Transcript No Slide Title

A. Yu. Smirnov
ICTP, Trieste & INR, Moscow
* Context
* Refraction, Resonance, Adiabaticity
* MSW: physical picture of the effect
* Large mixing MSW solution of the solar neutrino problem
* Supernova neutrinos and MSW effect
W. Pauli
E. Fermi
B. Pontecorvo,
Z. Maki, M. Nakagawa, S. Sakata
L.Wolfenstein
J.N.Bahcall
G.T.Zatsepin, V.A. Kuzmin
R. Davis Jr.,
D.S. Hammer,
K.S. Hoffman
A Yu Smirnov
[1] L. Wolfenstein, ``Neutrino oscillations in matter’’, Phys. Rev. D17, (1978) 2369-2374.
[2] L. Wolfenstein, ``Effect of matter on neutrino oscillations’’, In Proc. of ``Neutrino -78’’,
Purdue Univ. C3 - C6.
[3] L. Wolfenstein, ``Neutrino oscillations and stellar collapse’’,
Phys. Rev. D20, (1979) 2634 - 2635.
[4] S. P. Mikheyev and A. Yu. Smirnov, ``Resonance enhancement of oscillations in matter
and solar neutrino spectroscopy’’, Sov. J. Nucl. Phys. 42 (1985) 913 - 917.
[5] S. P. Mikheyev and A. Yu. Smirnov, ``Resonance amplifications of n- oscillations
in matter and solar neutrino spectroscopy’’, Nuovo Cimento C9 (1986) 24.
[6] S. P. Mikheyev and A. Yu. Smirnov, ``Neutrino oscillations in variable-density
medium and n-bursts due to gravitational collapse of stars’’,
Sov. Phys. JETP, 64 (1986) 4 - 7.
[7] S. P. Mikheyev and A. Yu. Smirnov, Proc. of the 6th Moriond workshop on
``Massive neutrinos in astrophysics and particle physics, Tignes, France,
eds. O Fackler and J. Tran Thanh Van, (1986) p.355.
Mass eigenstates
Flavor neutrino states:
ne
e
nm
m
nt
n1
n2
n3
m1
m2
m3
t
correspond to certain
charged leptons
interact in pairs
Eigenstates of the
CC weak interactions
ns
Flavor
states
=
Mass
eigenstates
Sterile
neutrinos?
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ne
nm nt
|2
|Ue3
n2
n1
Dm2atm
n2
n1
Normal mass hierarchy
(ordering)
Dm2sun
mass
mass
n3
Dm2atm
|Ue3|2
Dm2
n3
sun
Inverted mass hierarchy
(ordering)
Type of mass spectrum: with Hierarchy, Ordering, Degeneracy
Type of the mass hierarchy: Normal, Inverted
Ue3 = ?
absolute mass scale
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vacuum
mixing
angle
ne = cosq n1 + sinq n2
inversely
nm = - sinq n1 + cosq n2
n2 = sinq ne + cosq nm
n1 = cosq ne - sinq nm
coherent mixtures
of mass eigenstates
ne
n2
n1
nm
n2
n1
The relative phases
of the mass states
in ne and nm
are opposite
flavor composition of
the mass eigenstates
wave
packets
n2
n1
Flavors of eigenstates
ne
n2
n1
nm
n2
n1
Interference of the parts of
wave packets with the same
flavor depends on the
phase difference Df
between n1 and n2
A. Yu. Smirnov
Propagation in vacuum:
Flavors of mass eigenstates do not change
Determined by q
Admixtures of mass eigenstates
do not change: no n1 <-> n2 transitions
ne
n2
n1
Df = 0
Df = Dvphase t
Due to difference of masses n1 and n2
have different phase velocities:
Dm2
Dvphase =
2E
Dm2 = m22 - m12
Oscillation length:
ln = 2p/Dvphase = 4pE/Dm2
effects of the phase difference
increase which changes
the interference pattern
Amplitude (depth) of oscillations:
A = sin22q
A. Yu. Smirnov
L. Wolfenstein, 1978
Elastic forward
scattering
ne
Potentials
Ve, Vm
V ~ 10-13 eV inside the Earth for E = 10 MeV
Difference of potentials is important
W
for ne nm :
Refraction index:
e
Refraction length:
~ 10-20 inside the Earth
< 10-18 inside the Sun
~ 10-6 inside the neutron star
Neutrino optics
ne
Ve- Vm = 2 GFne
n-1= V/p
n-1
e
l0 = 2p / (Ve - Vm)
= 2 p/GFne
focusing of neutrinos fluxes by stars
complete internal reflection, etc
Effective
Hamiltonean
H0
H = H0 + V
Eigenstates
n1, n2
n1m, n2m
Eigenvalues
m1, m2
m12/2E , m22/2E
m1m, m2m
H1m, H2m
n1m
depend
on ne, E
ne
n1
is determined with respect
to eigenstates in matter
V = Ve - Vm
n2m
q
n2
qm is the mixing angle in matter
qm
nm
In resonance:
sin2 2qm
sin2 2qm = 1
n
n
sin2
2q = 0.08
Mixing in matter is maximal
Level split is minimal
sin2 2q = 0.825
ln = l0 cos 2q
Vacuum
oscillation
length
l n / l0
Resonance width:
Resonance layer:
~nE
DnR = 2nR tan2q
n = nR + DnR
~
~
Refraction
length
For large mixing: cos 2q = 0.4 - 0.5
the equality is broken
the case of strongly coupled system
shift of frequencies
A Yu Smirnov
resonance
H
sin2 2q = 0.825
n2m
Dependence of the neutrino eigenvalues
on the matter potential (density)
ln
=
l0
2E V
Dm2
V. Rubakov, private comm.
N. Cabibbo, Savonlinna 1985
H. Bethe, PRL 57 (1986) 1271
ln
= cos 2q
l0
Crossing point - resonance
the level split in minimal
the oscillation length is maximal
ne
nm
Large
mixing
n1m
ln/ l0
n
sin2 2q = 0.08
ne
Small
mixing
n2m
nm
ln/ l0
n1m
For maximal mixing: at zero density
A Yu Smirnov
Resonance enhancement
of neutrino oscillations
Density
profiles:
Constant density
Degrees of
freedom:
Change of the phase
difference between
neutrino eigenstates
In general:
Adiabatic
(partially adiabatic)
neutrino conversion
Variable density
Change of mixing, or
flavor of the neutrino
eigenstates
Interplay of oscillations
and adiabatic conversion
A Yu Smirnov
In uniform matter (constant density)
mixing is constant
qm(E, n) = constant
Flavors of the eigenstates do not change
Admixtures of matter eigenstates
do not change: no n1m <-> n2m transitions
Monotonous increase of the phase difference
between the eigenstates Dfm
ne
as in vacuum
n2m
n1m
Dfm = 0
Parameters of oscillations (depth and length)
are determined by mixing in matter
and by effective energy split in matter
Dfm = (H2 - H1) L
sin22q, ln
sin22qm, lm
ne
n
F0(E)
Source
k = p L/ l0
F (E)
F0(E)
F(E)
Layer of matter with constant density, length L
thin layer
ne
Detector
thick layer
k=1
sin2 2q = 0.824
E/ER
k = 10
sin2 2q = 0.824
E/ER
A Yu Smirnov
ne
n
F0(E)
Source
k = p L/ l0
