A. Yu. Smirnov

A. Yu. Smirnov

International Centre for Theoretical Physics, Trieste, Italy

Planck 2011, May29, Lisbon

Mix with active neutrinos

s

Couple with usual neutrinos via (Dirak) mass terms

No weak interactions:- singlets of the SM symmetry group

Light

RH - components

of neutrinos

may have Majoranamass termsmaximal mixing?in the context of idea of neutrino–antineutrino oscillations

Sov. Phys. JETP 26 984 (1968)

e

Large Scintillator Neutrino Detector

Los Alamos Meson Physics Facility

e+

e + p e+ + n

Cherenkov cone + scintillations

p

e+ + e +

e

t

Oscillations?

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

3.8excess

Sterile neutrinos as solution of all the problems

450 t (mineral oil) 1280 PMT12 m diameter tank

L = 541 m, <E> ~ 800 MeV

G.Mention et al, arXiv: 1101.2755

Increase of the Mean flux by 3%

m2 > 1.5 eV2

sin2 2 = 0.17 +/- 0.1

Revised value of cross-section

Rreact = 0.937 +/- 0.027

2.14

Source + reactor

G.Mention et al, arXiv: 1101.2755

RGa = 0.87 +/- 0.05

Gallex/GNO 51CrSAGE 51 Cr, 37Ar

Calibration

C Giunti, M. Lavedersin22 = 0.24

m2 = 2.15 eV2

With reactor anomaly global fit of data in terms of nu-sterile becomes better

Limit on Ue4 becomes weaker

|Ue4|2 : 0.02 0.04

Smaller values of U4 are allowed to explain LSND/MiniBooNE –less tension with SBL experiment bounds

|U4|2 : 0.04 0.02

J Kopp, M. Maltoni,T.Schwetz1103.4570 [hep-ph]

3 + 2scheme

m412 = 0.47

eV2Ue4 = 0.128 Ue5 = 0.138

U4 = 0.165 U5 = 0.148

m512 = 0.87

eV2

45

Controversial and not convincing

Neff = 4.34 (68 % CL) + 0.86- 0.88

- WMAP-7- Barion Acoustic Oscillations- Hubble constant

Neff = 5.3 +/- 1.3 (68% CL) - WMAP–7 - Atacama Cosmology Telescope

Neff = (0.02 – 2.2) (68% CL)

Effective number of neutrino species

BBN

Neff = 3.68 (68 % CL) + 0.80- 0.70

E. Komatsu et alarXiv: 1001.4538 [astro-ph.CO]

J. Dunkley et alarXiv:1009.0866[astro-ph.CO]

J. Hamann et alPRL 105 (2010)181301

Y. I. Izotov and T X Thuan Astrophys J 710 (2010) L67

E Giusarma et al 1102.4774 [astro-ph]

run 1 (blue)

95%68 %

m2 < 0.25 eV2

run 2 (red)

- WMAP- SDSS (red galaxy clustering)- Hubble (prior on H0 )

- Supernova Ia Union Compilation 2 (in add)

+ BBN

Inverse approach:

J R Kristiansen, O Elgaroy 1104.0704 [astro-ph]

wCDM + 2S

1). w < -1

2). Age of the Universe 12.58 +/- 0.26 Gyr

too young?

The oldest globular clusters 13.4 +/- 0.8 +/- 0.6 Gyr

ruling out

CDM

(2 – 4) 10-3 eV

0.5 - 2 eV

~ 10 keV

40 - 70 MeV - LSND, MiniBooNE

- Warm Dark matter- Pulsar kick

- Solar neutrinos- Extra radiation in the Universe

- LSND, MiniBooNE- Reactor anomaly- Calibration experiments- Extra radiation

s

1 eV

1 keV

1 MeV

10-3 eV

mee me me … m m … … m For mSS ~ 1 eV

For mSS ~ 1 eV

Mass matrix

Mass matrix

e

e

meS mS mS

mSS … … …

SS

tanjS = mjS/mSS

mSS >> mab , maS mSS >> mab , maS

~ 0.2 - is not small

produces large corrections to the active neutrino mass matrix

In general can not be considered as small perturbation!

mij ~ - taniStanjS mSS ~ 0.04 mSS

Active neutrino spectrum is quasi degenerate

meS mS mS have certain symmetry

Effect can be small if

mSS ~ mab mSS ~ mab

J. Barry, W. Rodejohann,He ZhangarXiv: 1105.3911

m = ma + m

produce dominant - block

with small determinant

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

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

m can change structure (symmetries) of the original mass matrix completely (not a perturbation)

m can change structure (symmetries) of the original mass matrix completely (not a perturbation)

