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Lectures on Neutrino Physics
Fumihiko Suekane
Research Center for Neutrino Science
Tohoku University
[email protected]
http://www.awa.tohoku.ac.jp/~suekane
France Asia Particle Physics School
@Ecole de Physique Les Houchess
18-20/Oct./2011
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* This lecture is intended to give intuitive
understanding of neutrino physics for
students and young physicists of other field.
* I will try to make this lecture to be a bridge
between general text books and scientific
papers.
* 3 lectures are very short to mention about
all the varieties of neutrino physics and only
limited but important topics are mentioned.
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Scientific Papers
This lectures
Introduction to
Particle Physics
text books
2
Contents
* History
* Neutrinos in the Standard Model
* Neutrino Oscillations (Main)
* Double Beta decays
* Prospects
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Day-1
Day-2
Day-3
3
What is known for neutrinos
PDG2010
Only a few things are
known about neutrinos.
.... There is much room
to study.
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Basic Fermion
Strong Interaction
NO
YES
Lepton
Quark
u,d,s,c,b,t
YES
Charged Lepton
e, m, t
EM Interaction
NO
Neutrino
e , m , t
We call Fermions which do not perform strong nor EM interaction,
Neutrinos
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big bang 
Neutrinos in Nature
e e   in early universe.
Most abundant next to photons (~100/cc)
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 Timeline
(years are approximate)
1899 Discovery of b-decay
[Rutherford]
1914 b-ray has continuous energy spectrum
[Chadwick]
1930 Neutrino hypothesis
[Pauli]
1956 1st Evidence of neutrino @ reactor
[Reines & Cowan]
1961 Discovery of m
[Shwartz, Ledermann, Steinberger]
1969~ Deficit of solar neutrino
[Davis]
1977 Discovery of t lepton ( indirect evidence of t )
[Perl]
1985 Proposal of MSW effect
[Mikheyev, Smirnov, Wolfenstein]
1987 Detection of neutrinos from SN1987A
[Koshiba]
1989 N=3 by Z0 shape
[LEP]
1995 Nobel prize to Reines
(1996, 1997Claim of m->e oscillation
[LSND])
1998 1st evidence of neutrino oscillation by atmospheric  [SuperKamiokande]
2000 Direct evidence of t
[DONUT]
(2001 Claim of neutrinoless bb decay
[Klapdor])
2002 Nobel prize to Davis & Koshiba
2002 Flavor transition
[SNO]
Reactor Neutrino Deficit
[KamLAND]
2004 m disappearance @ Accelerator
[K2K]
2010 mt
[OPERA]
2011 Indication of e appearance @ Accelerator
[T2K]
1st Indication of Neutrino
(The 1st anomaly in neutrino
which lead great discovery.)
~1914, an anomaly found
g &  decays  The energy of the decay particle is unique
M’
M
m
n
M  m  M 2

T 
2
T/g
2M

However, for b-decays,
it is continuous.
Why??
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J.Chadwick, 1914
n
T
b
8
Neutrino Hypothesis
* Energy conservation low is broken （N.Bohr, 1932）
A’
A
Eb  EA  EA
b
Wikipedia
* b-decay is a 3 body reaction (W.Pauli, 1930)

A  B  b  
ν
M’
Wikipedia
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M
m
Eb  EA  EA  E  EA  EA
Neutrino Hypothesis
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4/Dec./1930
Letter from Pauli
to participants of
a conference.
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Expected properties of  from b-decays
(1) Q=0  charge conservation
(2) s=1/2  spin conservation
(3) mass is small if exists  maximum energy of b-rays.
(4) Interact very weakly  lifetime of b-decays.
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How -N cross section was estimated in early days.
Fermi's model
p
e-
Dirac
e
e
e2
M 2
q
p
Fermi
Analogy
n
GF
p

e-
e-
M  GF
Various b -decays & Electron caputure  GF~10-11/MeV2
2
G

2
20
Then,    p  e  n F pCM ~ 10 b!!


