The MSW effect

1
The MSW effect
and
Neutrino Astrophysics
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
2
Context
Neutrino mass

W. Pauli E. Fermi
Neutrino mixing
and Oscillations
Matter effect
B. Pontecorvo, Z. Maki, M. Nakagawa, S. Sakata
Neutrino
Refraction
L.Wolfenstein
Spectroscopy of
Solar Neutrinos
Homestake
J.N.Bahcall G.T.Zatsepin, V.A. Kuzmin
Experiment
R. Davis Jr., D.S. Hammer, K.S. Hoffman
A Yu Smirnov
3
References

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.
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Flavors, masses, mixing

Mass eigenstates
Flavor neutrino states
n2
n1
n3
nm
nt
ne
m1
m2
m3
m
e
t
correspond to certain charged leptons
Mixing
interact in pairs
Eigenstates of the CC weak interactions
Flavor states
Mass eigenstates

ns
Sterile neutrinos?
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Mass spectrum and mixing
ne
nm
nt

Ue32
n2
n3
Dm2sun
n1
mass
Dm2atm
Dm2atm
mass
Ue32
n2
n1
n3
Dm2sun
Inverted mass hierarchy (ordering)
Normal mass hierarchy (ordering)
Type of mass spectrum with Hierarchy, Ordering,
Degeneracy absolute mass scale
Type of the mass hierarchy Normal, Inverted
Ue3 ?
A Yu Smirnov
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Two aspects of mixing
vacuum mixing angle
n2 sinq ne cosq nm
ne cosq n1 sinq n2
inversely
n1 cosq ne - sinq nm
nm - sinq n1 cosq n2
coherent mixtures of mass eigenstates
flavor composition of the mass eigenstates
n2
ne
n2
n1
wave packets
n1
n2
nm
n1
Flavors of eigenstates
n2
ne
Interference of the parts of wave packets with
the same flavor depends on the phase difference
Df between n1 and n2
n1
The relative phases of the mass states in ne
and nm are opposite
n2
nm
n1
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Vacuum oscillations
Propagation in vacuum
Flavors of mass eigenstates do not change
Determined by q
Admixtures of mass eigenstates do not change
no n1 lt-gt n2 transitions
n2
ne
n1
Df Dvphase t
Df 0
Dm2 2E
Dvphase
Dm2 m22 - m12
Due to difference of masses n1 and n2 have
different phase velocities
Oscillation length
oscillations
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
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Matter Effect Refraction

L. Wolfenstein, 1978
ne
e
Elastic forward scattering
Potentials
Ve, Vm
W
ne
V 10-13 eV inside the Earth for E 10 MeV
e
Difference of potentials is important
for ne nm
Ve- Vm 2 GFne
Refraction index
n - 1 V / p
Refraction length
10-20 inside the Earth
l0 2p / (Ve - Vm)
lt 10-18 inside the Sun
n - 1
2 p/GFne
10-6 inside the neutron star
focusing of neutrinos fluxes by stars complete
internal reflection, etc
Neutrino optics
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Neutrino eigenstates in matter

in vacuum
in matter
Effective Hamiltonean
H H0 V
H0
V Ve - Vm
n1m, n2m
n1, n2
Eigenstates
depend on ne, E
m1m, m2m
m1, m2
Eigenvalues
m12/2E , m22/2E
H1m, H2m
Mixing in matter
ne
n1
n2m
is determined with respect to eigenstates in
matter
n1m
q
n2
nm
qm
qm
is the mixing angle in matter
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Resonance
In resonance

sin2 2qm 1
sin2 2qm
n
n
Mixing in matter is maximal Level split is minimal
sin2 2q 0.08
sin2 2q 0.825
ln l0 cos 2q

Refraction length
Vacuum oscillation length

For large mixing cos 2q 0.4 - 0.5 the
equality is broken the case of strongly coupled
system shift of frequencies
ln / l0
n E
Resonance width DnR 2nR tan2q
Resonance layer n nR DnR
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n
resonance
H
Level crossing
sin2 2q 0.825

ne
n2m
Dependence of the neutrino eigenvalues on the
matter potential (density)
nm
Large mixing
ln l0
2E V Dm2
ln/ l0
n1m

