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Status & interpretation. of neutrino mixing. A. Yu. Smirnov. International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia. Launch. Heidelberg, March-07. 1. Status. 50 years ago. B. Pontecorvo. ``Mesonium and antimesonium’’. - PowerPoint PPT Presentation
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A. Yu. Smirnov
International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia
``Mesonium and antimesonium’’
Zh. Eksp.Teor. Fiz. 33, 549 (1957)[Sov. Phys. JETP 6, 429 (1957)] translation
First mentioning of a possibility of neutrino mixing and oscillations
Another line:Wu experiment, 1957: Parity violation V-A theory, two-component massless neutrino
B. Pontecorvo
Discovery of non-zero neutrino masses
Determination of the dominant structure of the lepton mixing:discovery of two large mixing angles
Establishing strong difference of the quark and lepton mass spectra and mixing patterns
The main results:
New phase starts in 2008 – 2010 the main objectives - determination of the absolute scale of neutrino mass; - subdominant structures of mixing matrix; - identification of the mass hierarchy, etc.
of studies of neutrino mass and mixing is essentially over
of studies of neutrino mass and mixing is essentially over
12o
= 33.7 +/- 1.3
M.C. Gonzalez-Garcia, M. Maltoni, Moriond, March 2007 (Phys. Rep.)
M.C. Gonzalez-Garcia, M. Maltoni, Moriond, March 2007 (Phys. Rep.)
+ 4.3- 3.5
+ 4.3- 3.5
1 (3 )1 (3 )
23o
= 43.3 small shift from maximal mixing
small shift from maximal mixing
+ 4.3- 3.8
+ 4.3- 3.8
+ 9.8- 8.8
+ 9.8- 8.8
13o
= 0.0 + 5.3- 0.0
+ 5.3- 0.0
+ 11.5- 0.0
+ 11.5- 0.0
b.f. value is zero;stronger upper bound
b.f. value is zero;stronger upper bound
0.81 – 0.85 0.53 – 0.58 0.00 – 0.120.32 – 0.49 0.52 – 0.69 0.60 - 0.760.27 – 0.46 0.47 – 0.64 0.65 – 0.80
Mixing matrix (moduli of matrix elements)Mixing matrix (moduli of matrix elements)
very good agreement with other fits
very good agreement with other fits
UPMNS =UPMNS =
The anglesThe angles
90 % C.L.90 % C.L.
29 31 33 35 37 39 12
Fogli et al
Strumia-Vissani
32
1SNO (2)
QLCl tbm QLC
12+ C ~/4
90%99%
Utbm = Utm Um13 UQLC1 = UC Ubm Give the almost
same 12 mixing
Give the almost same 12 mixing
31 Gonzalez-Garcia, Maltoni
/4 - C
0 0.01 0.02 0.03 0.04 0.05 sin213
Fogli et al
Strumia-Vissani
321
T2K
90%99%
Double CHOOZ
Cm212/m32
2
* Non-zero central value (Fogli, et al): Atmospheric neutrinos, SK spectrum of multi-GeV e-like events
QLCQLCQLCl
QLCl
Gonzalez-Garcia, MaltoniGonzalez-Garcia, Maltoni31
* MINOS lead to stronger the bound on 1-3 mixing (G-G, M.)
0.2 0.3 0.4 0.5 0.6 0.7 sin223
Fogli et al
32
1
T2K
SK (3one mass scale)90%
QLC
* in agreement with maximal, though all complete 3 - analyses show shift * shift of the bfp from maximal is small* still large deviation is allowed: (0.5 - sin223)/sin 23 ~ 40% 2
maximal mixing
Gonzalez-Garcia, Maltoni, A.S.
SK: sin2223 > 0.93, 90% C.L.