"I 
did something a physicist should never do. I predicted something
which will never be observed experimentally..".（W.Pauli)
"There
 is no practically possible way of observing the neutrino"
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(Bethe & Peierls, 1934)
Then 30 years had passed ....
235
n
236
n
e
e
Very strong  sources are necessary,
 Chain reactions of nuclear fissions.
U
*
U
94
140
Te
n
Rb
e
e-
94
140
I
e
-
140
Xe
94
Energy release:
200MeV/fission
b-decays:
~ 6 /fission
Sr
e
e
Discovery of 
e-
Y
1.9x1011/J
e
e
e-
140
Cs
94
Zr e
Reactor or Nuclear Explosion
E~ MeV
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An early idea to detect  (not realized)
by Reines & Cowan
Reines & Cowan
Nuclear Explosion
Vacuum shaft
Neutrino Detector
Free fall to prevent
the shock wave.
=> Physicists make use of everything available
While preparing the experiment, they realized nuclear
reactor is more relevant to perform experiment.
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Then they moved to a Savannah River Reactor
200L Cd loaded water tanks
1400L liquid scintillator tanks
P=700MW
1982 Wikipedia
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Principle of  detection
*  flux:
@15m from Savannah Liver P reactor core. (P=700MW)
flux~5x1012/cm2/s
* Detection Principle:
 e  p  e  n 
e  e  2g 0.5MeV 

n  Cd  Cd*  Cd  ng 9MeV 
n
e+
~10ms
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Delayed Coincidence Technique
Still used in modern experiments
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2 examples of delayed coincidence
LS tank ID
http://library.lanl.gov/cgibin/getfile?00326606.pdf#search='delayed%20coincidence%20cadmium%20neutrino'
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An episode
At the same time of Reines& Cowan, R.Davis and L.Alvarez
performed neutrino experiment at a Savannah river reactor, too.
Their detection principle was,
  Cl  e  Ar
However, they failed to detect positive result.
But this actually means the reactor neutrino (anti neutrino) dose not

cause the reaction
  Cl 
/ e  Ar
and neutrino and anti-neutrino are different particles
(concept of that time)
Later on, Davis also won Novel prize by detecting solar neutrinos

with the same technique.
Lessons : Negative result can be an important signature.
: Hanging on is important for success.
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Discovery of μ-neutrino
* Neutrino Source:
@ Brookhaven AGS p15GeV   Be    X
  m 
π decays with 21m decay space.
  e   
 10 4
  m   

99.99% of neutrinos are associated with muon production
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
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Detection of neutrino
* Target: 90 x 2.5cmt Al slab
m  X
Looked for   Al  
e  X
spark chambers
m signal => a single track
e signal => EM shower

They observed
34 single track μ events
22 μ+X
6 backgrounds (not like e )
 The neutrinos from b-decay and  decay are different particle
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t neutrino
(2000 DONUT group)
* Production of t neutrino
FNAL TEVATRON
pE  800GeV  W  DS m  1.97GeV   X
Then
DS  t  m  1.78GeV    t


cosC
DS
s
mDs  mt

Cabibbo favor
t
c
Br ~ 4%
W
t
E ~ 70GeV,
~ 0.05
 m
t
e,
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Detection principle
Look for the "kink"
t  A  t  X
t decays after ct~87um,
neutral(s)

85% for 1 prong mode
t
t




e , m ,  , K
数百ミクロン
15% for 3 prongs mode.
t
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t

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the Detector
Nuclear Emulsion
(~thick camera film)
position resolution <1mm
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Results (2000)
3 prongs
1prong
4  0.44 t was observed in 1000 neutrino events. (9 significance)
"We did R&D for t-neutrino detection around 1980 but once
gave up because it seemed too difficult to success". K.Niwa
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Direct neutrino mass detection
electron neutrino
Principle
A  B  e   e
2


m
2
2
N  pe dpe  pe E0  Ee  1 
 dpe
 E 0  Ee 

EeMAX  E0  E0  m
Distortion of energy
spectrum at the end point

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3
Source: Tritium
H 3 He  e   e
Q  18.6KeV , t
E0=small  good m sensitivity
Lifetime  reasonably short & long

Z＝small  small correction
12
 12.3y
ideal isotope to seek for mν
* Strong Source
* Large Acceptance
* Energy measurement
by Electric potential
V
Electric potential
detector
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me Results
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K. Eitel (Neutrino04)
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K. Eitel (Neutrino04)
From current to future experiments
Mainz:
m2 = -1.2(-0.7) ± 2.2 ± 2.1 eV2
m < 2.2(2.3) eV (95%CL)
Troitsk:
m2 = -2.3 ± 2.5 ± 2.0 eV2
m < 2.1 eV (95%CL)
C. Weinheimer, Nucl. Phys. B (Proc. Suppl.) 118 (2003) 279
C. Kraus, EPS HEP2003 (neighbour excitations self-consistent)
V. Lobashev, private communication
(allowing for a step function near endpoint)
aim: improvement of m by one order of magnitude (2eV  0.2eV )
 improvement of uncertainty on m2 by 100 (4eV2  0.04eV2)
statistics:
 stronger Tritium source (>>1010 b´s/sec)
 longer measurement
(~100 days  ~1000 days)
energy resolution:
 DE/E=Bmin/Bmax
 spectrometer with DE=1eV
 Ø 10m UHV vessel suekane@FAPPS
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A famous picture
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K. Eitel (Neutrino04)
KATRIN sensitivity & discovery potential
expectation:
after 3 full beam years
syst ~ stat
m = 0.35eV (5)
5
m = 0.3eV (3)
discovery potential
m < 0.2eV (90%CL)
sensitivity
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m mass limit
 stop  m   m


