of neutrino mass

A. Yu. Smirnov

Max-Planck Institute for Nuclear Physics, Heidelberg, Germany

NOW 2014 September 8– 13, 2014

strongly suppresses

There is something hidden and beyond the standards which

badly confuses and mixes violates the law

or maybe, does not violate the

law which is difficult to prove

and probably the first and the second are because of the third

1. Smallness of neutrino mass in comparison to masses of the charged leptons and quarks

what is behind of

2. “Unusual” lepton mixing pattern with two large mixing angles (one is close to maximal) and one small which differs from the quark mixing3. Weaker (or no) mass hierarchy than the hierarchy of charged leptons and quarks

In general, what is the type of mass spectrum and mass ordering?

New

physics?

are they of Dirac or Majorana type?

are they “hard” or “soft” (medium dependent)?

Does the nature of neutrino mass differ from the nature of the quarks and charged lepton masses?

Are sterile neutrinos (if exist) relevant for the solution ?

Nature of neutrino mass

Recall that in oscillation experiments we probe dispersion relations and not masses immediately Effective neutrino masses in oscillation experiments in beta decay in cosmology and bb-decay can be different

Usual neutrino masses can be strongly suppressed, e.g. by the seesaw, so that ”unusual contributions” dominate

are we asking right questions?

do we interpret the data correctly?

It is not excluded that the correct solution (or the key to the solution) already exists among hundreds of approaches, models, mechanisms, schemes, etc.

The problem is

then to identify the

correct solution

Still something fundamental can be missed

Special

m3 mt

~ 3 10-

11

Normal? Neutrinos: no clear generation structure as well as the correspondence light flavor – light mass, especially if the mass hierarchy is inverted or spectrum is quasi-degenerate

m3 me

~ 3 10-

6

me mt

~ 3 10-6

106

Similar for other generations if spectrum is hierarchical

103 101210910-3 100

mass, eV

gap

comparing within generation:

?due to neutrality of neutrinos?

The riddle is formulated as comparison with masses (and mixing) of quarksThere is no solution of the riddle of quark

masses

Yes, if

Can we solve the neutrino mass riddle?Do efforts make sense?

neutrino mass generation and generation of the charged lepton and quark masses are independent we will try to explain

the difference of masses and mixing of neutrinos and quarks, and not masses and mixing completely

we still hope (as it was before) that neutrinos will uncover something simple and insightful which will allow to solve the quark mass riddle

Higgs triplet Radiative mechanismsSeesaw type III, etc.

Should mixing be included in the riddle?

QuarksRelation between masses and mixing md

ms

sinqC ~

LeptonsMaximal mixing - quasi-

degenerate mass states ?

Tri-Bi-Maximal mixing (TBM)

no connection between masses and mixing (at least in the lowest order)

Realized in the residual symmetry approach

In 3 generations: Fritzsch ansatz

Form invariance of the mass matrices

Completelyrelated

Partiallyrelated

Largely unrelated

Higgs triplet

Radiative mechanisms

Seesaw type II and III

Seesaw type I, Quark-lepton unification

with the only difference that originates from Majorana nature of neutrinos, symmetries

GUT, seesaw type II

Dark MatterRiddle

Dark EnergyRiddle

Neutrino massriddle

Solution may come

from unexpected

side

Dark radiation

Baryon asymmetry in the UniverseInflation

The riddle of new physics

additional structures in lepton sector such as the see – saw

responsible for small quark mixing and hierarchical structure of the Dirac masses

common for quarks and leptons

responsible forsmallness of neutrino mass and large lepton mixing

These two types are different but probably should somehow “know” about each other

A guess

Counter example, seesaw with degenerate RH neutrinos does not work in this framework

High scale seesawQuark- lepton symmetry /analogyGUT

Low scale seesaw, radiative mechanisms, RPV, high dimensionaloperators

Scale of neutrino masses themselves Relation to dark energy, MAVAN?

VEW2

mn

Uni

ficat

ion

Looking under the lamp

Neutrino mass itself is the fundamental scale of new physics

28 orders of

magnitude

Spurious scale?

mn = - mDT mD 1MR

MGUT2

MPl

for the heaviest in the presence of mixingMGUT ~ 1016 GeV

Leptogenesis

N ~ 102

many heavy singlets (RH neutrinos)…string theory

q – l similarity: mD ~ mq ~ ml

MR ~ 108 - 1014 GeV

double seesaw

1016 - 1017 GeV

Gauge coupling unification

BICEP-II ?

