A Yu Smirnov

e

2

1

mas

s

1

2

3

3

mas

s m2atmm2

atm

m2sun

m2sun

Inverted mass hierarchy(ordering)

Normal mass hierarchy (ordering)

|Ue3|2

|Ue3|2

Type of the mass hierarchy: Normal, Inverted Type of mass spectrum: with Hierarchy, Ordering, Degeneracy absolute mass scale

Ue3 = ?

?

Hierarchy of mass squared differences: m12

2 m232 | = 0.02 - 0.08

mh > m232 > 0.04 eV

|m2 m3| > |m12

2 m232 | = 0.19

No strong hierarchy of masses:

+ 0.09- 0.05

|sin |

Bi-large or large-maximalmixing between neighboring families (1- 2) (2- 3):

bi-maximal + corrections? 0 0.2 0.4 0.6 0.8

1-3

1-2

2-31

The heaviest mass: mh ~ (0.04 - 0.3) eV

12C 23 12C 23

3

m > m2 From oscillations:

Kinematic methods:

From neutrinoless double beta decay

If the effective Majorana mass mee is measured

m > mee /3

Troitsk: me < 2.05 eV (95%) after ``anomaly’’ subtraction

Mainz: me < 2.3 eV (95%) updated, 2004

Future: KATRIN

If me = 0.35 eV

me < 0.2 eV (90%) upper bound

5 (statistical) from 0 discovery potential

mee = k Uek2 mk eimee = k Uek2 mk ei

x

p

p

n

n

e

e

meeNeutrinoless double beta decay

Z (Z + 2) + e- + e- + +

2 neutrino double beta decay:

Z (Z + 2) + e- + e-

H-M, NEMO ~ 200 000 events

Spectrum total energy of the electron pair

F

EeeQ

2

0

Mechanisms of 0 -decay

Majorana mass of the electron neutrino

Rate ~ |mee| 2

Fifth detector

Heidelberg-Moscow experiment

EvidenceCosmology? If 2 0 -> mechanism?

EvidenceCosmology? If 2 0 -> mechanism?

76 Ge -> 76Se + e- + e-

4.2 - evidence

5 detectors, 71.7 kg yr

Qee = 2039 keV

T1/2 = 1.19 x 1025 y

T1/2 = (0.69 – 4.18) x 1025 y

(3range)

mee = 0.44 eV

mee = 0.24 – 0.58 eV (3)

Spectrum near the end point

Positive claim

mee =k mee(k) eik)

Assuming 3 Majorana neutrinosmL – is the lightest eigenvalue (mee -mL) - plot

VissaniKlapdor-KleingrothhousPas, A.S

mee(k) contribution from k-eigenvalue

mee(1) = Ue1

2 mL

mee(2) = Ue2

2 mL2 + m21

2

mee(3) = Ue3

2 mL2 + m31

2

Ue12 > Ue2 2 > Ue3

2

For normal mass hierarchym3 > m2 > m1 = mlightest

m212 m31

2

mee

mL

Cancellationis possible

mee(3)

mee(2)

mee(1)

(mee -mL) - plot

mee(3) = Ue3

2 mL

mee(1) = Ue1

2 mL2 + m13

2

mee(2) = Ue2

2 mL2 + m13

2

For inverted mass hierarchym2 > m1 > m3 = mL

m312 No crossing of trajectories

- no cancellation

mee(2)/mee

(1) = Ue22/Ue1

2 = tan2sol

mee(3) << mee

(2)

mee(3)/mee

(2) < Ue32/Ue2

2 < 1/7

mL

mee

mee(3)

mee(2)

mee(1)

A. Strumia, F. Vissani

Neutr

inole

ss d

ouble

beta

deca

y

Kinematic searches, cosmology

Sensitivity limit

mL

Heidelberg-Moscow

mee < 0.05 eV

- excludes degenerate spectrum

mee < 0.01 eV

- excludes inverted mass hierarchy

Problems: - uncertainties of nuclear matrix elements- possible other contributions apart from neutrino mass