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m  mm  pm  m  pm
2
2
2
2


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m  0.34m
pm
1 0
pm
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K.Assamagan et al. PRD53,6065(1996)
A precise spectrometer
@PSI
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K.Assamagan et al. PRD53,6065(1996)
energy loss in the target
pmmax  29.79200  0.00011MeV / c
0.1MeV/c

pm
m m  0.19MeV 90%CL 
(PDG average)

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m mass limit
m  0.34m
pm
1 0
pm
2


1
m
m

p

m

m
2
2  m 
m m ~ m  mm

2


m
p

1
m
m

m


m



~ 0.15MeV  49MeV
m


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pm
pm
~ 0.1MeV
δmπ limits the precision

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τ neutrino mass limit
e e  t  t 
t   t  X LEP,CLEO

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t   t  X LEP,CLEO
distribution of mX & Ex,
d
 f m X , E X ; m 
dm X dE X
 obtain most likely m
Better precision for smaller Q-value, but low statistics,
t  5   t are used.
PDG average； mt  18.2MeV 95%CL 
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Quark-Lepton
masses
 mass is very
small
t
m
Lower limit
of heaviest
neutrino mass
is ~50meV
  oscillation
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Neutrinos in the Standard Model
* Q=0,
* No color
* m=0,
* s=1/2
*  

* only L exists
(or L may exist
but it does not
interact at all)

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eL
W+
e
gW 
~ 1.4e
2 sin W
igW eRg  L Wm
m

L

L
igZ  Rgm  L Z m0

Z0
e
gZ 
~ 1.2e
sin 2W
L

2
sin W~0.23 (Weinberg
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angle)
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
R
L
e
eL

m
 eL R
L m R
 eL  R
 eL
gw


W+
 
WLepton
number
violation
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

W+
Flavor
violation
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

Z0

Z0
Flavor
violation
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'Helicity' Suppression of -decay
 e
 1.2 10 4
 m
Experimental fact:
How it is explained?

R
L
e


W+
u
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
d

eR
L

only LH  and RH e.

You may say W couple
So that J(e=1, while pion spin=0
=> violates spin conservation
However, this decay exists if very small.
And for   m   decay, the spin
conservation seems to strongly violated.
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Helicity and Chirality
Sometimes Helicity and Chirality are used in confuse.
Here they are defined and their relations are discussed.
Dirac equation in free space is,
ig mm  mx  0
General solution is,
r r
 u  i  pr xr Et    v  i  pr xr Et 
 x   r r e

e

  u 
 v 
r
r
 u1 
 v1 
p
r2
2
, E   p  m , u   , v   
 
Em
u 2 
v2 

r
Nowwe take initial condition as positive energy and p  0, 0, p
 u 
 0  

 z u 

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
Helicity is the spin component to the direction of the movement.
r
s
rˆ
p

rˆ r
ps
If the movement is along the z-direction, helicity components are,
  1
u
 1 
1
rˆ r
 R  1p     1  z    u1  
2
2

u 
1 

 u 
 2 
1
1
rˆ r

  1 p     1  z 
  u2 

 L 2 
2
u 
 2 
These helicity states show actual spin direction.

Here after we call Right(Left) handed Helicity =RH (LH)
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What W couples to: Chirarity
W couples to negative Chirality (NC) particle and positive Chirality
(PC) state anti-particle.
W


Chirality components of  is defined by,
1
1  1 1 u  1  z  u 
  1 g 5   

 
 
2
2 1 1  z u 
2 u 
For m  0, 1 and
1  z  u  m0 1  z  u 

 
   
    R/ L
2 u 
2 u 
For high energy, the helicity and chirality are same and
sometimes they are confused.
For low energy, NC has RH component.

