neutrino oscillations and the msw effect
DESCRIPTION
NEUTRINO OSCILLATIONS AND THE MSW EFFECT. S. P. Mikheyev INR RAS Moscow. LEP: Number of light, active neutrinos 3. 35. 25. (nb). 15. 5. 90. 92. 94. 96. 88. s = E cm (GeV). - PowerPoint PPT PresentationTRANSCRIPT
S. P. MikheyevINR RAS Moscow
S. P. Mikheyev INR Moscow
Erice 9 July 2004 2
s = Ecm (GeV)
5
15
25
35
(n
b)
88 90 92 94 96
LEP: Number of light, active neutrinos 3
S. P. Mikheyev INR Moscow
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Non-zero neutrino masses introduce
lepton mixing matrix, U, which, in general, is not expected to be diagonal. The matrix connects the flavor eigenstates (e, , , …) with the mass eigenstates (1, , , …).
Neutrino Oscillations
B. Pontecorvo (1957), Z. Maki, M. Nakagawa, S. Sakata (1962)
S. P. Mikheyev INR Moscow
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Flavor Neutrino States
Eigenstates of the CC Weak Interactions
m1 m2 m3
Mass Eigetstates
Correspond to certain charged
leptonInteract in pairs
= Ui ii
2 cossinsincos
U = ( )
e
e
12 3
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e = cos1sin
= - sin1cos 1 = cosesin
2 = sinecos
e 1
2
1
2
1
2
e
1
2
1
2
coherent mixtures of mass eigenstates
wavepackets
Interference of the parts of wave packets with the sameflavor depends on the phase difference between 1 and 2
flavor composition of the mass eigenstates
The relative phases of the mass states in e and are opposite
Flavors of eigenstates
inserting
inversely
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21
Due to difference of masses 1 and 2 have different phase velocities:
effects of the phase difference increase which changes the interference pattern
=vphase t
Flavors of mass eigenstates do not change
Admixtures of mass eigenstates do not change: no 1transitions
Determined by
=
vphase =m2
2Em2 = m2
2 - m12
Propagation in vacuum:
e
Oscillation length:
lvphase= 4E/m2
Amplitude (depth) of oscillations:
A = sin22
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(i) = U*()
ddt
(i) = Mdiag(i)i
ddt
() = UMdiagU*()i
it =UiUie-iE t* i
<t = UiUiUjUje-i(E – E )t
i,j* i j*
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1.0
0.2
0.4
0.6
0.8
102 103 104
L/E (km/GeV)
Pro
bab
ilit
y(L/E) = 0.1(L/E) = 0.25(L/E) = 0.5
P(ee ) = 1 - sin22 sin2 (1.27m2(eV2)L(km)/E(GeV))
2- Oscillations in Vacuum
S. P. Mikheyev INR Moscow
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P( ) = 1 - P( )
Oscillation Measurements Disappearence experiment: P( )
Appearence experiment: P( )
<P> = P( )
S. P. Mikheyev INR Moscow
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Difference of potentials is important for e :
e
e
e
e
W
Ve- V = 2 GFne
Elastic forward scattering
PotentialsVe, V
L. Wolfenstein, 1978
Refraction index:
n - 1 = V / p
~ 10-20 inside the Earth< 10-18 inside the Sun~ 10-6 inside the neutron star
V ~ 10-13 eV inside the Earth for E = 10 MeV
n - 1
Refraction length:
l0 = 2 / (Ve - V)
= 2 /GFne
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V = Ve - V
is determined with respect to eigenstates in matter
is the mixing angle in matter
1m2m
H = H0 + VEffectiveHamiltonean
Eigenstatesdepend on ne, EEigenvalues
H0
12
m12/2E , m2
2/2Em1, m2
H1m, H2m
m1m, m2m
e
2m
1m
2
1
m m
S. P. Mikheyev INR Moscow
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2m1m
Flavors of the eigenstates do not change
Admixtures of matter eigenstates do not change: no 1m2mtransitions
m= m=H2 - H1) L
Monotonous increase of the phase differencebetween the eigenstates m
Parameters of oscillations (depth and length) are determined by mixing in matter and by effective energy split in matter
In uniform matter (constant density)mixing is constant
m(E, n) = constant
as in vacuum
e
sin22, l sin22m, lm
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sin2 2m = 1
Mixing in matter is maximalLevel split is minimal
In resonance:
l = l0 cos 2
Vacuumoscillation length
Refractionlength
~~
For large mixing: cos 2the equality is brokenthe case of strongly coupled system shift of frequencies
l / l0
sin2 2m
sin2 2 = 0.08
sin2 2 = 0.825
~ n E
Resonance width: nR = 2nR tan2Resonance layer: n = nR + nR
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Resonance enhancement Resonance enhancement of neutrino oscillationsof neutrino oscillations
Adiabatic Adiabatic (partially adiabatic)(partially adiabatic)neutrino conversionneutrino conversion
Constant density Variable density
Change of mixing, or flavor of the neutrinoeigenstates
Change of the phase difference between neutrino eigenstates
Degrees of freedom:
Interplay of oscillations Interplay of oscillations and adiabatic conversionand adiabatic conversion
Density profiles:
In general:
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Layer of matter with constant density, length LSource Detector
F0(E) F(E)
F (E)F0(E)
E/ER E/ER
thin layer thick layerk = L/ l0
sin2 2 = 0.824
k = 1 k = 10
e e
sin2 2 = 0.824
S. P. Mikheyev INR Moscow
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Layer of matter with constant density, length LSource Detector
F0(E) F(E)
F (E)F0(E)
E/ER E/ER
thin layer thick layer
sin2 2 = 0.08
k = 1 k = 10
e e
sin2 2 = 0.08
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Continuity: neutrino and antineutrino semiplanes normal and inverted hierarchy
Oscillations (amplitude of oscillations) are enhanced in the resonance layer
E = (ER - ER) -- (ER + ER)
resonancelayer
ER0
= m2 / 2V
ER = ERtan 2 = ER0sin 2
With increase of mixing:
ER 0
ER ER0
l / l0
l / l0
P
P
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Admixtures of the eigenstates,1m 2m, do not change
Flavors of eigenstates change according to the density change
fixed by mixing inthe production point
determined by m
1m 2m are no more the eigenstates of propagation 1m2m transitions
Effect is related to the change of flavors of the neutrino eigenstates in matter with varying density
if the density changes slowly enough (adiabaticity condition) 1m <-> 2m transitions can be neglected
Non-uniform matter density changes on the way of neutrinos:ne = ne(t)
mm(ne(t)) mixing changes in the course of propagation
H = H(t) depends on time
However
Phase difference increases according to the level split which changes with density
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dm
dt Adiabaticity conditionH2 - H1
Crucial in the resonance layer: - the mixing angle changes fast - level splitting is minimal
rR > lR
lR = l/sin2is the oscillation width in resonance rR = nR / (dn/dx)R tan2is the width of the resonance layer
External conditions (density)change slowlyso the system has time to adjust itself
<< 1
transitions between the neutrino eigenstates can be neglected
1m2mThe eigenstatespropagate independently
if vacuum mixing is small
If vacuum mixing is large the point of maximal adiabaticity violation is shifted to larger densities
n(a.v.) nR0 > nR
nR0 = m 2/ 2 2 GF E
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The picture of conversion depends on how far from the resonance layer in the density scale the neutrino is produced
n0 > nR
n0 - nR >> nR
n0 ~ nR nR - n0 >> nR
n0 < nR
Non-oscillatory conversion
Oscillations with small matter effect
Interplay of conversion and oscillations
All three possibilities are realized for the solar neutrinos in different energy ranges
nR ~ 1/ E
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2m
1m
2m
1m
ne
2
1
2m
1m
Non-oscillatory transition
Adiabatic conversion + oscillationsn0 > nR
n0 >> nR
n0 < nR
2
1
2
1
Small matter corrections
Resonance
P = sin2
interference suppressedMixing suppressed
1m 2m
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2m
1m
2m 1m
ne
2
1
Admixture of 1m increases
n0 >> nR
Resonance
Fast density change
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y = (nR - n) / nR
surv
ival
pro
babi
lity
resonance
productionpointy0 = - 5
averagedprobability
oscillationband
(distance)
The picture of adiabatic conversion is universal in terms of variable y = (nR - n ) / nR
(no explicit dependence on oscillation parameters density distribution, etc.)Only initial value y0 matters.
resonance layer
For zero final density:y = 1/tan 2
LMA
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Oscillations in matterof the Earth
Oscillationsin vacuum
Adiabatic conversionin matter of the Sun
: (150 0) g/cc
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tan2m2 = 7.3 10-5 eV2
y
surv
ival
pro
babi
lity
surv
ival
pro
babi
lity
surv
ival
pro
babi
lity
surv
ival
pro
babi
lity
coreE = 14 MeV
E = 6 MeV E = 2 MeV
distancey
y y
resonance E = 10 MeV
surface
sin2
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tan2m2 = 7.3 10-5 eV2
y
surv
ival
pro
babi
lity
surv
ival
pro
babi
lity
E = 0.4 MeVE = 0.86 MeV
distance distance
y
Low energy part of the spectrum: vacuum oscillations with small matter corrections
Dashed lines: for pure vacuum oscillations
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p, He, …
N
N
A
(K
e
e
R = = 2
e
e
Atmospheric Neutrinos: Flux FeaturesAtmospheric Neutrinos: Flux Features
E3 d
F/d
E
E(GeV)
E(GeV)
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1
102
103
104
Cos
Path
len
gth
(k
m)
-1 -.6 .6-.2 .2
up horizontal down
Atmospheric Neutrinos: Flux FeaturesAtmospheric Neutrinos: Flux Features
L =
20km
L =
10 0
00km
L = 500km
cos = 0
cos
= -0
.8
cos
= 0
.8
Flux is up/down symmetricbut isn’t isotropic Fn~ 1/CosQ
L/E values from 0.1 (10 km/1000 GeV) to 104 (104 km/1 GeV) can be explored
to study neutrino oscillations.
