X << A << B
Neutrinos: B >> C, X ~ B
- Hierarchical mass spectrum
- Small quark mixing
- Degenerate neutrino
mass spectrum;
- Large lepton mixing
additional symmetries are needed to
explain hierarchies/equalities of parameters
nm - nt permutation
symmetry
A
B
B
B B
C D
D C
Matrix for the best fit values
of parameters (in meV)
3.2
6.0
24.8
0.6
21.4
30.7
sin2q13 = 0.01
sin2q23 = 0.43
Bari group
Substantial deviation from
symmetric structure
Structure of mass matrix is sensitive to small deviations
Of 1-3 mixing from zero and 2-3 mixing from maximal
Similar gauge structure,
correspondence
Very different mass
and mixing patterns
Particular symmetries in
leptonic (neutrino) sector?
Q-L complementarity?
Symmetry
correspondence
Is this seesaw?
Something beyond seesaw?
Neutrality
Qg = 0
Qc = 0
Majorana
masses
Basis of
seesaw
mechanism
mix with
singlets
of the SM
Dynamical
effects
Is this enough to
explain all salient
properties of
neutrinos?
Window to hidden world?
A
Standard Model
s
nl
l
lR
H
S
A
nR
L
S
...
...
M
S
s
Planck scale physics
Screening of the Dirac structure
Induced effects of new neutrino states
ur , ub , uj <-> n
dr , db , dj <-> e
Correspondence:
color
Symmetry:
Leptons as
Unification:
Can it be
accidental?
4th
color
Pati-Salam
form multiplet of the extended
gauge group, in particular,
16-plet of SO(10)
More complicated connection between quarks and leptons?
Complementarity?
generically
Provide with all the
ingredients necessary
for seesaw mechanism
Give relations
between masses of
leptons and quarks
mb = m t
In general: ``sum rules’’
RH neutrino components
Large mass scale
Lepton number violation
b - t unification
large 2-3
leptonic mixing
But - no explanation
of the flavor structure
approximate
I. Dorsner, A.S.
NPB 698 386 (2004)
is realized in terms of the mass matrices (matrices of the Yukawa couplings)
and not in terms of observables – mass ratios and mixing angles.
Eigenvalues = masses
Mass
matrices
M=YV
Eigenstates = mixing
Universal structure
for mass matrices of
all quarks and leptons
in the lowest approximation:
Small perturbations:
YU = YD = YnD = YL = Y0
Yf = Y0 + DYf
( Y0)ij >> (DYf)ij
f = u, d, L, D, M
Important example:
Y0 =
l4 l3 l2
l3 l2 l
l2 l
1
l ~ 0.2 - 0.3
Unstable with respect to small perturbations
Yfij = Y0ij (1 + efij)
Universal
singular
Small perturbations allow to explain
large difference in mass hierarchies
and mixings of quarks and leptons
f = u, d, e, n
Perturbations
e ~ 0.2 – 0.3
Form of perturbations
is crucial
Seesaw: m ~ 1/M
Nearly singular matrix of RH neutrinos leads to
- enhancement of lepton mixing
- flip of the sign of mixing angle,
so that the angles from the charged leptons
and neutrinos sum up
In some (universality) basis in the first approximation
all the mass matrices but Ml (for the charged leptons)
are diagonalized by the same matrix V:
For the charged leptons, the mass
is diagonalized by V*
Diagonalization:
V for
V* for
u, d, n
l
In the first approximation
Quark mixing:
Lepton mixing:
VCKM = V+ V = I
VPMNS = VT V
A Joshipura, A.S.
hep-ph/0512024
V+ Mf V = Df
VT Ml V* = Dl
Ml = MdT
SU(5) type relation
Another version
is when neutrinos
have distinguished
rotation:
V for u, d, l
V* for n
In general, up and down fermions can be diagonalized
by different matrices V’ and V respectively
VCKM = V’+ V
VPMNS = VT V’
VPMNS = VTV VCKM+ = V0PMNS VCKM +
VPMNS VCKM = VTV
V0PMNS
=
VTV
VPMNS
(with CKM corr.)