If HM result confirmed – strongly degenerate spectrum

A. Strumia, F. Vissani

mL

HM(3)

Cuoricino (90%)NEMO (90%)

GERDA II

CUORE

NEMO: 100Mo

Comments

Cuoricino, CUORE: 130Te

GERDA: 76Ge

IGEX (99%)

mee = sin2sol msol

2

mee = cos2sol matm2

1. Normal mass hierarchy: m2 >> m1

Ue32 << 0.04

2. Inverted mass hierarchy

Among observables

opposite CP phases

mee = matm2 the same CP phases

3. Degenerate mass spectrum

mee = me

mee = cos2sol me opposite CP phases

the same CP phases

Also implies:

Following Max Tegmark and Sasha Dolgov

Relative density fluctuations: =

1). If all components cluster:

~ a(t) ~ a(t)

= 3H2 mPl2/8 + c/a2

c = 3 mPl2 k/8 curvature

~ c/a2

since in the matter dominated epoch ~ a-3

a(t) - scale parameter

Indeed, from Einstein equation:

so

k – parameter in Friedman-Robertson-Walker metric,k = 0 in flat Universe

(matter dominated epoch)

~ c/a2 a -3

2). If only fraction * of matter density clusters, fluctuations grow slower:

~ ap ~ ap p ~ *3/5

p ~ *3/5

3). Neutrinos do not cluster on the small enough scales even if they are massive and non-relativistic due to high velocities

determined by the free streaming scale free

free ~ v t2Distance neutrino travel while Universe expands by factor of 2

< free neutrino clustering is suppressed (escape velocity is smaller than typical neutrino velocity) > free neutrinos cluster as cold dark matter, p = 1

On scales

Change shape of the power spectrum (in contrast to DE)

Fluctuation growth factor:

Dark energy (DE) and photons do not cluster. (Effect of photons can be neglected)

When DE dominates, * ~ 0 and clustering stops

Clustering occurs in the epoch between aMD matter start to dominate and aD when DE starts to dominate

k is the wavenumberaD aMD

p(k) aD aMD

~*(k)3/5

In the epoch aMD - aD * (k) ~ 1 – f(k)f(k) is the the energy density in neutrinos for which 1/k > free

The growth factor aD aMD

(1 – f(k))3/5

~aD aMD

(1 – 3/5 f(k))

4700 e –4f(k)

~

~

f(k)= i mi ni(k)

–8f(k)

Power spectrum: P(k) = < 2>

P(k,f)P(k,0) ~ e

For non-relativistic neutrinos:

For very large k – (small scales), all neutrinos in spectrum satisfy 1/k < free ni = 112/cm3

If neutrino mass spectrum is degenerate: f(k)= 3m n

f(k) and therefore suppression of powerspectrum decrease with k

Energy density in non-clusteringcomponent for given k

M. Tegmark, et al

solid line m = 0dashed line m = 1 eV

For small scales the power is suppressed by ~2

P = < k2>

M. Tegmark et al,

95% constraints

(Gala

xy clu

sterin

g)

m

= - 1

free = - 1

1

2

Dependence of bound on DE equation of state

S. Hannestad, astro-ph/0505551

imi

m0 > (0.08 - 0.10) eV

G. L. Fogli et al., hep-ph/0408045

m < 0.13 eV, 95% C.L.

U. Seljak et al.

Degeneratespectrum

Heidelberg-Moscow

e

Large Scintillator Neutrino Detector

Los Alamos Meson Physics Facility

e+

e + p => e+ + n e + p => e+ + n

Cherenkov cone + scintillations

p

e+ + e +

p

e+ + e +

e

t

Oscillations?

P = (2.64 +/- 0.67 +/- 0.45) 10-3 P = (2.64 +/- 0.67 +/- 0.45) 10-3

L = 30 m

n

decay at rest

m2 > 0.2 eV2

200 t mineral oil scintillator

Beyond ``standard’’ picture: - new sector, - new symmetry

Ultimate oscillation anomaly?