V. Rubakov, private comm. N. Cabibbo, Savonlinna
1985 H. Bethe, PRL 57 (1986) 1271
sin2 2q 0.08
ne
ln l0
cos 2q
n2m
nm
Small mixing
ln/ l0
Crossing point - resonance the level split in
minimal the oscillation length is maximal
n1m
For maximal mixing at zero density
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Two effects

Adiabatic (partially adiabatic) neutrino
conversion
Resonance enhancement of neutrino oscillations
Density profiles
Variable density
Constant density
Change of mixing, or flavor of the
neutrino eigenstates
Change of the phase difference between neutrino
eigenstates
Degrees of freedom
Interplay of oscillations and adiabatic
conversion
In general
MSW
A Yu Smirnov
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Oscillations in matter
In uniform matter (constant density)
qm(E, n) constant
mixing is constant
Flavors of the eigenstates do not change
Admixtures of matter eigenstates do not change
no n1m lt-gt n2m transitions
Oscillations
Monotonous increase of the phase
difference between the eigenstates Dfm
as in vacuum
n2m
ne
n1m
Dfm (H2 - H1) L
Dfm 0
Parameters of oscillations (depth and length)
are determined by mixing in matter and by
effective energy split in matter
sin22qm, lm
sin22q, ln
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Resonance enhancement of oscillations

n
ne
ne
F0(E)
F(E)
Layer of matter with constant density, length L
Source
Detector
k p L/ l0
thin layer
thick layer
F (E) F0(E)
k 1
k 10
sin2 2q 0.824
sin2 2q 0.824
E/ER
E/ER
A Yu Smirnov
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Resonance enhancement of oscillations

n
ne
ne
F0(E)
F(E)
Layer of matter with constant density, length L
Source
Detector
k p L/ l0
thin layer
thick layer
F (E) F0(E)
k 1
k 10
sin2 2q 0.08
sin2 2q 0.08
E/ER
E/ER
A Yu Smirnov
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Resonance enhancement
resonance layer
of oscillations

Continuity neutrino and antineutrino
semiplanes normal and inverted hierarchy
P
Oscillations (amplitude of oscillations) are
enhanced in the resonance layer
ln / l0
E (ER - DER) -- (ER DER)
DER ERtan 2q ER0sin 2q
ER0 Dm2 / 2V
P
With increase of mixing
q -gt p/4
ER -gt 0
ln / l0
DER -gt ER0
A Yu Smirnov
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MSW adiabatic conversion

H H(t) depends on time
Non-uniform matter density changes on the way
of neutrinos
n1m n2m are no more the eigenstates of
propagation -gt n1m lt-gt n2m transitions
qm qm(n e(t)) mixing changes in the
course of propagation
ne n e(t)
However
if the density changes slowly enough
(adiabaticity condition) n1m lt-gt n2m
transitions can be neglected
Flavors of eigenstates change according to the
density change
determined by qm
Admixtures of the eigenstates, n1m n2m, do
not change
fixed by mixing in the production point
Phase difference increases
according to the level split
which
changes with density
MSW
Effect is related to the change of flavors of
the neutrino eigenstates in matter with varying
density
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Adiabaticity

External conditions (density) change slowly so
the system has time to adjust itself
dqm dt
Adiabaticity condition
ltlt 1
H2 - H1
The eigenstates propagate independently
transitions between the neutrino eigenstates
can be neglected
n1m lt--gt n2m
Crucial in the resonance layer - the mixing
angle changes fast - level splitting is minimal
if vacuum mixing is small
DrR gt lR
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.) -gt nR0 gt nR
nR0 Dm2/ 2 2 GF E
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Adiabatic conversion

and initial condition
The picture of conversion depends on how far from
the resonance layer in the density scale the
neutrino is produced
n0 lt nR
n0 gt nR
n0 nR
nR - n0 gtgt DnR
n0 - nR gtgt DnR
Interplay of conversion and oscillations
Oscillations with small matter effect
Non-oscillatory conversion
nR 1/E
All three possibilities are realized for the
solar neutrinos in different energy ranges
A Yu Smirnov
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Adiabatic conversion
n1m lt--gt n2m

