Neutrino mass and mixing:

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Neutrino mass and mixing

Leptons versus Quarks
A. Yu. Smirnov
International Centre for Theoretical Physics,
Trieste, Italy Institute for Nuclear
Research, RAS, Moscow, Russia
NO-VE 2006 Ultimate Goals
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Leptons vs Quarks

Unification of
Understanding
particles and forces
Fermion
Masses
GUT's, Strings...
Two fundamental issues
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Comparing results

Quarks
Leptons
Mixing
1-2, q12
13o
34o
2-3, q23
2.3o
45o
1-3, q13
0.5o
lt10o
Hierarchy of masses
m2 /m3 0.2
Neutrinos
2-3
Charged leptons
m m/mt 0.06
1-2
ms /mb 0.02 - 0.03
Down quarks
1s
1-3
mc /mt 0.005
Up-quarks
0 0.2 0.4 0.6
0.8
sin q
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Mass Ratios

up down charged
neutrinos quarks quarks leptons
Regularities?
1
10-1
mu mt mc2
10-2
Vus Vcb Vub
10-3
Koide relation
10-4
Mass-mixing
10-5
relation?
at mZ
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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
Can this symmetry be extended to quark sector?
A B B B C D B D C
Are quarks and leptons fundamentally different?
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Universal 2-3 symmetry?

A. Joshipura, hep-ph/0512252
2-3 symmetry
2-3 symmetry Does not contradict mass hierarchy
Maximal (large) 2-3 leptonic mixing
Smallness of Vcb
X A A A B C A C B
Universal mass matrices
dm
- Hierarchical mass spectrum - Small quark mixing
Quarks, charged leptons B C, X ltlt A ltlt B
- Degenerate neutrino mass spectrum - Large
lepton mixing
Neutrinos B gtgt C, X B
additional symmetries are needed to explain
hierarchies/equalities of parameters
Still
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Remark

nm - nt permutation symmetry
Matrix for the best fit values of parameters (in
meV)
A B B B C D B D C
3.2 6.0 0.6 24.8 21.4
30.7
sin2q13 0.01
Bari group
sin2q23 0.43
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
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Additional structure?

Very different mass and mixing patterns
Similar gauge structure, correspondence
Particular symmetries in leptonic (neutrino)
sector?
Q-L complementarity?
Lepton sector
Quark sector
Symmetry correspondence
Additional structure exists which produces the
difference.

Is this seesaw? Something beyond seesaw?
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The hope is

Neutrality
Majorana masses
Basis of seesaw mechanism
Qg 0 Qc 0
Is this enough to explain all salient
properties of neutrinos?
mix with singlets of the SM
Dynamical effects
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Window to hidden world?

A
S
Standard Model
A
nl
nR
S
l
...
s
L
lR
...
H
M
S
s
Planck scale physics
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Plan

Symmetry Unification
Quark-lepton
Universality
Complementarity
Diversity
Screening of the Dirac structure Induced effects
of new neutrino states
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Quark-Lepton symmetry

ur , ub , uj lt-gt n dr , db , dj lt-gt e
Correspondence
color
Pati-Salam
Symmetry
Leptons as 4th color
form multiplet of the extended gauge group, in
particular, 16-plet of SO(10)
Unification
Can it be accidental?
More complicated connection between quarks and
leptons? Complementarity?
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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
But - no explanation of the flavor structure
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2. Quark-Lepton
universality
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Universality
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 Y V
diagonalization
Eigenstates mixing
Universal structure for mass matrices of all
quarks and leptons in the lowest approximation
YU YD YnD YL Y0
Yf Y0 DYf
( Y0)ij gtgt (DYf)ij
Small perturbations
f u, d, L, D, M
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Singular mass matrices

Important example
Det M 0
l4 l3 l2 Y0 l3 l2
l l2 l 1
l 0.2 - 0.3
Unstable with respect to small perturbations
Yfij Y0ij (1 efij)
f u, d, e, n
Perturbations e 0.2 0.3
Universal singular
Small perturbations allow to explain large
difference in mass hierarchies and mixings of
quarks and leptons
Form of perturbations is crucial
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Seesaw plays crucial role
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
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Universality of mixing

A Joshipura, A.S. hep-ph/0512024
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
V Mf V Df
For the charged leptons, the mass
VT Ml V Dl
is diagonalized by V
V for u, d, n V for l
Ml MdT
Diagonalization
SU(5) type relation
In the first approximation
Another version is when neutrinos have
distinguished rotation
Quark mixing
VCKM V V I
Lepton mixing
VPMNS VT V
V for u, d, l V for n
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In general

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
Quark and lepton rotations are complementary to
VVT
VPMNS VCKM VTV
- symmetric, characterized by 2 angles - close
to the observed mixing for q/2 f 20 25o -
1-3 mixing near the upper bound
V0PMNS VTV

• gives very good description of data
• predicts sin q13 gt 0.08

VPMNS (with CKM corr.)
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Origin of universal mixing

Universal mixing and universal matrices
Ml m D A D
Mu, n m D A D
Md m DA D
D diag(1, i, 1)
A is the universal matrix
e12 e22 e12 e2 e1 e2 . . .
e1 e 2 e1 1
ei 0.2 0.3
A
Can be embedded in to SU(5) and SO(10) with
additional assumptions
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3. Quark-Lepton
complementarity
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Quark-Lepton Complementarity

