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?

?