In favor

Natural, minimalistic, in principles

Realizes relations:

Neutrality,

zero charges Majorana

Nature Smallness of

mass – high

mass scale Large mixing

Testable? - Proton decay- Majorana masses

Fine tuning

“Neutrinoful Universe” Seesaw sector is responsible for inflation (scalar which breaks B-L and gives masses of RH neutrinos), dark matter, leptogenesis

T. Higaki et al, arViv:1405.0013

Partial relation of the quark and neutrino properties

<< MPl

New physics below Planck scale

dmH2 ~ MR

2 log (q /MR)

HH

nL

nR

“Partial” SUSY?

Simplest seesaw implies new physical scale

MR ~ mD2

/mn ~ 1014 GeV

nR

F. Vissanihep-phl9709409

(Another indication: unification of gauge couplings)

y2 (2 p )2

~ log (q /MR)MR

3 mn

(2 p v)2

J Elias-Miro et al, 1112.3022 [hep-ph]

MR < 107 GeVSmall Yukawas,Leptogenesis ?

Cancellation?M. Fabbrichesi

AYS

Neutralino as RH neutrino

Rp-SUSY

L-RnMSM

- No hierarchy problem (even without SUSY) - testable at LHC, new particles at 0.1 – few TeV scale- LNV decays

Higgs Triplet

New Higgs

doublets

0ne loopTwo loops

Three loops

Low scale

Inverseseesaw Connection

to Dark Matter

High dimensional operators

L R

NormalMass hierarchy

3 - 10 kev - warm dark matter - radiative decays 3.5 kev line

Few 100 MeV – GeV

- generate light mass of neutrinos- generate via oscillations lepton asymmetry in the Universe- can be produced in B-decays (BR ~ 10-10 )

split ~ eV

M. Shaposhnikov et al

BAU

WDM

Everything below EW scale small Yukawa couplings

EW seesaw Higgs inflation

Nothing new below Planck scale

RH neutrino?

very small split

very small mixing

Maybe related to Dark energy, MAVAN

Very light sector which may include

eV scale Seesaw with RH neutrinos for sterile anomalies LSND/ MiniBooNE ....

- new scalar bosons, majorons, axions, - new fermions (sterile neutrinos, baryonic nu) , - new gauge bosons (e.g. Dark photons)

A. De Gouvea

Tests: 5th force searches experimentsModification of dynamics of neutrino oscillationsChecks of standard oscillation formulas,searches for deviations

Generate finite neutrino masses, usual Dirac masses can be suppressed by seesaw with MR = MPl or multi singlet mechanism

M. Pospelov

H. Minakata, A Y S

From charged leptons or Dirac matrices of charged leptons and neutrinos

Related to mechanism of neutrino mass generation

UPMNS = VCKM

+ UX C. Giunti, M. Tanimoto

CKM type new physics

New neutrino structure

In a spirit two types of new physics and partial relations

In general, has similar hierarchical structure determined (as in Wolfenstein parametrization) by powers of

Related to (any) mechanism that explains smallness of neutrino mass Should be fixed to reproduce correct Lepton mixing angles VCKM ~ I UX ~ UTBM

l = sin qC

H. Minakata, A Y S……………………………….

Realized in QLC (Quark-Lepton Complementarity)

U12 (qc) U23(p/2)

q13~ ½ qc

permutation - to reduce the lepton mixing matrix to the standard form leads to

UPMNS = VCKM

+ UX

e.g. UX = UBM, UTBM

C. Giunti, M. Tanimoto

Pheno. level

UX = U23(p/2) U12

sin 2q13~ ½sin2qC

can be obtained in the context of

if

TBM-Cabibbo schemeS. F. King et al

q13 ~ ½ qc

``Naturalness’’ , absence of fine tuning of mass matrix

Dm212

Dm322

O(1)

sin2q13

~ ½sin2qC

Quark-Lepton ComplementarityGUT, family symmetry, …

~ ½cos2 2q23universal nm - nt – symmetry violation

The same value with completely different implications

Mixing anarchy

> 0.025

¼ sin2q12sin2q23

Analogy with quark mixing relation

q13 = 21/2( /4p - q23)

Eby,Frampton, Matsuzaki

relation implications

?