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K.Nishikawa’s talkAtmospheric Neutrino DetectionAtmospheric Neutrino Detection
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Atmospheric Neutrino DetectionAtmospheric Neutrino DetectionSuper-Kamiokande
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Atmospheric Neutrino EventsAtmospheric Neutrino Events
e
e
Partially contained
Fullycontained
1/10t/yearAcceptance 4
100 101 102 103
0.2
0.4
0.6
0.8
Neutrino energy (GeV)
Even
ts/
day
Ed Kearns for the SK Collaboration Neutrino2004,
June 15, Paris
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Atmospheric Neutrino EventsAtmospheric Neutrino Events
Upward through-going
Upward stopping
1/10m2/yearAcceptance 2
100 101 102 103
0.02
0.06
0.10
0.14
Neutrino energy (GeV)
Even
ts/
day
0.18
Ed Kearns for the SK Collaboration Neutrino2004,
June 15, Paris
S. P. Mikheyev INR Moscow
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Ed Kearns for the SK Collaboration Neutrino2004,
June 15, Paris
Zenith Angle Distributions
Sub-GeV Evis < 1.3 GeV
Multi-GeV Evis > 1.3 GeV
Atmospheric NeutrinosAtmospheric Neutrinos
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Atmospheric NeutrinosAtmospheric Neutrinos oscillations
Ed Kearns for the SK Collaboration Neutrino2004,
June 15, Paris
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Atmospheric NeutrinosAtmospheric Neutrinos
oscillations L/E analysis Ed Kearns for the SK
Collaboration Neutrino2004, June 15, Paris
Oscillation deep @ L/E 500 km/GeV
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K2K experimentK2K experimentK2K experimentK2K experiment• K2K is the first accelerator-based long-baseline neutrino
oscillation experiment to investigate the neutrino oscillation observed in atmospheric neutrinos.
KKEK-EK-12GeV 12GeV
PSPS
Super-Super-KKamiokanamiokan
dedeAtm.- K2K
L 10~104km 250km(fix.)
E 0.1~100GeV ~ 1.3GeV
m2 10-1 ~10-4eV2 > 2 ・ 10-3 eV2
e 0.50 ~0.01
L=250 kmL=250 km
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p+Al + e+ + e (1.3%) + (0.5%)
Neutrino Beam Production
K2K experimentK2K experimentK2K experimentK2K experiment
Near Detector Far Detector
- disappearance
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K2K experimentK2K experimentK2K experimentK2K experimentShape of energy spectrum
CC – quasielastic reactions
Erec (GeV)
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K2K experimentK2K experimentK2K experimentK2K experimentBoth disappearance and energy spectrum distortion have the consistent result
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Solar NeutrinosSolar NeutrinosG.Fogli et al. hep-ph/0106247
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Solar NeutrinosSolar Neutrinos
All solar neutrino data
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Experiment KamLANDExperiment KamLANDExperiment KamLANDExperiment KamLAND
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Experiment KamLANDExperiment KamLANDExperiment KamLANDExperiment KamLAND
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Experiment KamLANDExperiment KamLANDExperiment KamLANDExperiment KamLAND
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Experiment KamLANDExperiment KamLANDExperiment KamLANDExperiment KamLAND
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Experiment KamLANDExperiment KamLANDExperiment KamLANDExperiment KamLAND
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3 mixing angles (12,23,13)& phase of CP violation ()
сij = cosij
sij = sinij
1 0 0 0 с23 s23
0 -s23 c23
1 0 0 0 с23 s23
0 -s23 c23
с13 0 s13 ei
0 1 0 -s13 e-i 0 c13
с13 0 s13 ei
0 1 0 -s13 e-i 0 c13
с12 s12 0 -s12 c12 0 0 0 1
с12 s12 0 -s12 c12 0 0 0 1
U = U =
Atmospheric neutrinosm2 (1.310-3 3.010-3) eV2
Sin22 > 0.923
m32
m21
12
Solar neutrinosm2 (5.410-5 9.510-5) eV2
Sin22 (0.71 0.95)
3 – neutrino mixing
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( , , sin2212, sin2223)( , , sin2212, sin2223)m2
1 m2
1
22 m3
1 m3
1
22
… and limit for sin2213… and limit for sin2213
Known parameters
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sin2213 0.2sin2213 0.2
Sign of m31 Sign of m31 22
- phase of CP violation - phase of CP violation
Mass hiererchy Mass hiererchy
1
2
3
normal
3
1
2
inverted
Unknown parameters