K.Babu, S Pakvasa

Disfavored by anew analysis of KARMEN collaboration

Disfavored by anew analysis of KARMEN collaboration

Disfavored byatmospheric neutrino data, no compatibilityof LSND and all-but LSND databelow 3-level

Disfavored byatmospheric neutrino data, no compatibilityof LSND and all-but LSND databelow 3-level

O. Peres, A.S.M. Sorel, J. Conrad, M. Shaevitz

M.C. Gonzalez-Garcia,M. Maltoni, T. Schwetz

G. Barenboim, L. Borissov, J. Lykken

S. Palomares-Ruiz, S. Pascoli, T.Schwetz R.Fardon, A. E. Nelson,

N. Weiner

CPT + (3+1)

e

2

1

4

mas

s

m2atm

m2sun

3

m2LSND

s

Generic possibility of interest even independently of the LSND result

Generation of large mixing of active neutrinos due to small mixing with sterile state

Produces uncertainty in interpretation of results

The problem is

P ~ |Ue4 |2 |U|2

Restricted by short baseline experiments CHOOZ, CDHS, NOMAD

2 - 3 below the observed probability

1-3 subsystem of levelsis frozen

Compatibility of short baseline Experiments and LSND datasets

95%90%

99%

Allowed regions from combined fit of LSND and short baseline experiments

hep-ex/0407027

e

2

1

4mas

s

m2atm

m2sun

3

m2LSND

’

s

5

s’

m2LSND

FINeSE

M. Sorel, J. Conrad, M. Shaevitz

x

x

450 t (mineral oil)1280 PMT

12 m diameter tank

L = 541 m, <E> ~ 800 MeV

Search for e appearance

M.H. Shaevitz

A Yu Smirnov

For vacuum oscillations:

(t) = k Uke k -ik

P() = |< |(t)>|2

P() = |kUk*Uke |2-ik

A Yu Smirnov

CP-asymmetry:ACP = P() - P( )

T-asymmetry: AT = P() - P( )

ACP = 4 JCP sin t + sin t + sin t

m122

2Em23

2

2Em31

2

2E

JCP = Im [Ue2 U* Ue3* U] = = s12 c12 s13 c13

2 s23 c23 sin where

is the leptonic analogue of the Jarlskog invariant

L. Wolfenstein,C. Jarlskog,V. Barger,K. Whisnant,R. Phillips

For vacuum oscillations:

A Yu Smirnov

P = | j Uj* U

j e |2

ijTransition probability

CP-transformation: PCP

= | j Uj Uj

*e |2

PT = | j Uj

* Uj e |2 = P

CP

ij

JCP < 0.03Oscillating factor is small unless long baseline (2000 - 3000 km) are taken

Earth matter effect is important

Uj --> Uj

*

T-transformation: ijin v

acuu

m:

Usual matter is CP-asymmetric CP-violation in neutrino oscillations even for (Uj

m)CP = ( U jm

)*in matter:

Problem is to distinguish:

fundamentalCP violation

CP-violationdue to matter effect

Precise knowledge of oscillation parameters, resolve ``degeneracy’’ of parameters, ambiguity…T-violation?Global fit

(m232) ~ 0.0001 eV

0.7 GeVT2K JPARC SuperKamiokandeaccelerator, off-a

295 km 2009start

NOAFermilab Ash Riveraccelerator, off-a

810 km 2.2 GeV

Double CHOOZreactor

baseline L

mean energy goal status

1.05 km 0.004 GeV

project

(sin2223 ) ~ 0.01Hierarchy ?

m232

sin213 < 0.005 – 0.008

<E>

2008start- 2011

sin213 < 0.005

90% C.L.

e

e

ee

2008start ?