Induced mass matrix due to mixing with nu sterile

Induced mass matrix due to mixing with nu sterile

Enhance lepton mixing

Generate TBM mixing

UPMNS

Be origin of difference of

VCKMand

P. C. de Holanda, A. Yu. S. 1012.5627 [hep-ph]

P. de Holanda, A.S. Phys. Rev. D69 (2004) 113002 hep-ph 0307266

QArexp < QAr

LMA

2.55 +/- 0.25 SNU > 3.1 SNU

No turn up of the spectrum in SK

Light sterile neutrino R= m012 / m21

2 << 1

- mixing angle of sterile- active neutrinos

dip in survival probability

Motivation for the low energy solar neutrino experiments BOREXINO, KamLAND …

pp 7Be CNO 8B

gap

e- survival probability from solar neutrino data vs LMA-MSW solution

e

2

1

0

mas

s m2atm

m2sun

3

m2dip

s

s

2m

1m

0m sterile resonances

He

density

m012 > (0.2 - 2) 10-5 eV

2

sin2 2 = 10-4 - 10-3

non-adiabatic level crossing

se

a

0

1

2

U = U U

U - rotation in 01- plane on

U - rotation in 12-plane on s mixes in

0and1

ee

2 2m

1m

0m

1

0

Scheme of transitions

P(e e) ~ |Ue1m

A11 + Ue0mA01|2 |Ue1 |2 + |Ue2

m|2|Ue2|2

s

interference wiggles

- dip- wiggles

sin22= 10-3 (red), 5 10-3 (blue)

SK-I

SK-III

SNO-LETA

R = 0.2

m2 = 1.5 10-5 eV2

SNO-LETA

Borexino

P. De Holanda, A.S.

dataexcluded

pepBe

pep-suppressed

R = 0.007 - 0.07

excluded

m012 > 0.5 10-5

eV2

Predictions for pep-neutrinos

R = 0.07 - 0.115

P(pep) = 0.2 – 0.3

P(Be) = 0.55

R > 0.12 P(pep) = 0.53

2 fit of spectra with sterile neutrino dip:SK-I, SK-III, SNO-LETA, SNO-NC, Borexino

Best fit values: m012 ~ 1.5 10-5 eV2 sin2 2 ~ 10-3 2 = 7.5

m012 = (1 – 2) 10-5 eV2sin22 ~ (0.5 – 1) 10-3

2 > 6

m0 > 0.003 eV

Alternative: mixing with level 2m

R= m012 / m21

2 = 1.1

sin22 ~ (0.5 – 1) 10-3

Interval with

sin2 2 ~ 10-3

m0 ~ 0.003 eV M2 MPlanck

m0 = M ~ 2 - 3 TeV

mixing

h vEW M ~

sin2 2 ~ 10-1 vEW M

~

h = 0.1

P. De Holanda, A.S.

Mixing with the third active state

s

Production of sterile in the Early universe

’ = cos23 + sin23

3 = cos ’ + sins

Atmospheric neutrinos:

sin2 < 0.2 – 0.3 (90%)

MINOS:

sin2 < 0.23 (90%)

m302 ~ 2.5 10-3 eV2

M Cirelli G Marandella A Strumia F Vissani

tan2

Mixing of s in 3

where

’ – s resonance ER ~ 12 GeV

s resonance peak 10 – 15 GeV

IceCube Deep Core

Additional suppression of e flux

S Razzaque and A. S.arXiv:1104.1390 [hep-ph]

H Nunokawa O L G PeresR Zukanovich-FunchalPhys. Lett B562 (2003) 279

- s oscillations with m2 ~ 1 eV2 are enhanced in matter of the Earth in energy range 0.5 – few TeV

This distorts the energy spectrum and zenith angle distribution of the atmospheric muon neutrinos, also modifies /e ratio

Can be tested by IceCube

First data from IceCube

- Check theoretical considerations, generalize … - perform analysis of the data

S Choubey JHEP 0712 (2007) 014

Unfolded neutrino spectrum

Zenith angle distribution

R. Abbasi et al, arXiv:1010.3980 [astro-ph.CO]

April 2008 – May 200940 strings100 GeV – 400 TeV18 000 up-going muons

e

2

1

4

mas

s

m2atm

m2sun

3

m2LSND

s

P ~ 4|Ue4 |2|U4 |2

Restricted by short baseline experiments CHOOZ, CDHS, NOMAD

LSND/MiniBooNE: vacuum oscillations

With new reactor data:

m412 = 1.78

eV2Ue4 = 0.15

U4 = 0.23

Normal mass hierarchy in the flavor block; m0 ~ 1 eV

|Ue4 |2 |U|2

are large enough, so that evel crossings are adiabatic

Three new level crossings

Ve - Vs = 2 GF (ne – nn /2)