QLCl
13 Gonzalez-Garcia, Maltoni,
2007
m31
2 = 2.74 x 10-3 eV2 MINOS:MINOS: + 0.44 - 0.26 (1 )
in future:tension with SK?new physics?
in future:tension with SK?new physics?
m312 = 2.6 +/- 0.2 (0.6) x 10-3 eV2
Global fit:Global fit:
1.27 1020 p.o.t.1.27 1020 p.o.t.
m212 = 7.90 x 10-5 eV2 + 0.27
- 0.28
+ 0.27- 0.28
+ 1.10- 0.89
+ 1.10- 0.89 M. Gonzalez-Garcia,
M. Maltoni, 2007
M. Gonzalez-Garcia, M. Maltoni, 2007
|m2 /m3| > 0.18 the weakest mass hierarchythe weakest mass hierarchy
Cosmology: Cosmology: i mi < 0.42 eV (95% C.L. ) i mi < 0.42 eV (95% C.L. )
i mi < 0.17 eV (95% C.L. ) i mi < 0.17 eV (95% C.L. ) U. Seljak et alU. Seljak et al
m ~ 0.05 – 0.10 eVAt least for one neutrino:At least for one neutrino:
Heidelberg-Moscow:Heidelberg-Moscow: mee = 0.24 – 0.58 eVmee = 0.24 – 0.58 eVif confirmed, other than light neutrino Mass mechanism?
S. Hannestadt S. Hannestadt
< 0.6 eV< 0.6 eV
MINOS: results 2 years data taking (double statistics)
SNO: results of the third phase: He counters
m2 = (2.5 - 3.1) x 10-3 eV2
Improvements of the 1-2 mixing determination Ue2
KAMLAND: update + calibration Improvement of sensitivity to 1-2 mixing comparable to solar neutrino sensitivity
MiniBooNE: oscillation results Tests of LSND, overall picture of mass and mixing
BOREXINOCNGS
1. There are only 3 types of light neutrinos
2. Interactions are described by the Standard (electroweak) model
3. Masses and mixing have pure vacuum origin; they are generated at the EW and probably higher mass scales
= ``Hard’’ masses= ``Hard’’ masses
Tests of these statements; Search for physics beyond
LSND: not clear that light neutrinos are relevant
Gallium calibration C. Giunti, M. LavederC. Giunti, M. Laveder
Cosmology: effective number of light neutrino species in the epoch when structures start to form
Warm dark matter: very small mixing, produced in EU by some mechanism which differs from mixing with light neutrinos.
How inclusion of these neutrinos affect standard neutrino model?
Small perturbations
Strong changes?
M. ShaposhnikovM. Shaposhnikov
R. Zukanovic-Funchal, A.S.R. Zukanovic-Funchal, A.S.
X-raysX-rays
LSSLSS
CMBCMB
reactorsreactors
atmosphericatmospheric
Contours of constant induced mass and bounds
Contours of constant induced mass and bounds
thermalization line: above if S are in equilibrium
thermalization line: above if S are in equilibrium
For benchmark parametersS were thermalized
For benchmark parametersS were thermalized
Bounds - in non-equilibrium region
Bounds - in non-equilibrium region
Heavy particle exchange
Heavy particle exchange Light particlesLight particles
New scalars exchange New scalars exchange
SUSY with R-parity breakingSUSY with R-parity breaking
New scalarsNew scalars
Majorons,Accelerons Cosmons…
Majorons,Accelerons Cosmons… With some
cosmologicalmotivations
With some cosmologicalmotivations
Restrictions: see talk S. Hannestadt
Restrictions: see talk S. Hannestadt
Phenomenology: T. OtaPhenomenology: T. Ota
Exchange by very light scalar
in the context of MaVaN scenario
m ~ 10-8 - 10-6 eV
L R
fLfR
f = e, u, d,
msoft = fnf /m
generated by some short range physics (interactions) EW scale VEV
chirality flip – true mass:
mvac mvac + msoft
f
D B Kalplan, E. Nelson, N. Weiner , K. M. ZurekM. Cirelli, M.C. Gonzalez-Garcia, C. Pena-GarayV. Barger, P Huber, D. Marfatia
medium and energy dependent mass
In the evolution equation:
f ~ /M Pl
Are neutrino masses usual?
M3 ~ MGUT M3 ~ MGUT
Problem of unification: difference of mass and mixing patternsProblem of unification: difference of mass and mixing patterns
Origin of difference: seesaw? Origin of difference: seesaw?
FUT + flavor symmetry – even more complicatedFUT + flavor symmetry – even more complicated
EW scale? EW scale?
kev-scale mechanisms?
kev-scale mechanisms?