F (E)
F0(E)
F(E)
Layer of matter with constant density, length L
thin layer
ne
Detector
thick layer
k=1
sin2 2q = 0.08
E/ER
k = 10
sin2 2q = 0.08
E/ER
A Yu Smirnov
resonance
layer
Continuity:
neutrino and antineutrino semiplanes
normal and inverted hierarchy
P
Oscillations (amplitude of oscillations)
are enhanced in the resonance layer
l n / l0
E = (ER - DER) -- (ER + DER)
DER = ERtan 2q = ER0sin 2q
ER0 = Dm2 / 2V
P
With increase of mixing: q -> p/4
ER -> 0
DER -> ER0
l n / l0
A Yu Smirnov
Non-uniform matter
density changes on
the way of neutrinos:
ne = n e(t)
H = H(t) depends on time
qm = qm(n e(t))
mixing changes in the
course of propagation
n1m n2m are no more the
eigenstates of propagation
-> n1m <-> n2m transitions
However
if the density changes slowly enough (adiabaticity condition)
n1m <-> n2m transitions can be neglected
Flavors of eigenstates change
according to the density change
Admixtures of the eigenstates,
n1m n2m, do not change
Phase difference increases
determined by qm
fixed by mixing in
the production point
according to the level split
which changes with density
Effect is related to the change of flavors
of the neutrino eigenstates in matter with varying density
External conditions (density)
change slowly
so the system has time to
adjust itself
dqm
dt
H2 - H1
transitions between
the neutrino eigenstates
can be neglected
Crucial in the resonance layer:
- the mixing angle changes fast
- level splitting is minimal
<< 1
Adiabaticity condition
n1m <--> n2m
The eigenstates
propagate
independently
DrR > lR
if vacuum mixing
is small
lR = ln/sin2q is the oscillation width in resonance
DrR = nR / (dn/dx)R tan2q is the width of the resonance layer
If vacuum mixing is large
the point of maximal adiabaticity violation
is shifted to larger dencities
n(a.v.) -> nR0 > nR
nR0 = Dm2/ 2 2 GF E
The picture of conversion depends on how far from the resonance layer in the density
scale the neutrino is produced
n0 > nR
n0 - nR >> DnR
Non-oscillatory
conversion
n0 ~ nR
Interplay of
conversion and
oscillations
n0 < n R
nR - n0 >> DnR
Oscillations with
small matter effect
nR ~ 1/E
All three possibilities are realized for the solar neutrinos
in different energy ranges
A Yu Smirnov
n1m <--> n2m
n0 >> nR
Non-oscillatory transition
P = sin2 q
n2m
n1m
n2
n1
Mixing suppressed
n0 > nR
Resonance
interference suppressed
Adiabatic conversion + oscillations
n2m
n1m
n2
n1
n0 < nR
Small matter corrections
n2m
n1m
A. Yu. Smirnov
n2
n1
ne
survival probability
The picture of adiabatic conversion is universal in terms of variable y = (nR - n ) / DnR
(no explicit dependence on oscillation parameters density distribution, etc.)
Only initial value y0 matters.
production
point
y0 = - 5
resonance
oscillation
band
averaged
probability
(nR - n) / DnR
(distance)