= cos23 + sin23

0 = - sin + coss

3 = cos + sins

= cos23 - sin23 2 = ~

~

~

~

~

s mixes with ~

Uf = U23 U

Propagation basis: s, ,2~ ~

S

s mixes in the mass states and 0

Evolution is reduced to 2-problem exactly

s

where

0

s s

fU23

s

s

S

~

Propagation basis~

~

~

~

projection projectionpropagation

P( ) = |cos223A22 + sin223A33 |2

A22

A33

decouples

antineutrinos

MSW resonance dip

neutrinos

Effect of phase shift for the

oscillations

due to matter effects

Eth = 0.1 TeV

S = N(osc.)/N(no osc.)

S - mass mixing case

Free normalization and tilt factor

sin2 > 0.04 LSND: + 5% uncorrelated systematic errors

Statistical errors + free normalization + tilt

Illustrative fit in the simplestmixing scheme

0 = - sin + coss

3 = - cossin23 + cos 23 - sinsin23s

Uf = U U23

Propagation basis = flavor basis

s mixes with

s

0

s-

2 = - sincos23 + sin 23 - coscos23s

Evolution is not reduced to the 2 - evolution exactly

neutrinosantineutrinos

Free normalization and tilt factor

S - mixing

Fit with sterile is even better

Eth = 0.1 TeV

Eth =

0.1

TeV

Eth =

1 T

eV

Light sterile neutrino mixed in 1 or/and 2 with

m012 ~ 1.5 10-5

eV2sin2 2 ~ 10-3

leads to the dip in the spectrum which explains an absence of the up turn of the spectrum, reduces prediction for the Ar production rate

Being mixed in 3 with sin2 ~ 0.2 sterile can be generated in the Early Universe Neff ~ 1, thus explaining additional radiation

New evidences/hints of existence of sterile: MiniBooNE, reactors,

Gallium calibration, solar, additional radiation in the Universe

Convincing? Consistent? Controversial?

Depending on values of parameters, U4, U, m422

large variety of zenith angle distribution can be obtained.

With present data only part of the parameter space relevant for LSND/MiniBooNE can be excluded and in some ranges the fit can be even improved.

Future high statistics studies of the zenith angle distributions

in different energy regions (with different energy thresholds)

can provide sensitive search of sterile in whole parameter space

and discriminate different mixing scenarios.

IceCube has high sensitivity to sterile mixing with

m012 ~ 1 eV2

sin2 > 0.01

E = 200 MeV E = 475 MeV

In the lowest order at high energies P( ) ~ | sin2 ’ A33() + cos2 ’|2

V0T = ( US0 , U0 , U0 )

In general, the Hamiltonian H = 0 V0 x V0

T + 2 V2 x V2T

i = mi32 / 2E Vi

T = ( USi , Ui , Ui ), (i = 0, 2)

H ~ 0 V0 x V0T

tan ’ = - U0 / U0 sin2 = |U0|2 + | U0|2

|U0|2 ~ 0.02 – 0.04

|U0|2 < 0.5 MINOS, Atmospheric neutrinos

m032 = 1 eV2 LSND/MiniBooNE

Gallium calibration Reactor, miniboone

G.Mention et al, arXiv: 1101.2755

RGa = 0.87 +/- 0.05

Gallex/GNO 51CrSAGE 51 Cr, 37Ar

Calibration

C Giunti, M. Laveder

Evolution between two sterile resonances

Interference of two amplitudesof transition

e

Ue1m

Ueom

adiabatic

non-adiabatic

projection transitions

1m

0m

1

Eth = 1 TeV

Narrowing the zenith angle interval – enhancesEffect 40 %

E F Aeff

F = F0 P + Fe

0 Pe +

Flux of muon neutrinos:

~ F0 P

+ F0 P(kE) B

Production of sterile in the Early universe

Neff = 0.8 - 1

A D Dolgov, F L Villante

can be generated

sin2 2sin2 2

log(

m2

/eV

2 )

sin2

sin2

0.5 S - mass mixing

sin2 = 1

1.0 S --mixing

With increase of |U0|2

sin2 decreases

sin2 increases, resonance disappears

distortion of the E and Z

distributions becomes weaker

sin2 =

no strong suppression in vertical bin

For different mixing schemes

Varying |U0|2

sin2 = s24

2 s24

2 + s342