A. Yu. Smirnov
International Centre for Theoretical Physics, Trieste, Italy

Kyoto, November 24, 2011,

LightNo weak interactions:- singlets of the SMsymmetry group

Couple with usual neutrinos
via (Dirak) mass terms
Mix with active neutrinos
Sov. Phys. JETP 26 984 (1968)
in the context of idea ofneutrino–antineutrino oscillations

ns40 - 70 MeV- LSND, MiniBooNE

1 - 10 keV- Warm Dark matter- Pulsar kick

0.5 - 2 eV

- LSND, MiniBooNE- Reactor anomaly- Ga-calibration experiments- Extra radiation

1 MeV

1 keV

1 eV

10-3 eV(2 – 4) 10-3 eV - Solar neutrinos- Extra radiationin the Universe

Sterile neutrinos (effectively) propagate fasterthan light in 4D, ``short-cut’’ in extra dimensions

H Pas, S Pakvasa,T Weiler
hep-ph/0504096
Only small part of neutrino flux (state) propagates
faster than light or/and
whole the nm signal is strongly suppressed
contradicts OPERA result (especially the latest one
with 3 ns neutrino bunches )SAGE

Steriles are back?

LSND

Double-Chooz

MiniBooNE

Gallex,GNO

Effective number of neutrino species+ 0.86
Neff = 4.34 - 0.88 (68 % CL)- WMAP-7- Barion Acoustic Oscillations- Hubble constant

Neff = 5.3 +/- 1.3 (68% CL)- WMAP–7
J. Dunkley et al- Atacama Cosmology Telescope arXiv:1009.0866

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

D Neff = (0.02 – 2.2) (68% CL)

J. Hamann et al
PRL 105 (2010)181301

BBN+ 0.80
Neff = 3.68 - 0.70

(68 % CL)

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

E Giusarma et al 1102.4774 [astro-ph]

LCDM

Dm2 < 0.25 eV2

J R Kristiansen, O Elgaroy
1104.0704 [astro-ph]Inverse approach:wCDM + 2nS1). w < -1

68 % 95%

ruling out L2). Age of the Universe
12.58 +/- 0.26 Gyr
too young?

- WMAPrun 1 (blue) - SDSS (red galaxy clustering)- Hubble (prior on H0 )+ BBN
run 2 (red) - Supernova Ia Union
Compilation 2 (in add)

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

Accelerator neutrinos

A. Sousa|Um4|2 < 0.015 (90% CL)

nm - ns mixing
In assumption ofno-oscillations in ND|Um4|2 < 0.015 (90% CL)

q13 = 0|Um4|2 < 0.019 (90% CL)

q13 = 11.5o

LSND/MiniBooNE require:|Um4|2 > 0.025

Dm412 < 0.5 eV2

cosmology
BUGEY+MINOS

or modification of Cosmology:
DN = 1.23 (massless)w = - 1.11
chemical potential for ne

J Hamann et al 1108.4136

S

SO(10)
Standard
ModelS
also contact
Interactions
With q & luduR
dR

Snl

LSAnR

S S
S SLSSSSsSSlRSMSSASSSHidden sector
with certain
symmetries
Planck scale physics

Massmatrix
For mSS ~ 1 eV

nenmntmee mem met meS…
mmm mmt mmS…
… mtt mtSnS

…

…

…

mSStanqjS = mjS/mSS ~ 0.2 - is not small

produces large corrections to the active neutrino mass matrix
dmij ~ - tanqiStanqjS m SS ~ 0.04 mSS
mSS >> mab , maS
In general can not be considered as small perturbation!
Effect can be small if
Active neutrino spectrum
is quasi degeneratemSS ~ mabmeS mmS mtS havecertain symmetry

J. Barry,
W. Rodejohann,He Zhang
arXiv: 1105.3911

mn = ma + dm
Original active mass
matrix e.g. from see-saw

Induced mass matrix
due to mixing with nu steriledm can change structure (symmetries) of the original
mass matrix completely (not a perturbation)