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In   e- decay, e- is NC state and  is PC state.
Then the The RH component of electron in the  decay is,
u
1 
1

rˆ r
 R  1 p    
1  z  
2
4
u 
So that the probability which is RH is,

 R
1  †
g 1 b  2 m E1  m 2  2


u1   2  u1
u 1  z u
2
2
8
g 1
2
 4E 
This means the electron has right handed component with probability
P  me2 4Ee2  ~ 1.310 5
R
This conserve spin
eL

 muon case, m /E ~1 and the suppression is not strong.
For

m m
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 e
Taking into account the phase
space the theoretical prediction is  m
 m 2  m 2  m 2 
4
e
  e   2

1.28
10

2
m
m

m
 m  
m
1.23x10-4
while observation is

Likewise for K decay,
K e
K m
 m 2  m 2  m 2 
5
e
  e   K2

2.4
10

2
m
m

m
 m  K
m
 2.5x10-5
while observation is

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neutrino flavor counting using Z0
e  e  Z 0  f  f
f
e

Z
0
igZ g eg 
igZ g f g 
g f  cVf  cVf g m
q2  2E 
2
Mz=91GeV
f

e

4M
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If M=1, =0.1


2
Z

ge2 g 2f
q  MZ
2

2
 Z2 4

suekane@FAPPS

50
The width of the Z0:  is inverse of the lifetime of Z0: t
The lifetime is proportional to inverse sum of decay width.
1
1
t 
Z
Z uu  Z dd L  Z  e e
If the number of neutrino flavors is n,
Z  6U  9D  3L  n 

8
32 2
4
8 2
2
 1, L 1 4xw  8xw , U 1 xw  xw , D 1 xw  xw
3
9
3
9
xw  sin w ~ 0.23
measurement
Z  6U  9D  3L
known
n 

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Z0 data
４ experiments at LEP (ALEPH, DELPHI, OPAL, L3) showed
n  2.984  0.008
If 4th neutrino exists m4 > 45GeV or
it does not couple to Z0, called sterile neutrino.
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
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 Oscillation: An Introduction
Neutrino oscillation is phenomena in which flavor of neutrino
oscillatory changes as time passed by.
e
m
e
m
e
t
If we start from e, the probability to find m at time t is expressed as:
2
2
m

m
1
P e  m t   sin 2 2 sin 2 2
t
4E
Where m2 and m1 are masses of energy-eigenstate neutrinos,
 is called mixing angle.
st firm evidence beyond the standard model and
 oscillation
is
the
1

its studies are important to understand the nature.
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Phenomena of spin-1/2 for  Oscillation
The formalism of the  oscillation is very similar to
that of spin-1/2 under magnetic field.
So let's review the spin motion as introduction.
The spin motion under magnetic field is described by the
Pauli equation:
r r
iÝ mB  
r
Where B  Bx , By , Bz  is the magnetic field and
m is magnetic dipole moment of the particle.

This equation was 1stly introduced empirically by Pauli,
and later on obtained by taking non relativistic limit
of the Dirac equation with electro-magnetic interaction.
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Phenomena of spin-1/2 for  Oscillation
rr
iÝ mB
The wave function is a mixture of spin up and down states
 t 
 t    t    b t     b t 
  
Here, we think the case that magnetic field is along the x axis.
r
B  B,0,0
z 
y r
Then the Pauli equation becomes
B
Ý
 0 1  
 
  Ý  imB
b 
 1 0  b 
  x

  b 
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Phenomena of spin-1/2 for  Oscillation
Ý imBb

bÝ imB
by taking the delivertive of the 1st equation,
and replacing bÝ by the 2nd equation,

2
Ý
Ý mB 
This is the harmonic oscillator and we know the general solution;

 t   peimBt  qeimBt


imBt
imBt
b
t

pe

qe
 
Where p & q are integral constants to be determined by initial condition.
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
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Phenomena of spin-1/2 for  Oscillation
Then the general spin state is,
 t   peimBt  qeimBt   peimBt  qeimBt 
Now we assume that at t=0, the spin pointed upward.
 0  

z
y r
B
1 x
 0   
0

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Then we can determine p and q for this case,

 0   p  q    p  q   

1
pq
2
suekane@FAPPS
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Phenomena of spin-1/2 for  Oscillation
Then we get specific wave function;
 t   cosmBt    i sin mBt  
This means at later time,  state is generated with oscillating probability

z
P t   sin 2 mBt 
r
B
If we recall that the wave function of the spin,
which is in z-y plane and polar angle is  is
mBt

y

   mBt,   0
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    cos   i sin  
Physically it corresponds to the precession
of the spin, caused by the torque by B and m.

suekane@FAPPS
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Phenomena of spin-1/2 for  Oscillation
Ý
 0 1  
 Ý  imB
 
b 
 1 0  b 
Quantum Mechanically, this is understood as the effect
that magnetic field causes transition between   

with amplitude
mB.
We will draw this kind of effect schematically as follows.



mB
The neutrino oscillation
can be
 understood as exactly same manner.