P sin2 q
n0 gtgt nR
Non-oscillatory transition
n2m n1m
n2 n1
interference suppressed
Resonance
Mixing suppressed
n0 gt nR
Adiabatic conversion oscillations
n2m n1m
n2 n1
n0 lt nR
Small matter corrections
n2m n1m
n2 n1
ne
A. Yu. Smirnov
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The MSW effect

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
survival probability
oscillation band
averaged probability
(nR - n) / DnR
(distance)
A Yu Smirnov
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Adiabaticity violation

n2m n1m
Fast density change
n0 gtgt nR
n2m n1m
n2 n1
ne
Resonance
Admixture of n1m increases
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Solar Neutrinos
4p 2e- 4He 2ne 26.73 MeV
Adiabatic conversion in matter of the Sun
electron neutrinos are produced
F 6 1010 cm-2 c-1
r (150 0) g/cc
total flux at the Earth
Oscillations in vacuum
n
Oscillations in matter of the Earth
J.N. Bahcall
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Large mixing MSW solution

solar data
solar data KamLAND
P. de Holanda, A.S.
sin2q13 0.0
Dm2 6.8 10-5 eV2
Dm2 7.3 10-4 eV2
tan2q 0.40
tan2q 0.41
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Profile of the effect
Adiabatic solution

npp
nBe
nB
Survival probability
Earth matter effect
sin2q
I
II
III
ln / l0 E
Non-oscillatory transition
Conversion with small oscillation effect
Conversion oscillations
Oscillations with small matter effect
A Yu Smirnov
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Conversion inside the Sun
tan2q 0.41, Dm2 7.3 10-5 eV2

surface
core
survival probability
survival probability
resonance
E 14 MeV
E 2 MeV
y
y
distance
distance
survival probability
survival probability
E 0.86 MeV
E 6 MeV
y
y
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LMA MSW solution
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
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Inside the Earth. Regeneration
Oscillations in the matter of the Earth
n2
n2
Regeneration of the ne flux
core
Day - Night asymmetry Variations of
signal during nights (zenith angle
dependence), Seasonal variations
mantle
Spectrum distortion
Parametric effects for the core crossing
trajectories
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freg
Inside the Earth

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
ln /l0
Regeneration of the ne flux
ln /l0 0.03
E 10 MeV
P sin2 q freg
freg 0.5 sin 22q ln /l0
The Day -Night asymmetry
Oscillations adiabatic conversion
AND freg/P 3 - 5
distance
A Yu Smirnov
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Supernova neutrinos

r (1011 - 10 12 ) g/cc 0
E (ne) lt E (ne) lt E ( nx )

A Yu Smirnov
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SN neutrinos and MSW effect

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
A way to probe the hierarchy and value of s13
Type of the mass hierarchy
The conversion effects strongly depend on
Strength of the 1-3 mixing (s13)
Small mixing angle realization of the MSW effect
In the case of normal mass hierarchy
ne lt-gt nm /nt
almost completely
If 1-3 mixing is not too small
s132 gt 10- 5
F(ne) F0( nm)
hard ne- spectrum
No earth matter effect in ne - channel but in
ne - channel
strong non-oscillatory conversion is driven by
1-3 mixing
Neutronization ne - peak disappears
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SN87A and the Earth matter effect
C.Lunardini A.S.
p
F(ne) F0(ne) p DF0
p (1 - P1e) is the permutation factor
P1e is the probability of n1-gt 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
p
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
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Shock Wave Effect

The shock wave can reach the region relevant for
the neutrino conversion
R.C. Schirato, G.M. Fuller, astro-ph/0205390
r 104 g/cc
During 3 - 5 s from the beginning of the burst
Influences neutrino conversion if sin 2q13 gt 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
C.Lunardini, A.S., hep-ph/0302033
Density profile with shock wave propagation at
various times post-bounce
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Monitoring shock wave with neutrinos

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
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Summary

I. Resonance enhancement of oscillation in
matter with constant density
2. Adiabatic (quasi-adiabatic) conversion
in medium with varying density (MSW)
Two matter effects
(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 ...)
Resonance enhancement of oscillations
Provides the solution of the solar
neutrino problem
Large mixing MSW effect
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
Small mixing MSW effect
A Yu Smirnov