Quark and lepton rotations
are complementary to VVT
- symmetric, characterized by 2 angles;
- close to the observed mixing for q/2 ~ f ~ 20 – 25o
- 1-3 mixing near the upper bound
- gives very good description of data
- predicts sin q13 > 0.08
Universal mixing and universal matrices
Mu, n ~ m D* A D*
Md ~ m D*A D
D = diag(1, i, 1)
A~
e12 e22
...
Ml ~ m D A D*
A is the universal matrix:
e12 e2
e1 e 2
e1 e2
e1
1
ei ~ 0.2 – 0.3
Can be embedded in to SU(5) and SO(10)
with additional assumptions
ql
ql
12
23
+
qq12 ~
+
qq23
p/4
~ p/4
qsol + qC = 46.7o +/- 2.4o
A.S.
M. Raidal
H. Minakata
qatm + V cb = 45o +/- 3o
1s
Difficult to expects exact equalities
but 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
H. Minakata, A.S.
Phys. Rev. D70: 073009 (2004)
[hep-ph/0405088]
``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
In the lowest
approximation:
Vquarks = I, Vleptons =Vbm
m1 = m 2 = 0
sin qC = 0.22
as ``quantum’’ of
flavor physics
sinqC = mm /mt
sinqC ~ sin q13
Appears in different
places of theory
F. Vissani
V. Barger et al
Ubm = U23mU12m
Two maximal
rotations
Ubm =
½ ½ 0
-½ ½ ½
½ -½ ½
UPMNS = Ubm
- maximal 2-3 mixing
- zero 1-3 mixing
- maximal 1-2 mixing
- no CP-violation
In the lowest order?
Corrections?
As dominant structure?
Zero order?
Contradicts
data at
(5-6)s level
UPMNS = U’ Ubm
U’ = U12(a)
Generates
simultaneously
Deviation of
1-2 mixing
from maximal
Non-zero
1-3 mixing
H. Minakata, A.S.
R. Mohapatra,
P. Frampton,
C. W.Kim et al.,
S. Pakvasa …
QLC-1
Charged
leptons
Neutrinos
sinq12 =
sinq13 =
QLC-2
CKM mixing
m l ~ md
q-l symmetry
Maximal mixing
mDT M-1 mD
sin(p/4 - qC) + 0.5sin qC( 2 - 1)
tan2q12 = 0.495
sin qC/ 2
Maximal mixing
CKM mixing
mD ~ m u
q-l symmetry
sin(p/4 - qC)
~ Vub
Utbm = Utm Um13
UQLC1 = UC Ubm
Give the almost
same 12 mixing
coincidence
QLC2
QLC1 tbm
3s
2s
1s
SNO (2n)
Strumia-Vissani
99%
90%
Fogli et al
29
31
33
3n - analysis does change bft
but error bars become smaller
35
37
39
q12 + qC ~ p/4
q12
L. Wolfenstein
P. F. Harrison
D. H. Perkins
W. G. Scott
Utbm = U23(p/4)U12
Utbm =
2/3
1/3
- 1/6
1/3
1/6 - 1/3
- maximal 2-3 mixing
- zero 1-3 mixing
- no CP-violation
0
1/2
1/2
n3 is bi-maximally mixed
n2 is tri-maximally mixed
sin2q12 = 1/3 in agreement with 0.315
Mixing parameters - some simple numbers 0, 1/3, 1/2
Relation to group matrices?
S3 group matrix
In flavor basis…
relation to masses?
No analogy in the
Quark sector?