M. ShaposhnikovM. ShaposhnikovR. MohapatraR. Mohapatra With many O(100)
RH neutrinos
With many O(100) RH neutrinos
W. Buchmuller, M. Ratz et al
W. Buchmuller, M. Ratz et al
Large mixing is related to weak mass hierarchy of neutrinos
Large mixing is related to weak mass hierarchy of neutrinos
No-symmetryNo-symmetry
Have different implications
Have different implications
P. F. HarrisonD. H. PerkinsW. G. Scott
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
immediate relation to group matrices?
In flavor basis…relation to masses?No analogy in theQuark sector? Implies non-abelian symmetry
L. Wolfenstein
Clebsch-Gordan coefficientsClebsch-Gordan coefficients
Utbm = Umag U134)
1 1 1Umag = 1 1
= exp (-2i/3)
Relation to masses?No analogy in the quark sector? Unification?
Symmetry:Symmetry:
A4
symmetry group of even permutations of 4 elements
representations: 3, 1, 1’, 1’’
tetrahedron
T’ , D4 , S4 , (3n2 ) …T’ , D4 , S4 , (3n2 ) …C.HadedornC.Hadedorn
Other possibilities:Other possibilities:
Extended higgs sector,Auxiliary symmetries, Flavor alignment, Extra dimensions?
1
lq
12 12C = 46.5o +/- 1.3o
A.S.M. RaidalH. Minakata
H. Minakata, A.S.Phys. Rev. D70: 073009 (2004) [hep-ph/0405088]
lq
23 23Vcb = 43.9o + 5.1/-3.6o
2-3 leptonic mixing is close to maximalbecause 2-3 quark mixing is small
Qualitatively correlation: Qualitatively correlation:
1-2 leptonic mixing deviates from maximal substantially because 1-2 quark mixing is relatively large
QLC- relations: QLC- relations:
Quark-lepton symmetry
Existence of structure which produces bi-maximal mixing
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’’
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
0
Ubm =
As dominant structure?Zero order?
LeptonsLeptons
sin12 = sin(C) + 0.5sinC ( 2 - 1- Vcb)
In the symmetry basis
V = Vbm
Vl = VCKM
Vu = I
Vd = VCKM
VPMNS = Vl+
V = VCKM+
Vbm
Vquarks = Vu+
Vd = VCKM
QuarksQuarks
q-l symmetry
sin13 = sin23 sinC = 0.16
sin212 = 0.330
Seesaw?
Predictions:Predictions:
D23 = 0.5 sin2C + cos2C Vcbcos = 0.02 +/- 0.04
H. Minakata, A.S.
large !
(or both rotations from neutrinos)(or both rotations from neutrinos)
LeptonsLeptons
sinsun ~ sin
(C )
V = VCKM
+
Vl = Vbm
+
Vd = I
Vu =
VCKM+
Vleptons = Vbm VCKM
+ Vleptons = Vbm
VCKM + Vquarks = Vu
+ Vd =
VCKM
Vquarks = Vu+
Vd = VCKM
QuarksQuarks
q-l symmetry
sin13 = - sinsun Vcb = 0.03
``Lopsided’’
H. Minakata, A.S.
M. Raidal
Predictions: Predictions:
D23 = cossun Vcb cos < 0.03
Global fit: 0.53 – 0.58 (90% C.L.)
tbm: 0.577
Physical parameterPhysical parameter
QLC: 0.576 – 0.584
0.53 0.55 0.57 0.590.53 0.55 0.57 0.59
(depending on Majorana CP –phases)(depending on Majorana CP –phases)
Ue2 = cos 13 sin 12
Ue2
RGERGE
tbmtbm
QLCQLC
datadata RGE for tbm:A. Dighe, S. Goswami,W. Rodejohann hep-ph/0512328
RGE for tbm:A. Dighe, S. Goswami,W. Rodejohann hep-ph/0512328
tbm: RGE < 10-3 for hierarchical nu tbm: RGE < 10-3 for hierarchical nu
0.1 for degenerate nu 0.1 for degenerate nu
tan
m1/eV
m1/eV
MSSMMSSMSMSM
positivepositive
M. A. Schmidt, A.S. hep-ph/0607232
M. A. Schmidt, A.S. hep-ph/0607232
seesaw-I bi-maximal mixing,seesaw-I bi-maximal mixing, mD ~ mu ml ~ md
Maximal 2-3 mixing
Maximal 2-3 mixing
Small 1-3mixing
Small 1-3mixing
Tri-bimaximalmixing
Tri-bimaximalmixing
Q-L-complementarityQ-L-complementarity
Koide relationKoide relation
Mf = M0 + Mf Mf = M0 + Mf
Determined by symmetry?
