A. Yu. Smirnov
International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia
NO-VE 2006: ``Ultimate Goals’’NO-VE 2006: ``Ultimate Goals’’
Two fundamental issuesTwo fundamental issues
Hierarchy of masses:Hierarchy of masses:
|m2 /m3| ~ 0.2
|sin |0 0.2 0.4 0.6 0.8
1-3
1-2
2-3
1
1-2, 12
2-3, 23
1-3, 13
QuarksQuarks LeptonsLeptons
13o
2.3o 45o
~ 0.5o
34o
<10o
MixingMixing
|m /m| = 0.06
Neutrinos
Chargedleptons
|ms /mb| ~ 0.02 - 0.03Down
quarks|mc
/mt| ~ 0.005Up-quarks
up down charged neutrinosquarks quarks leptons
10-1
10-2
10-3
10-4
10-5
1
mu mt = mc2
mu mt = mc2
Vus Vcb ~ Vub Vus Vcb ~ Vub
at mZ
Regularities?
Koide relationKoide relation
permutation symmetry
Neutrino mass matrix in the flavor basis:
A B B B C DB D C
Discrete symmetries S3, D4
Can bothfeatures be accidental?
Often related to equality of neutrino masses
For charged leptons: D = 0
For charged leptons: D = 0
Are quarks and leptons fundamentally different?
Are quarks and leptons fundamentally different?
Can this symmetry be extended to quark sector?
Can this symmetry be extended to quark sector?
A. Joshipura, hep-ph/0512252
A. Joshipura, hep-ph/0512252
Smallness of VcbSmallness of Vcb Maximal (large)
2-3 leptonic mixing
Maximal (large) 2-3 leptonic mixing
2-3 symmetry2-3 symmetry
X A AA B C A C B
X A AA B C A C B
Universal mass matrices
Universal mass matrices + m+ m
Quarks, charged leptons: B ~ C, X << A << BQuarks, charged leptons: B ~ C, X << A << B
Neutrinos: B >> C, X ~ BNeutrinos: B >> C, X ~ B
- Hierarchical mass spectrum- Small quark mixing
- Hierarchical mass spectrum- Small quark mixing
- Degenerate neutrino mass spectrum; - Large lepton mixing
- Degenerate neutrino mass spectrum; - Large lepton mixing
additional symmetries are needed to explain hierarchies/equalities of parameters
additional symmetries are needed to explain hierarchies/equalities of parameters
2-3 symmetryDoes not contradictmass hierarchy
2-3 symmetryDoes not contradictmass hierarchy
A B B B C DB D C
permutation symmetry
Matrix for the best fit valuesof parameters (in meV)
Matrix for the best fit valuesof parameters (in meV)
3.2 6.0 0.6 24.8 21.4 30.7
Bari groupBari groupsin213 = 0.01sin223 = 0.43
Substantial deviation from symmetric structure
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
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 Similar gauge structure,correspondence
Very different massand mixing patternsVery different massand mixing patterns
Particular symmetries in leptonic (neutrino) sector?
Particular symmetries in leptonic (neutrino) sector?
Q-L complementarity?Q-L complementarity?
Additional structure
exists which
produces
the difference.
Additional structure
exists which
produces
the difference.
Is this seesaw? Something beyond seesaw?
Is this seesaw? Something beyond seesaw?
Symmetrycorrespondence
Symmetrycorrespondence
Majorana massesMajorana masses
Q = 0 Qc = 0
Is this enough to explain all salient properties of neutrinos?
mix with singlets of the SM
mix with singlets of the SM
Neutrality
Basis of seesawmechanism
Basis of seesawmechanism
Dynamicaleffects
Dynamicaleffects
l
lL
lR
Standard Model
...
...
H
S
Window to hidden world?
M
S
s
R
A
A
Planck scale physicsPlanck scale physics
s
SS
Screening of the Dirac structureInduced effects of new neutrino states
Correspondence: ur , ub , uj <-> dr , db , dj <-> e
color
Symmetry: Leptons as 4th color
Unification:form multiplet of the extendedgauge group, in particular, 16-plet of SO(10)
Pati-Salam
Can it be accidental?