B. Dasgupta, A.S.

UPMNS ~ VCKM

+ UX

If the only source of CP violation

No CPV

sinq13 sin dCP = (-cos q23) sinq13q

sindqsin dCP ~ l3/s13 ~ l2

~ 0.046

dq = 1.2 +/- 0.08 rad

dCP ~ - d or p + d

where d = (s13q /s13) c23

sin dq

New sources may have specific symmetries or structures which lead to particular values of dCP e.g. -p /2, and q - l unification will give just small corrections

l3l

If the phase dCP deviates substantially from 0 or p, new sources of CPV beyond CKM should exists (e.g. from the RH sector) or another framework

sin dCP = s13-1 [sin(am + dX)Vud|Xe3| – sin ae |Vcd|Xm3

]

neglecting terms of the order ~ l3

here am , dX and ae are parameters of the RH neutrinos

if Xe3 = 0 we have

sin dCP ~ – sin ae

if ae = p /2

Some special values of dCP can be obtained under certain assumptions

dCP ~ 3p/2

One can find structure of the RH sector which lead to these conditions

B Dasgupta A.S

MX = - mDdiag

UR+ (MR)-1 UR

* mDdiag

Ux is the matrix diagonalizes

mD = UL (mD

diag) UR

+

Here

Minimal extension is the L- R symmetry:

UR = UL ~ VCKM

* and no CPV in MR

Seesaw can enhance this small CPV effect so that resulting phase in PMNS is large

In contrast to quarks for Majorana neutrinos the RH rotation that diagonalizes mD becomes relevant and contributes to PMNS

mDn ~

mDq

UX = UR

US In the LR symmetric basis

From seesaw

Normal mass hierarhy, relation between masses and mixing Flavor alignment in mass matrix

Similar structure of mass matrices but with different expansion parameter

sinq13 ~ ½ sinq12

sinq23

The same relations between coupling strength between generations

Vub = ½ Vus Vcb

Fritzsch Anzatz similar to quark sector, RH neutrinos with equal masses

A guess

ll = 1 - lq

Realization:

Expectations:

(2 – 4) 10-3 eV

0.5 - 2 eV

5 - 10 keV- Warm Dark matter- Pulsar kick

- Solar neutrinos- Extra radiation in the Universe

- LSND, MB- Reactor Ga anomalies - Extra radiation

ns

1 eV

1 keV

1 MeV

10-3 eV

mixing

dm ~ qaS2

mS

(1 – 2) 10-8 eV2 10-11

10-6 eV

qaS2

0.02 0.02 eV

10-3

Compare with large elements of the mass matrix 0.02 eV

mn = ma + dm

Original active mass matrix e.g. from see-saw

dm can change structure (symmetries) of the original mass matrix completely

Induced mass matrix due to mixing with nu sterile

UPMNS

be origin of difference of VCKM

and

on the 3n structure

For keV

ma = 0.025 eV

dm << ma

Decouples from generation of the light neutrino masses argument that this is not RH neutrino but has some other origin

For eV dm ~ ma Not a small perturbation

For meV dm << ma can be be considered as very small perturbation of the 3n system

L H F

where F is the fermionic operator

nL nR

S

S

S

H

nR

is the key to the solution of the riddle?

New structure (but physics is the same) 1

Ln(F) - 3/2

Neutrino new physics

Through this portal neutrino gets mass

S

S

S

Ss

s

ss

Scalesymmetries

Two different types of new physics are involved in explanation of data: the CKM type common to quarks and leptons and physics responsible for smallness of neutrino mass and large lepton mixing. The latter may have certain symmetries

It makes sense to identify the second one which explains the difference between the quarks and leptons

Still generation of quark and neutrino masses can be essentially independent

High (GUT) scale new physics: still appealingEW scale: see LHC14 resultsSub eV –eV scale: interesting, worth to explore

New neutrino physics may have certain symmetries which leads to specific values of mixing angles and CP phase. Phase from CKM part is strongly suppressed

Sterile neutrinos may be the key to solution to a riddle