A.S. M. Raidal H. Minakata
ql12 qq12 p/4
qsol qC 46.7o /- 2.4o
qatm V cb 45o /- 3o
ql23 qq23 p/4
1s
H. Minakata, A.S. Phys. Rev. D70 073009 (2004)
hep-ph/0405088
Difficult to expects exact equalities but
qualitatively
2-3 leptonic mixing is close to maximal because
2-3 quark mixing is small
may not be accidental
1-2 leptonic mixing deviates from maximal
substantially because 1-2 quark mixing is
relatively large
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Possible implications

Lepton mixing bi-maximal mixing quark
mixing
Quark-lepton symmetry
sin qC 0.22 as quantum of flavor physics
or
Existence of structure which produces bi-maximal
mixing
sinqC mm /mt
Mixing matrix weakly depends on mass eigenvalues
sinqC sin q13
Appears in different places of theory
Vquarks I, Vleptons Vbm m1 m2 0
In the lowest approximation
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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
Deviation of 1-2 mixing from maximal
Generates simultaneously
In the lowest order? Corrections?
UPMNS U Ubm
Non-zero 1-3 mixing
U U12(a)
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H. Minakata, A.S. R. Mohapatra, P. Frampton, C.
W.Kim et al., S. Pakvasa
Possible scenarios

QLC-2
QLC-1
CKM mixing
Charged leptons
Maximal mixing
ml md
q-l symmetry
CKM mixing
Maximal mixing
Neutrinos
q-l symmetry
mD mu
mDT M-1 mD
sin(p/4 - qC) 0.5sin qC( 2 - 1)
sinq12
sin(p/4 - qC)
tan2q12 0.495
Vub
sinq13
sin qC/ 2
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1-2 mixing
Utbm Utm Um13
UQLC1 UC Ubm

Give the almost same 12 mixing
coincidence
tbm
QLC2
QLC1
3s
SNO (2n)
2s
1s
Strumia-Vissani
99
90
Fogli et al
29 31 33 35 37 39
q12
3n - analysis does change bft but error bars
become smaller
q12 qC p/4
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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 U23(p/4)U12
Utbm
n3 is bi-maximally mixed
n2 is tri-maximally mixed
- maximal 2-3 mixing - zero 1-3 mixing - no
CP-violation
sin2q12 1/3 in agreement with 0.315
In flavor basis relation to masses? No analogy
in the Quark sector? Implies non-abelian
symmetry
Mixing parameters - some simple numbers 0, 1/3,
1/2
Relation to group matrices?
S3 group matrix
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1-3 mixing
In agreement with 0 value

T2K
Double CHOOZ
Dm212/Dm322
qC
QLC1
Strumia-Vissani
99
90
3s
Fogli et al
2s
1s
0 0.01 0.02 0.03 0.04 0.05
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
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4. Effects of new
neutrino states
1). Superheavy MS gtgt vEW - decouple
2). Heavy vEW gtgt mS gtgt mn
3). Light mS mn play role in dynamics
of oscillations
two applications
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Screening of Dirac structure

M. Lindner M. Schmidt A.S. JHEP0507, 048 (2005)
Double (cascade) seesaw
0 mD 0 m mDT
0 MDT 0 MD MS
n N S
Additional fermions
mD ltlt MD ltlt MS
R. Mohapatra PRL 56, 561, (1986)
MR - MDT MS-1 MD
R. Mohapatra. J. Valle
MS Majorana mass matrix of new fermions S
mn mD MD-1 MS MD-1mD
A.S. PRD 48, 3264 (1993)
A vEW/MGU
If MD A-1mD
mn A2 MS
mD similar (equal) to quark mass matrix -
cancels
Structure of the neutrino mass matrix is
determined by MS -gt physics at highest (Planck?)
scale immediately
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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 MPl ?
MS
leads to quasi-degenerate spectrum if e.g. MS
I,
origin of neutrino symmetry
origin of maximal (or bi-maximal) mixing
Q-l complementarity
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Induced mass matrix

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
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Effects and benchmarks

Induced matrix can reproduce the following
structures of the active neutrino mass
mind sinqS2 M
Dominant structures for normal and inverted
hierarchy
sinqS2 M gt 0.02 0.03 eV
Sub-leading structures for normal hierarchy
sinqS2 M 0.003 eV
Effect is negligible
sinqS2 M lt 0.001 eV
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Tri-bimaximal mixing

In the case of normal mass hierarchy
0 0 0 0 1 -1 0 -1 1
1 1 1 1 1 1 1 1 1
m2 Dmsol2
mtbm m2/3 m3/2
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
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Bounds on active-sterile mixing

Two regions are allowed
R. Zukanovic-Funcal, A.S. in preparation
MS 0.1 1 eV
MS gt (0.1 1) GeV
and
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Summary

• 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.

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2-3 mixing
SK (3n) - no shift from maximal mixing
sin22q23 gt 0.93, 90 C.L.

T2K
maximal mixing
QLC1
QLC2
SK (3n)
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
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
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Bounds on active-sterile mixing

R. Zukanovic-Funcal, A.S. in preparation
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Are Neutrino Particles just like

the other Fundamental Fermions?
Possibility that their properties are related to
very high scale physics
Why not?
Violate fundamental symmetries, Lorentz
inv. CPT, Pauli principle?
Smallness of mass Large mixing
Can propagate in extra dimensions
Manifestations of non- QFT features?