Enhance lepton mixing
Be origin of difference ofandP. C. de Holanda, A. Yu. S. 1012.5627 [hep-ph]QArexp < QArLMA
2.55 +/- 0.25 SNU> 3.1 SNU

No turn up of the spectrum in SK

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

Light sterile neutrino RD = Dm012 / Dm212 << 1 << 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

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

S. Abe, at al., [The KamLAND collaboration]
1106.0861 [hep-ex]nsmass

Dm2atmn0n1nmntVery light sterile neutrino

n3n2

neMotivated by- solar neutrino data

Dm2sunDm2dip- additional radiationin the Universe if mixed in n3- no problem with LSS(bound on neutrino mass)

H

n2m

D m012 > (0.2 - 2) 10-5 eV 2

nesin2 2 = 10-4 - 10-3

ns
nm/t
n0m

sterile resonancesn1m
density

non-adiabaticlevel crossing

ns
ne
na

U = Uq Un0n1n2

Uq - rotation in 12-plane on q12

ns mixes in n0 and n1

U - rotation in 01- plane on 
Scheme of transitions

n2mn2

ne

n1m

n1

neinterference
 wiggles

n0mn0nsP(ne ne) ~ |Ue1m A11 + Ue0mA01|2 |Ue1 |2 + |Ue2 m|2|Ue2|2

- dip- wiggles

sin22 = 10-3 (red), 5 10-3 (blue)

SK-I
SNO-LETA
P. De Holanda, A.S.

SK-III

Borexino
SNO-LETA
RD = 0.2
Dm2 = 1.5 10-5 eV2

data

excludedBe

RD = 0.007 - 0.07
Be

pep

Dm012 > 0.5 10-5 eV2
BOREXINO:
pep- flux is consistent
with the LMA suppression
P(pep) = 0.53
RD > 0.12
Dm012 > 0.9 10-5 eV2

BOREXINO Collaboration,
ArXiv: 1110.3230

c2 fit of spectra with sterile neutrino dip:
SK-I, SK-III, SNO-LETA, SNO-NC, Borexino
Best fit values:

Dm012 ~ 1.5 10-5 eV2Interval with
Dc2 > 6

D m012 = (1 – 2) 10-5 eV2

sin2 2 ~ 10-3

sin22 ~ (0.5 – 1) 10-3

m0 > 0.003 eVAlternative: mixing with level n2m
RD = Dm012 / Dm212 = 1.1

Dc2 = 7.5

sin22 ~ (0.5 – 1) 10-3

m0 =M2
MPlancksin2 2 ~ 10-3

~h vEWM

sin2 2b ~ 10-1b~vEW
M

m0 ~ 0.003 eV

M ~ 2 - 3 TeVmixing
h = 0.1

P. De Holanda, A.S.

Mixing with the third active statens

Mixing of ns in n3

n3 = cosb nt ’ + sinb ns

Production of sterile in the Early universe
M Cirelli G Marandella A Strumia F Vissani

where nt’ = cosq23 nt + sinq23 nm
Dm302 ~ 2.5 10-3 eV2Atmospheric neutrinos:

sin2b < 0.2 – 0.3 (90%)
MINOS:

sin2b < 0.23 (90%)
tan2b

nt’ – n s resonanceER ~ 12 GeVnm  n s resonance peak 10 – 15 GeVInterplay of nm  n s andnm  nt oscillations

Phase shift and decrease ofamplitude of oscillations:

P. De Holanda, A. S.

With sterile

difference

IceCube Deep Core

~ 20 % suppression of rate of events in themuon energy bins 5 – 15 GeV

S Razzaque and A. S.
arXiv:1104.1390 [hep-ph]Large Scintillator
Neutrino Detectorp ->Los Alamos Meson Physics Facility
ne + p  e+ + np+ -> m+ + nm-> e+ + ne + nm
decay at restnmnm  ne

ne

P = (2.64 +/- 0.67 +/- 0.45) 10-3
Oscillations?
Dm2 > 0.2 eV2ne+

3.8s excess- now less?

tCherenkov cone + scintillations

200 t mineraloil scintillator

Now an excess is observed bothin neutrino and antineutrino channels
In both channels an excess exists bothat small (below 475 MeV) and at high energies
An excess smoothly increases with decreaseof energy starting from ~800 MeV
It seems this is the same effect andthere is no justification to split data
Neutrino and antineutrino data are consistent
No need to introduce second sterile
Not possible to explain by oscillations?

