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>
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
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
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.