Implies non-abelian
symmetry
In agreement with 0 value
T2K
Double CHOOZ
Dm212/Dm322
QLC1
qC
99% Strumia-Vissani
90%
3s
2s
1s
0
0.01
0.02
0.03
0.04
0.05
Fogli et al
sin2q13
Non-zero central value (Fogli, et al): Atmospheric neutrinos,
SK spectrum of multi-GeV e-like events
Lower theoretical bounds: Planck scale effects
RGE- effects
V.S. Berezinsky F. Vissani
M. Lindner et al
1). Superheavy MS >> vEW - decouple
2). Heavy: vEW >> mS >> mn
3). Light: mS ~ mn play role in dynamics of oscillations
Double (cascade) seesaw
m=
0
mDT
0
mD 0
0
MDT
MD MS
n
N
S
MR = - MDT MS-1 MD
mn = mD MD-1 MS MD-1mD
If MD = A-1mD
mn = A2 MS
Additional
fermions
mD << MD << MS
M. Lindner
M. Schmidt
A.S.
JHEP0507,
048 (2005)
R. Mohapatra
PRL 56, 561, (1986)
R. Mohapatra.
J. Valle
MS – Majorana mass
matrix of new fermions S
A ~ vEW/MGU
A.S.
PRD 48, 3264 (1993)
mD similar (equal) to quark mass matrix - cancels
Structure of the neutrino mass matrix is determined by MS
-> physics at highest (Planck?) scale immediately
Reconciling Q-L symmetry
and different mixings
of quarks and leptons
Seesaw provides scale and not
the flavor structure of neutrino mass matrix
Structure of the neutrino mass matrix is determined by
MS
origin of
``neutrino’’
symmetry
MS ~ MPl ?
leads to quasi-degenerate
spectrum if e.g. MS ~ I,
origin of maximal
(or bi-maximal) mixing
Q-l complementarity
Mixing with sterile states change structure
of the mass matrix of active neutrinos
Active neutrinos acquire (e.g. via seesaw) the Majorana mass matrix ma
Consider one state S which has
- Majorana mass M and
- mixing masses with active neutrinos, miS (i = e, m, t)
After decoupling of S the active neutrino mass matrix becomes
(mn)ij = (ma )ij - miSmjS/M
induced mass matrix
sinqS = mS/M
mind = sinqS2 M
mind = sinqS M
2
sinqS2 M > 0.02 – 0.03 eV
sinqS M ~ 0.003 eV
2
sinqS2 M < 0.001 eV
Induced matrix can reproduce the following
structures of the active neutrino mass
Dominant structures for normal and
inverted hierarchy
Sub-leading structures for normal
hierarchy
Effect is negligible
In the case of normal mass hierarchy
mtbm
1
~ m2/3 1
1
1
1
1
1
1
1
+ m3/2
0
0
0
0 0
1 -1
-1 1
m2 = Dmsol2
Assume the coupling of S with active neutrinos is flavor blind (universal):
miS = mS = m2 /3
Then mind can reproduce the first matrix
mtbm = ma + mind
ma is the second matrix
Two sterile neutrinos can reproduce whole tbm-matrix
R. Zukanovic-Funcal, A.S.
in preparation
Two regions are allowed:
MS ~ 0.1 – 1 eV
and MS > (0.1 – 1) GeV
Q & L:
- strong difference of mass and mixing pattern;
- possible presence of the special leptonic (neutrino) symmetries;
- quark-lepton complementarity
This may indicate that q & l are fundamentally different
or some new structure of theory exists (beyond seesaw)
Still approximate quarks and leptons
universality can be realized.
Mixing with new neutrino states can play the
role of this additional structure:
- screening of the Dirac structure
- induced matrix with certain symmetries.
SK (3n) - no shift from maximal mixing
sin22q23 > 0.93, 90% C.L.
T2K
QLC1
3s
2s
1s
90%
maximal mixing
QLC2
SK (3n)
Gonzalez-Garcia,
Maltoni, A.S.
Fogli et al
0.2
0.3
0.4
0.5
0.6
0.7
sin2q23
1). in agreement with maximal
2). shift of the bfp from maximal is small
3). still large deviation is allowed:
(0.5 - sin2q23)/sin q23 ~ 40%
2s
R. Zukanovic-Funcal, A.S.
in preparation
Possibility that their
properties are related
to very high scale physics
Smallness of mass
Large mixing
Violate fundamental
symmetries, Lorentz inv.
CPT, Pauli principle?
Can propagate
in extra dimensions
Manifestations of
non- QFT features?