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A simple case of  Oscillation
We assume 2 neutrino system; e & m
The general state is;
 t    t   e  b t   m
We assume something makes transition: em

m
e
me
Then there are correspondences to the spin case
If the initial state is pure e state, like beta decay,
 e  
then
2

P
t

sin
Amet


 e  m
 m  

This is the very basic of neutrino oscillation.
 Ame  mB
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A simple case of  Oscillation
However, we often see the neutrino oscillation probability as
2
2
m

m
1
P m t   sin 2 2 sin 2 2
L
4E

111018
Where does this come from?
What is the analogy of spin motion?
suekane@FAPPS
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Still spin-1/2 for  Oscillation
In actual case, mass term has to be included in the Pauli equation
rr
iÝ m  mB 
and the most general equation with arbitrary magnetic field is,
 m  mBz
Ý

 Ý  i
b 
 mB
z
Spin transition amplitudes are
r
B
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


y

 
  
 b
mB  
 ; B  Bx  iBy
m  mBz  b 
x
=


mB



mB




mmBz
suekane@FAPPS





mmBz
62
Still spin-1/2 for  Oscillation
 m  mBz
Ý
 Ý  i
b 
 mB
mB  
 
m  mBz  b 
This equation has the general form
*



 

Ý
P
Q

 , P, R  Re al
 Ý  i
b 
Q R  b 
Relation between Polar angle  of the magnetic field and transition
r
amplitudes is,
z
B
B 2Q

tan  

Bz R  P


x,y

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Still spin-1/2 for  Oscillation
 P Q*  
Ý
 , P, R  Re al
 Ý  i
b 
Q R  b 
Then the general solution can be
expressed using  as,
 t   C1 cos 2eiE t  C2 cos 2eiE t

iE t
iE t
b
t

C
sin

2
e

C
cos

2
e
 
  1  
2
where, 
1
2
2
E

P

R

P

R

4
Q
 

  2 

E  1 P  R  P  R2  4 Q 2
  2
(Note: by definition, E+>E-)


111018
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


2Q

R-P

2Q
tan  
RP
64
Still spin-1/2 for  Oscillation
The general wave function is,
t   C1 cos 2eiE t  C2 sin  2eiE t 


 C1 sin  2eiE t  C2 cos 2eiE t 
2Q

Again we start with
 0  
Then, the integral constants are determined.
R-P

2Q
tan  
RP
C1 cos 2  C2 sin  2  1
 C1  cos 2
 

C2  sin  2
C1 sin  2  C2 cos 2  0

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Still spin-1/2 for  Oscillation
In this case, the specific wave function is
1
2
iE  t
2
iE  t
t   cos  2e
 sin  2e   sin  eiE t  eiE t 
2
This state corresponds to spin precession within
the plane perpendicular to the magnetic field.
r
B
z
y
The time dependent probability of spin-down state is
sin  iE t iE t
2
2
P t  
e

e

sin

sin
mBt


2
corresponds to the angle between
the precession plane and z axis.
2

x
  t 

 bt 
 t   


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Difference of the energies in the
energy eigenstate
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66
Still spin-1/2 for  Oscillation
Look for Energy eigenstate,
Remember the
general state
 t   C1 cos 2eiE t  C2 sin  2eiE t 


 C1 sin  2eiE t  C2 cos 2eiE t 
If we choose, C1=1, C2=0,
 t   cos 2   sin  2  eiE t



This means
  cos 2   sin  2 
is energy eigenstate with energy E+.
Similarly, if we choose, C1=0, C2=1,
  t   sin  2   cos 2  eiE t   eiE t

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Still spin-1/2 for  Oscillation
The spin states  ,  itselvs are NOT energy eigenstate
and do not have definite energy.
(If you try to measure the energy of  state, you will see 2 energies.)

But the mixed state,



  cos 2 sin  2   

 
sin

2
cos

2
 
   
 
ARE energy eigenstate and have definite energy.
/2 is called mixing angle between energy eigenstate and spinr state.

=The mixing angle corresponds to 1/2 of the polar angle of B.
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
68