More complicated connection between quarks and leptons? Complementarity?
Provide with all the ingredients necessary for seesaw mechanism
Large mass scaleLarge mass scale
Lepton number violationLepton number violation
RH neutrino componentsRH neutrino components
Give relations between masses of leptons and quarks
genericallygenerically
mb = m
b - unification
In general: ``sum rules’’
But - no explanation of the flavor structure
But - no explanation of the flavor structure
large 2-3 leptonic mixing
is realized in terms of the mass matrices (matrices of the Yukawa couplings) and not in terms of observables – mass ratios and mixing angles.
YU = YD = YD = YL = Y0 YU = YD = YD = YL = Y0
Universal structure for mass matrices of all quarks and leptonsin the lowest approximation:
Yf = Y0 + Yf Yf = Y0 + Yf ( Y0)ij >> (Yf)ij
( Y0)ij >> (Yf)ij f = u, d, L, D, M
approximate
Mass matricesM = Y V
Mass matricesM = Y V
diagonalization
Eigenvalues = masses
Eigenstates = mixing
Small perturbations:
I. Dorsner, A.S.NPB 698 386 (2004)
I. Dorsner, A.S.NPB 698 386 (2004)
Small perturbations allow to explain large difference in mass hierarchies and mixings of quarks and leptons
Unstable with respect to small perturbations
Yfij = Y0
ij (1 + fij)
Yf
ij = Y0ij (1 + f
ij)
Universalsingular
f = u, d, e,
Perturbations ~ 0.2 – 0.3
4 3 2
Y0 = 3 2 2 ~ 0.2 - 0.3 ~ 0.2 - 0.3
Form of perturbationsis crucial
Form of perturbationsis crucial
Important example:Important example:
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
Seesaw: m ~ 1/MSeesaw: m ~ 1/M
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:
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 For the charged leptons, the mass VT Ml V* = Dl
is diagonalized by V*is diagonalized by V*
Ml = MdTV for u, d,
V* for l
V for u, d, V* for lDiagonalization:Diagonalization:
SU(5) type relationSU(5) type relation
Quark mixing:Quark mixing:VCKM = V+ V = IVCKM = V+ V = I
Lepton mixing:Lepton mixing:VPMNS = VT V VPMNS = VT V
In the first approximationIn the first approximation
A Joshipura, A.S.hep-ph/0512024
A Joshipura, A.S.hep-ph/0512024
Another version is when neutrinos have distinguished rotation:
Another version is when neutrinos have distinguished rotation:
V for u, d, l V* for
V for u, d, l V* for
VCKM = V’+ V VCKM = V’+ V VPMNS = VT V’ VPMNS = VT V’
In general, up and down fermions can be diagonalized by different matrices V’ and V respectively
In general, up and down fermions can be diagonalized by different matrices V’ and V respectively
VPMNS = VTV VCKM+ = V0
PMNS VCKM
+ VPMNS = VTV VCKM+ = V0
PMNS VCKM
+
VPMNS VCKM = VTV VPMNS VCKM = VTV Quark and lepton rotations are complementary to VVT
Quark and lepton rotations are complementary to VVT
V0PMNS = VTV V0
PMNS = VTV - symmetric, characterized by 2 angles;- close to the observed mixing for /2 ~ ~ 20 – 25o - 1-3 mixing near the upper bound
- symmetric, characterized by 2 angles;- close to the observed mixing for /2 ~ ~ 20 – 25o - 1-3 mixing near the upper bound
- gives very good description of data - predicts sin 13 > 0.08
- gives very good description of data - predicts sin 13 > 0.08 VPMNS
(with CKM corr.)
VPMNS (with CKM corr.)