A Yu Smirnov
Fast density change
n2m
n1m
n0 >> nR
n2m
n1m
n2
n1
Resonance
Admixture of n1m increases
ne
4p + 2eAdiabatic conversion
in matter of the Sun
r : (150
4He
+ 2ne + 26.73 MeV
electron neutrinos are produced
F = 6 1010 cm-2 c-1
0) g/cc
Oscillations
in vacuum
n
J.N. Bahcall
total flux at the Earth
Oscillations
in matter
of the Earth
solar data
solar data + KamLAND
P. de Holanda, A.S.
sin2q13 = 0.0
Dm2 = 6.8 10-5 eV2
tan2q = 0.40
Dm2 = 7.3 10-4 eV2
tan2q = 0.41
Survival probability
Adiabatic
solution
npp
nBe
nB
Earth matter
effect
sin2q
III
II
I
l n / l0 ~ E
Oscillations with
small matter effect
Conversion +
oscillations
Conversion with
small oscillation
effect
Non-oscillatory
transition
A Yu Smirnov
survival probability
survival probability
tan2q = 0.41,
Dm2 = 7.3 10-5 eV2
core
resonance
E = 14 MeV
surface
E = 2 MeV
y
y
distance
survival probability
survival probability
distance
E = 6 MeV
y
E = 0.86 MeV
y
An example: E = 10 MeV
Resonance layer:
nR Ye = 20 g/cc
RR= 0.24 Rsun
In the production point:
sin2qm0 = 0.94
cos2 qm0 = 0.06
n2m
n1m
Evolution of the eigenstate n2m
Flavor of neutrino state follows density change
n
n2 2
Regeneration of
the ne flux
Day - Night asymmetry
Variations of signal
during nights (zenith
angle dependence),
Seasonal variations
Spectrum distortion
Parametric effects for the
core crossing trajectories
Oscillations
in the matter
of the Earth
core
mantle
freg
Averaging of oscillations,
divergency of the wave packets
incoherent fluxes of n1 and n2
arrive at the surface of the Earth
n1 and n2 oscillate inside the Earth
Regeneration of the ne flux
ln /l0
ln /l0 ~ 0.03
E = 10 MeV
P ~ sin2 q + freg
freg ~ 0.5 sin 22q ln /l0
The Day -Night asymmetry:
AND = freg/P ~ 3 - 5 %
Oscillations
+ adiabatic
conversion
distance
A Yu Smirnov
r ~ (1011 - 10 12 ) g/cc
0
E (ne) < E (ne) < E ( nx )
A Yu Smirnov
The MSW effect can be realized
in very large interval of
neutrino masses ( Dm2 ) and mixing
Dm2 = (10-6 - 107) eV2
sin2 2q = (10-8 - 1)
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)
Small mixing angle realization
of the MSW effect
If 1-3 mixing is not too small
s132 > 10- 5
strong non-oscillatory conversion
is driven by 1-3 mixing
A way to probe
the hierarchy and
value of s13
In the case of normal mass hierarchy:
ne <-> nm /nt
F(ne) = F0( nm)
almost completely
hard ne- spectrum
No earth matter effect in ne - channel
but in ne - channel
Neutronization ne - peak disappears
F(ne) =
F0(n
e)
+p
DF0
p
p = (1 - P1e) is the permutation factor
P1e is the probability of n1-> ne transition
inside the Earth
DF0 = F0(nm) - F0(ne)
p depends on distance traveled
by neutrinos inside the earth to a given
detector:
4363 km Kamioka
d=
8535 km IMB
10449 km Baksan
Can partially explain the difference
of energy distributions of events
detected by Kamiokande and IMB:
at E ~ 40 MeV the signal is suppressed
at Kamikande and enhanced at IMB
p
C.Lunardini
A.S.
R.C. Schirato, G.M. Fuller, astro-ph/0205390
The shock wave can reach the region
relevant for the neutrino conversion
r ~ 104 g/cc
During 3 - 5 s from the beginning
of the burst
Influences neutrino conversion if
sin 2q13 > 10-5
The effects are in the neutrino
(antineutrino) for normal (inverted)
hierarchy:
h - resonance
change the number of events
R.C. Schirato, G.M. Fuller, astro-ph/0205390
``wave of softening of spectrum’’
K. Takahashi et al, astro-ph/0212195
delayed Earth matter effect
Density profile with shock wave propagation
at various times post-bounce
C.Lunardini, A.S., hep-ph/0302033
G. Fuller
Studying effects of the shock wave
on the properties of neutrino burst
one can get (in principle) information on
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
I. Resonance enhancement of oscillation
in matter with constant density
Two matter effects:
Resonance enhancement
of oscillations:
Large mixing MSW effect:
Small mixing MSW effect:
2. Adiabatic (quasi-adiabatic) conversion
in medium with varying density (MSW)
(a number of other matter effects exist)
Can be realized for neutrinos propagating
in the matter of the Earth (atmospheric
neutrinos, accelerator LBL experiments,
SN neutrinos ...)
Provides the solution of the solar neutrino
problem
Determination of oscillation parameters
Dm122 q12
Can be realized in supernova for 1-3 mixing
probe of 1-3 mixing, type of mass hierarchy
astrophysics, monitoring of a shock wave
A Yu Smirnov