Cosmology-MINOS

Large uncertainties in neutrino cross-sections
Energy determination?

In spite of this….
New experiments:- Reactors (NUCIFER, SCRAAM)- MegaCurie strength sources- Accelerator SBL experiments
OscSNS BooNE
MicroBooNE (LArTPC),
CERN-PSC Giunti, M Laveder
1107.1452 [hep-ph]

IceCube

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

nm - ns oscillations with Dm2 ~ 1 eV2are enhanced in matter of theEarth in energy range 0.5 – few TeVThis distorts the energy spectrum
and zenith angle distribution of theatmospheric muon neutrinos
Can be tested by IceCube
S Choubey JHEP 0712 (2007) 014
S Razzaque and AYS ,1104.1390, [hep-ph]R. Abbasi et al, arXiv:1010.3980[astro-ph.CO]

Zenith angle distribution

Unfolded neutrino spectrum
April 2008 – May 2009
40 strings
100 GeV – 400 TeV
18 000 up-going muons

nsne
nm

nt

LSND/MiniBooNE: vacuum
oscillations

n4mass

P ~ 4|Ue4 |2|Um4 |2
Dm2LSNDn3n2n1Dm2atm
Dm2sunRestricted by short baseline
experiments CHOOZ, CDHS,NOMAD
With new reactor data:
Dm412 = 1.78 eV2
Ue4 = 0.15
Um4 = 0.23

Normal mass hierarchy inthe flavor block; m0 ~ 1 eVThree new level crossings|Ue4 |2 |Um4 |2
are large enough, so thatevel crossings are adiabatic
Ve - Vs = 2 GF (ne – nn /2)

nS
s242 =nsnt
nm

s342

Uf = U23 Un0
n3
n2

ns mixes in the mass states n3 and n0

n0 = - sin ~n3 + cos ns
n3 = cos ~n3 + sin ns~

n2 = n2where~

n3 = cosq23 nt + sinq23 nm~
n = cosq
2~
ns mixes with n3Propagation basis:~~ ,nns, n32

Evolution is reduced to 2n-problem exactly

23 nm - sinq23 nt

Propagation basis

nf = U23 ~nnsnsnt~
n3nm~
n2projection

nsns

A33~
n3nt

A22~
n2nm

decouples

propagation

Sprojection

P(nm  nm) = |cos2q23A22 + sin2q23A33 |2

antineutrinos

neutrinosS = N(osc.)/N(no osc.)
Eth = 0.1 TeV

nS - mass mixing caseFree normalizationand tilt factor

Illustrative fit
in the simplest
mixing scheme

LSND:

sin2  > 0.04

Statistical errors +free normalization + tilt

+ 5% uncorrelated
systematic errors

ns-nmnsntnms342 = 0

Uf = Ub U23

n0n3n2ns mixes with nm

n0 = - sinb nm + cosb ns
n3 = - cosb sinq23 nm + cos q23 nt - sinb sinq23 ns
n2 = - sinb cosq23 nm + sin q23 nt - cosb cosq23 ns

Propagation basis = flavor basis
Evolution is not reduced to the 2n - evolution exactly

nS - nm mixing
Free normalizationand tilt factor
Fit with sterile is even better
Eth = 0.1 TeVIn General
For different
mixing schemes
Varying |Ut0|2
sin2b =s242
s242 + s342

Zenith angle distribution depends on admixture of nt in 4th mass stateEth = 1 TeV

Eth = 0.1 TeV

S. Razzaque, A.S.

at low energies

Shift of phase quantifies effectof sterile neutrino

IceCube DeepCore

S Razzaque
A.S.