Mu, ~ m D* A D*
Universal mixing and universal matricesUniversal mixing and universal matrices
Md ~ m D*A D Ml ~ m D A D*
D = diag(1, i, 1)D = diag(1, i, 1)A is the universal matrix: A is the universal matrix:
A ~ A ~
i ~ 0.2 – 0.3i ~ 0.2 – 0.3
Can be embedded in to SU(5) and SO(10) with additional assumptions
Can be embedded in to SU(5) and SO(10) with additional assumptions
1
lq
12 lq
12 solC = 46.7o +/- 2.4oA.S.M. RaidalH. Minakata
H. Minakata, A.S.Phys. Rev. D70: 073009 (2004) [hep-ph/0405088]
lq
23 lq
23 atmVcb = 45o +/- 3o
2-3 leptonic mixing is close to maximalbecause 2-3 quark mixing is small
2-3 leptonic mixing is close to maximalbecause 2-3 quark mixing is small
Difficult to expects exact equalities but qualitatively
Difficult to expects exact equalities but qualitatively
1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large
1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large
Quark-lepton symmetryQuark-lepton symmetry
Existence of structure which produces bi-maximal mixing
Existence of structure which produces bi-maximal mixing
sin C = 0.22 as ``quantum’’ of flavor physics
sin C = 0.22 as ``quantum’’ of flavor physics
sinC = m /m
sinC = m /msinC ~ sin 13sinC ~ sin 13
Appears in differentplaces of theory
Mixing matrix weakly depends on mass eigenvalues
In the lowest approximation:
Vquarks = I, Vleptons =Vbm
m1 = m2 = 0
``Lepton mixing = bi-maximal mixing – quark mixing’’``Lepton mixing = bi-maximal mixing – quark mixing’’
F. VissaniV. Barger et al
UPMNS = Ubm
Ubm = U23mU12
mUbm = U23
mU12m
Two maximal rotations
½ ½ -½ ½ ½ ½ -½ ½
- maximal 2-3 mixing- zero 1-3 mixing- maximal 1-2 mixing- no CP-violation
Contradictsdata at (5-6) level
In the lowest order?Corrections?
UPMNS = U’ Ubm
U’ = U12()
Generates simultaneously
Deviation of 1-2 mixing from maximal
Non-zero 1-3 mixing
0
Ubm =
As dominant structure?Zero order?
Charged leptons Charged leptons
sin(C) + 0.5sin C( 2 - 1)
NeutrinosNeutrinos q-l symmetry
tan212 = 0.495
H. Minakata, A.S.R. Mohapatra, P. Frampton, C. W.Kim et al.,S. Pakvasa …
Maximal mixing
CKM mixing
mD ~ mu
Maximal mixingml ~ md q-l symmetry
mDT M-1 mD
sin(C
)
CKM mixing
QLC-2QLC-1
sin12 =sin12 =
sin13 =sin13 =
sin C/ 2 ~ Vub~ Vub
29 31 33 35 37 39 12
Fogli et al
Strumia-Vissani
321
SNO (2)
QLC2 tbmQLC1
- analysis does change bft but error bars become smaller 12+ C ~/4
90%99%
Utbm = Utm Um13
UQLC1 = UC Ubm
Give the almost same 12 mixing
Give the almost same 12 mixingcoincidencecoincidence
P. F. HarrisonD. H. PerkinsW. G. Scott
Utbm = U23(/4)U12
Utbm = U23(/4)U12
- maximal 2-3 mixing- zero 1-3 mixing- no CP-violation
Utbm = 2/3 1/3 0- 1/6 1/3 1/2 1/6 - 1/3 1/2
2is tri-maximally mixed 3 is bi-maximally mixed
sin212 = 1/3 in agreement with 0.315
Mixing parameters - some simple numbers 0, 1/3, 1/2
S3 group matrixRelation to group matrices?