Determined by symmetry?
f = u, d, l, f = u, d, l,
correctionsdue to new interactionsPlanck scale effects…
correctionsdue to new interactionsPlanck scale effects…
Fermion mass matrices
Fermion mass matrices
What is zero order structure?What it should explain?
- third generation masses- 2-3 mixing- 1-3 mixing
The rest: from perturbations?The rest: from perturbations?
me + m + m me + m + m
( me + m + m )2( me + m + m )2
Koide relationKoide relation
= 2/3 = 2/3
mi = m0(zi + z0)2 mi = m0(zi + z0)2
i zi = 0 i zi = 0
z0 = i zi2
/3 z0 = i zi2
/3
with accuracy 10-5 with accuracy 10-5
tanC = 3tanC = 3 m - me m - me
2 m - m - me 2 m - m - me
Both relations can be reproduced ifBoth relations can be reproduced if
Y. Koide, Lett. Nuov. Cim. 34 (1982), 201
Y. Koide, Lett. Nuov. Cim. 34 (1982), 201
C A BrannenC A Brannen
Neutrinos,hierarchical spectrum
Neutrinos,hierarchical spectrum
all three families are substantially involved!
all three families are substantially involved!
* GUT* GUT* Existence of a number O(100)
of singlets of SM and GUT
symmetry group
* Several U(1) gauge factors* Several U(1) gauge factors* Discrete symmetries* Heavy vector-like families * Heavy vector-like families
* Incomplete GUT multiplets* Incomplete GUT multiplets* Explicit violation of symmetry* Explicit violation of symmetry* Selection rules for interactions* Selection rules for interactions* Non-renormalizable interaction* Non-renormalizable interaction
no simple relationsbetween masses and mixing
can not be described in terms of a few parameters
no simple relationsbetween masses and mixing
can not be described in terms of a few parameters
No simple ``one-step’’ explanations
No simple ``one-step’’ explanations
How one can get from this complicated structuresimple pattern we observed at low energies?
How one can get from this complicated structuresimple pattern we observed at low energies?
data look complicated data look complicated data look too simple data look too simple
Singlet sector: several (many ?) singlets (fermionic and bosonic) of SO(10), S, additional symmetries
their mixing corrects masses of charged fermions
their mixing corrects masses of charged fermions
Non-renormalizable interactions
String inspired…String inspired…
No higher representations no 126H
No higher representations no 126H
SO(10) 3 fermionic families in complete representations 16F, 10H , 16H
Non-abelian flavor (family symmetry) G with irreducible representation 3
Non-abelian flavor (family symmetry) G with irreducible representation 3
16F ~ 3
Heavy vector-like familiesof 10F, 16F
C. HagedornM. SchmidtA.S.
C. HagedornM. SchmidtA.S.
- several (many ?) singlets (fermionic and bosonic) of SO(10), - additional symmetries (U(1), discrete) hierarchy of masses and couplings with neutrinos from 16 - some singlets can be light – sterile neutrinos
Due to symmetries only certain restricted subset is relevant for neutrino mass and mixing
16F 16F
Singletsector
Singletsector
16H
Mixing of singlets with neutrinos (neutral components of 16). responsible for neutrino mass and mixing and strong difference of quark and lepton patterns
Easier realizations of symmetriesEasier realizations of symmetries
C. HagedornM. Schmidt, A.S. in progress
C. HagedornM. Schmidt, A.S. in progress
The EW-scale mechanisms of neutrino mass generation
The EW-scale mechanisms of neutrino mass generation
New Higgs bosons at the EW scale
New Higgs bosons at the EW scale
Zee, Babu-Zeeradiative mechanisms
Zee, Babu-Zeeradiative mechanisms
Double charged bosons
Double charged bosons
R-parity violationR-parity violation
New fermions?New fermions?
HE scale: seesawHE scale: seesaw
Can RH neutrinos be detected at LHC? Can RH neutrinos be detected at LHC?