Zenith angle distribution of events in different energy ranges

meV scale sterile neutrino mixed
in n1 or/and n2 withD m012 ~ 1.5 10-5 eV2leads 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 n3 with sin2b ~ 0.2 sterile can be generated
in the Early Universe DNeff ~ 1, thus explaining additional radiation

eV scale: Convincing? Consistent? Controversial?
IceCube has high sensitivity to sterile mixing with
Depending on values of parameters, Um4, Ut4 , Dm422
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 andin 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 spaceand discriminate different mixing scenarios.

Cosmology: eV + meV steriles ?

Gallium calibration

Calibration

Gallex/GNO 51Cr
SAGE 51 Cr, 37Ar

RGa = 0.87 +/- 0.05

C Giunti, M. Laveder

Reactor, miniboone

G.Mention et al,arXiv: 1101.2755

Evolution between two sterile resonancesInterference of two amplitudesof transition
projection
Ue1mtransitions

n1m

adiabatic

n1neUeomn0m

non-adiabatic

Eth = 1 TeV

Narrowing the zenith angle
interval – enhances
Effect 40 %

E Fm Aeff
Flux of muon neutrinos:
Fm = Fm0 Pmm + Fe0 Pem ++ Fm0 Pmt(kE) Bm~ Fm0 Pmm

Production of sterile in theEarly universe

D Neff = 0.8 - 1
can be generatedlog( Dm2 /eV2 )A D Dolgov, F L Villante

sin2 2bsin2 2b

sin2 b = 1

sin2b =0.5 nS - mass mixing
1.0 nS -nm -mixing

sin2b

no strong suppression in vertical bin

With increase of |Ut 0|2
sin2b decreases
sin2 increases,
resonance disappears
distortion of the E and qZ
distributions becomes weakersin2b

L = 541 m, <En> ~ 800 MeV
12 m diameter tank
450 t (mineral oil) 1280 PMT

Alma X Conzalelez-Morales, et al1106.5052 [astro-ph,CO]Controversial andnot convincing

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 Um4 are allowed to explain LSND/MiniBooNE –less tension with SBL experiment bounds|Um4|2 : 0.04  0.02
3+2
schemeJ Kopp, M. Maltoni,T.Schwetz
1103.4570 [hep-ph]n4n5

Dm412 = 0.47 eV2

Dm512 = 0.87 eV2

Ue4 = 0.128

Ue5 = 0.138

Um4 = 0.165

Um5 = 0.148

J. Kopp, M Maltoni, T. Schwetz
C Giunti, M Laveder
1107.1452 [hep-ph]Increase of theMean flux by 3%

Revised value ofcross-section

Rreact = 0.937 +/- 0.027
2.14 sDm2 > 1.5 eV2
sin2 2q = 0.17 +/- 0.1G.Mention et al,arXiv: 1101.2755

Calibration

Source + reactor

C Giunti, M. Laveder

G.Mention et al,arXiv: 1101.2755

Gallex/GNO 51Cr
SAGE 51 Cr, 37Ar
RGa = 0.87 +/- 0.05
sin22q= 0.24

Dm2 = 2.15 eV2antineutrinos

neutrinosIn general,
the Hamiltonian

H = D0 V0 x V0T + D2 V2 x V2T
ViT = ( USi , Ut i , Um i ), Di = D mi32 / 2E

In the lowest
order at highenergies

H ~ D0 V0 x V0T

V0T = ( US0 , Ut 0 , Um 0 )P(nm  nm) ~ | sin2q ’ A33() + cos2q ’|2tanq ’ = - Um 0 / Ut 0
sin2 = |Um 0|2 + | Ut 0|2|Um 0|2 ~ 0.02 – 0.04
|Ut 0|2 < 0.5

D m032 = 1 eV2

LSND/MiniBooNE

MINOS, Atmospheric neutrinos(i = 0, 2)