In flavor basis…relation to masses?No analogy in theQuark sector? Implies non-abelian symmetry
L. Wolfenstein
0 0.01 0.02 0.03 0.04 0.05 sin213
Fogli et al
Strumia-Vissani
32
1
T2K
90%99%
Double CHOOZ
Cm21
2/m322
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
In agreement with 0 value
QLC1QLC1
1). Superheavy MS >> vEW - decouple1). Superheavy MS >> vEW - decouple
2). Heavy: vEW >> mS >> m 2). Heavy: vEW >> mS >> m
3). Light: mS ~ m play role in dynamics of oscillations3). Light: mS ~ m play role in dynamics of oscillations
0 mD 0 m = mD
T 0 MD
T
0 MD MS
If MD = A-1mD
m = mD MD-1
MS MD-1mD
m = A2 MSm = A2 MS
Structure of the neutrino mass matrix is determined by MS
-> physics at highest (Planck?) scale immediately
mD similar (equal) to quark mass matrix - cancels
mD << MD << MS
Double (cascade) seesaw
MR = - MDT MS
-1 MD
Additional fermions
A ~ vEW/MGU
NS
R. MohapatraPRL 56, 561, (1986)
MS – Majorana mass matrix of new fermions S
M. LindnerM. SchmidtA.S. JHEP0507, 048 (2005)
A.S.PRD 48, 3264 (1993)
R. Mohapatra. J. Valle
R. Mohapatra. J. Valle
leads to quasi-degenerate spectrum if e.g. MS ~ I, leads to quasi-degenerate spectrum if e.g. MS ~ I,
Structure of the neutrino mass matrix is determined by
origin of ``neutrino’’ symmetry
origin of ``neutrino’’ symmetry
origin of maximal (or bi-maximal) mixing origin of maximal (or bi-maximal) mixing
MS
MS ~ MPl ?
Q-l complementarityQ-l complementarity
Reconciling Q-L symmetry and different mixings of quarks and leptons
Seesaw provides scale and not the flavor structure of neutrino mass matrix
Mixing with sterile states change structure of the mass matrix of active neutrinos
Consider one state S which has - Majorana mass M and - mixing masses with active neutrinos, miS (i = e, , )
Active neutrinos acquire (e.g. via seesaw) the Majorana mass matrix ma
After decoupling of S the active neutrino mass matrix becomes
(m)ij = (ma )ij - miSmjS/M(m)ij = (ma )ij - miSmjS/M
induced mass matrixinduced mass matrixsinS = mS/M
mind = sinS2 M mind = sinS2 M
mind = sinS2 M mind = sinS2 M
sinS2 M > 0.02 – 0.03 eV
Induced matrix can reproduce the following structures of the active neutrino mass
Induced matrix can reproduce the following structures of the active neutrino mass
sinS2 M ~ 0.003 eV Sub-leading structures for normal
hierarchy
Sub-leading structures for normal hierarchy
sinS2 M < 0.001 eV Effect is negligibleEffect is negligible
Dominant structures for normal and inverted hierarchy
Dominant structures for normal and inverted hierarchy
In the case of normal mass hierarchy
mtbm ~ m2/3 + m3/2
1 1 11 1 11 1 1
0 0 00 1 -10 -1 1
m2 = msol
2
Assume the coupling of S with active neutrinos is flavor blind (universal):
miS = mS = m2 /3
Then mind can reproduce the first matrixThen mind can reproduce the first matrix
mtbm = ma +mind ma is the second matrix
Two sterile neutrinos can reproduce whole tbm-matrixTwo sterile neutrinos can reproduce whole tbm-matrix
R. Zukanovic-Funcal, A.S.in preparation
R. Zukanovic-Funcal, A.S.in preparation
Two regions are allowed: Two regions are allowed:
MS ~ 0.1 – 1 eV MS > (0.1 – 1) GeVandand
Q & L:- strong difference of mass and mixing pattern;- possible presence of the special leptonic (neutrino) symmetries; - quark-lepton complementarity
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.
This may indicate that q & l are fundamentally differentor some new structure of theory exists (beyond seesaw)
0.2 0.3 0.4 0.5 0.6 0.7 sin223
Fogli et al
32
1
T2K
SK (3)90%
QLC1
SK (3) - no shift from maximal mixing
1). in agreement with maximal2). shift of the bfp from maximal is small3). still large deviation is allowed: (0.5 - sin223)/sin 23 ~ 40% 2
maximal mixing
Gonzalez-Garcia, Maltoni, A.S.
sin2223 > 0.93, 90% C.L.
QLC2
R. Zukanovic-Funcal, A.S.in preparation
R. Zukanovic-Funcal, A.S.in preparation
Smallness of massLarge mixing
Possibility that theirproperties are relatedto very high scale physics
Can propagate in extra dimensions
Manifestations ofnon- QFT features?
Violate fundamental symmetries, Lorentz inv.CPT, Pauli principle?