Type-I: RH neutrinos- singlets of the SM symmetry groupType-I: RH neutrinos- singlets of the SM symmetry group
W. Buchmuller, D. WylerW. Buchmuller, D. Wyler
Via mixing with light neutrinos
Via mixing with light neutrinos
Additional interactions
Additional interactions
RH neutrinos can be produced/decay
RH neutrinos can be produced/decay
Negligibleunless strong cancellation occurs
Negligibleunless strong cancellation occurs
- RH gauge bosons in LR models- New higgs bosons
- RH gauge bosons in LR models- New higgs bosons
Type-III seesawType-III seesaw
Type III seesaw: Type III seesaw:
xx T+ T = T0 T-
T+ T = T0 T-
T0T0
SS
HH HH
yyy ~ 10-6
MT ~ 100 GeV
In SU(5): In SU(5): 24F T, S24F T, S
y 5F 24F 5H + y’/M 5F 24F 24H 5Hy 5F 24F 5H + y’/M 5F 24F 24H 5H
EW production:EW production:
Type I + Type IIIone usual neutrino is mass less
Type I + Type IIIone usual neutrino is mass less
B. BajcG. SenjanovicM. NemevsekP. Filiviez-Perez
B. BajcG. SenjanovicM. NemevsekP. Filiviez-Perez
SU(2) triplet:SU(2) triplet:
T0 W l ,T0 W l ,Decay: Decay: T0 Z T0 Z ~ 10-16 - 10-13 sec T0 T+ l - T0 T+ l - W + * T+ T0, W + * T+ T0,
Z * T0T0Z * T0T0
~ (mixing) 2
~ (mixing) 2
(mi)ab = - mai x mbiT(mi)ab = - mai x mbi
T1Mi
1Mi
sin ai = mai / Mi (mi)ab = - sinai sin bi Mi
Single RH neutrino generate a contribution to neutrino mass matrix
Single RH neutrino generate a contribution to neutrino mass matrix
J. Kersten, A.S.J. Kersten, A.S.
(mi)ab < 0.1 eV ai < 10-6 ( 10 GeV / Mi)1/2
negligible effect at HE colliders
negligible effect at HE colliders
~ (ai)2
If If ai ~ 10-1M ~ 1 GeV
Cancellation at the level 10-10Cancellation at the level 10-10
Bound from e
Bound from e
Define mixing:Define mixing:
Neutrino data:Neutrino data:
W. BuchmullerC. Greub, G. Ingelman, J. RathsmanA. Pilaftsis
W. BuchmullerC. Greub, G. Ingelman, J. RathsmanA. Pilaftsis
For 2 and 3 RH neutrinos exact cancellation occurs if and only if
1. the Dirac mass matrix is singular
1. the Dirac mass matrix is singular
2. the Yukawa couplings and RH neutrino masses are related as
2. the Yukawa couplings and RH neutrino masses are related as
Imply conservation of the lepton number and one decoupled heavy neutrino
An examplemotivated by A4
J. Kersten, A.S.J. Kersten, A.S. y1 ay1 by1
mD = m y2 ay2 by2
y3 ay3 by3
y1 ay1 by1
mD = m y2 ay2 by2
y3 ay3 by3
y12/M1 + y2
2/M2 + y32/M3 =
0
1 1 1m D = hv
1 1 1m D = hv
M = M0 diag (1, 1, 1)M = M0 diag (1, 1, 1)
J. Gluza J. Gluza
Perturbations of the symmetric structure
non-zero usualneutrino mass
negligible consequences for HE (LHC) physics
Neutrino mass generation and HE physics ``decouple’’
Indirect relation:
Simple perturbations Simple perturbations
imprin
ted
imprin
ted
Pattern of neutrino mass and mixing reflectsfeatures that lead to cancellation, maximal 2-3 mixing and zero 1-3 mixing
J. Kersten, A.S.in progress
J. Kersten, A.S.in progress
correlationof light neutrinoproperties and heavy leptons
T. UnderwoodT. Underwood
ti-bimaximal mixing;possible presence of special leptonic (neutrino) symmetries
GUT + flavor (ultimate unification?): string inspired framework with extended singlet sector, non-renormalizable interactions ?
Q-L complementarity: bi-maximal mixing and Q-L symmetry/unification
Real or accidental?
Status: ``standard’’ model of neutrino mass and mixing – further confirmations/checks. Deviations?
Can LHC help?
?