sin213 < 0.006

Hierarchy

axis

detector

E = p*

1 + ()2

= E/m

p* = 0.03 GeV – momentum of neutrino in the rest frame of pion

E

E

narrowenergyspectrum

Narrow spectrum – to Reduce background from high energy NC

N X 0

e e

Searches for oscillations

T2KNOA

E (e) < E (e) < E ( x )

1011 - 10 12g/cc 0

Normal hierarchy Inverted hierarchy

Both resonances are in the neutrino channel

1-3 resonance is in the antineutrino channnel

The MSW effect can be realized in very large interval of neutrino masses m2 ) and mixing

Very sensitive way to search for new (sterile) neutrino states

The conversion effects strongly depend on

Type of the mass hierarchy

Strength of the 1-3 mixing (s13)

A way to probe the hierarchy and value of s13

m2 = (10-6 - 107) eV2

sin2 2 = (10-8 - 1)

If 1-3 mixing is not too small

s132 > 10- 5

strong non-oscillatory conversionis driven by 1-3 mixing

In the case of normal mass hierarchy:Small mixing angle realization of the MSW effect

almost completely

F(e) = F0( )

No earth matter effect in e - channelbut in e - channelNeutronization e - peak disappears

hard e- spectrum

e

Beam uncertainties can be controlled if

Two well separated detectors are used

Properties of medium are know

Comparison of signals from the two detectors:oscillation effects betweenthem and also test propertiesof the original flux

This is realized for oscillations of SN neutrinos inside the Earth:

D1 D2

L1

L2

Fluxes arriving at the surface of the earth are the same for both detectors

If sin213>10-4 an appearance of the Earth matter effect in e or ( e ) signal will testify for normal (inverted) mass hierarchy of neutrinos

A Yu Smirnov

Extremecases

A. Normal hierarchy large 1-3 mixing

composite, weakly (sin 2 ~ 1/3) mixed

e-spectrum

e-spectrum

Earth mattereffect

B. Inverted hierarchy large 1-3 mixing

C. Very small 1-3 mixing

unmixed, hard

in antineutrino channel

unmixed, hard

composite, strongly (cos2~ 2/3) permuted

in neutrino channel

composite, strongly (cos2~ 2/3) permuted

composite, weakly (sin 2 ~ 1/3) mixed

both in neutrinoand antineutrinochannels

Large 1-3 mixing: sin213 > 10-4

R.C. Schirato, G.M. Fuller, astro-ph/0205390 The shock wave can reach the region

relevant for the neutrino conversion ~ 104 g/cc

During 3 - 5 s from the beginningof the burstInfluences neutrino conversion ifsin 213 > 10-5

``wave of softening of spectrum’’

The effects are in the neutrino (antineutrino) for normal (inverted)hierarchy:

change the number of events

delayed Earth matter effectC.Lunardini, A.S., hep-ph/0302033

R.C. Schirato, G.M. Fuller, astro-ph/0205390

K. Takahashi et al, astro-ph/0212195

Density profile with shock wave propagationat various times post-bounce

h - resonance

G. Fuller

time of propagation velocity of propagation shock wave revival time density gradient in the front size of the front

Can shed some light on mechanism of explosion

Studying effects of the shock wave on the properties of neutrino burstone can get (in principle) information on

Steep front: breaks adiabaticity or make its violation stronger, - after passing can be restored again- influence transitions

F(e) = F0(e) + p F0

F0 = F0() - F0(e)

p is the permutation factorp

The earth matter effect can partially explain the difference of Kamiokande and IMB: spectra of events

p depends on distance traveled by neutrinos inside the earth toa given detector:

4363 km Kamioka d = 8535 km IMB 10449 km Baksan C.Lunardini, A.S.

One must take into account conversion effects of supernova neutrinos Conversion in the star

Earth matter effect

Normal hierarchy is preferableH. Minakata, H. Nunokawa, J Bahcall, D Spergel, A.S.

Avera

ge

energ

y o

f ob

serv

ed e

vents

Average energy of the original e-flux