Transcript Document 7187508

Neutrino Physics
Hitoshi Murayama
Taiwan Spring School
March 27, 2002
中性微子物理
村山 斉
台湾春期学校
二千二年三月二十七日
Neutrinos are Everywhere
3
“Wimpy and Abundant”
Neutrinos are Everywhere
• They come from the Big Bang:
– When the Universe was hot, neutrinos were created
equally with any other particles
– They are still left over: ~300 neutrinos per cm3
• They come from the Sun:
– Trillions of neutrinos going through your body every
second
• They are shy:
– If you want to stop them, you need to stack up lead
shield up to three light-years
4
Outline
•
•
•
•
Introduction
Neutrinos in the Standard Model
Atmospheric Neutrinos
Solar Neutrinos
5
Neutrinos in the Standard Model
Puzzle with Beta Spectrum
• Three-types of
radioactivity: a, b, g
• Both a, g discrete
spectrum because
Ea, g = Ei – Ef
• But b spectrum
continuous
F. A. Scott, Phys. Rev. 48, 391 (1935)
Bohr: At the present stage of atomic theory, however, we may say
that we have no argument, either empirical or theoretical, for
upholding the energy principle in the case of b-ray disintegrations
7
Desperate Idea of Pauli
8
Three Kinds of Neutrinos
• There are three
• And no more
9
Neutrinos are Left-handed
10
Neutrinos must be Massless
• All neutrinos left-handed  massless
• If they have mass, can’t go at speed of light.
• Now neutrino right-handed??
 contradiction  can’t be massive
11
Anti-Neutrinos are Right-handed
• CPT theorem in
quantum field theory
– C: interchange
particles & antiparticles
– P: parity
– T: time-reversal
• State obtained by CPT
_
from nL must exist: nR
12
Standard Model
• Therefore, neutrinos are strictly massless in
the Standard Model of particle physics
Finite mass of neutrinos imply the Standard
Model is incomplete!
• Not just incomplete but probably a lot more
profound
13
Lot of effort since ‘60s
Finally convincing
evidence for “neutrino
oscillation”
Neutrinos appear to
have tiny but finite mass
14
Atmospheric Neutrinos
Super-Kamiokande (SuperK)
• Kamioka Mine in
central Japan
• ~1000m
underground
• 50kt water
• Inner Detector
– 11,200 PMTs
• Outer Detector
– 2,000 PMTs
Michael Smy
16
SuperKamiokaNDE
Nucleon Decay Experiment
• pe+p0, K+n, etc
– So far not seen
– Atmospheric neutrino
main background
• Cosmic rays isotropic
– Atmospheric neutrino
up-down symmetric
17
A half of nm lost!
18
Neutrinos’ clock
• Time-dilation: the
clock goes slower
v2
  t 1  2
c
• At speed of light v=c,
clock stops
• But something seems
to happen to neutrinos
on their own
• Neutrinos’ clock is
going
• Neutrinos must be
slower than speed of
light
• Neutrinos must have a
mass
19
The Hamiltonian
• The Hamiltonian of a freely-propagating
massive neutrino is simply
H
2
m
p2  m 2  p 
2p
• But in quantum mechanics, mass is a matrix
in general. 22 case:
2
2
 m 211
M2   2
 m 21
2 
m 12

2
m 22 
M 1  m1 1
M 2 2  m22 2
20
Two-Neutrino Oscillation
• When produced (e.g., p+m+nm), neutrino is
of a particular type
n m ,t  1 cos  e
im12t |/ 2 p
 2 sin  e
im22t / 2 p

21

Two-Neutrino Oscillation
• When produced (e.g., p+m+nm), neutrino is
of a particular type
2
22
im
t
/
2
p
im
im
|
22t / 2 p
n m ,t  1 cos  e 1
 2 sin  e
• No longer 100% nm, partly n!
• “Survival
 probability” for
 nm after t
P  n m nm ,t
2
2 4

m
c GeV ct 
2
2

 1  sin 2 sin 1.27
2 c p km
eV


22
Survival Probability
p=1 GeV/c, sin2 2=1
m2=310–3(eV/c2)2
Half of the up-going
ones get lost
23
Lower Energy
24
Lowest Energy
25
Higher Energy
26
27
More cross checks
• Multi-ring events can be used to provide useful
cross checks (Hall, HM)
28
29
Confirmation with
Man-made neutrino beam
250km
K2K experiment
818 events if no oscillation
56 events observed
Deficit at 2 sigma level
30
MINOS (NuMI)
OPERA/ICARUS (CNGS)
• MINOS: precision
measurements of
(m232, sin2223)
2004–
• OPERA/ICARUS @
CNGS: tau appearance
in nmn
2005–
• Both L~750 km,
Extend reach in
sin2213
• MONOLITH aims at
verifying oscillation
curves with
atmospheric neutrinos
31
Public Interest in Neutrinos
32
33
Why does 2-flavor mixing work?
• Maki-Nakagawa-Sakata matrix for 3
Ue1 Ue2 Ue3 
generations


n m ,t  1 Um1
U MNS  Um1 Um 2 Um 3 


U 1 U 2 U 3 
im12t / 2 p
im22t / 2 p
e
 2U e
 3U
m2
m3
e
im32t / 2 p

34
Why does 2-flavor mixing work?
• Maki-Nakagawa-Sakata matrix for 3
Ue1 Ue2 Ue3 
generations


n m ,t  1 Um1
U MNS  Um1 Um 2 Um 3 


U 1 U 2 U 3 
im12t / 2 p
im22t / 2 p
e
 2U e
 3U
m2
m3
e
im32t / 2 p
*
*
*
n

1U

2
U

3U
1
2
3
 
n  n m ,t

 U*1Um1
U 2Um 2 e
*
e
im22 t / 2 p
im12 t / 2 p
U 3Um 3 e
*
im32 t / 2 p
35
Why does 2-flavor mixing work?
• If m1 and m2 not very different, it reduces to
the 2-flavor problem
n  n m ,t
 U*1Um1
U 2Um 2 e
*


U*1Um1
im22 t / 2 p
U 3Um 3 e

*
U 2Um 2 e
 U 3Um 3e
*
e
im12 t / 2 p
*
im12 t / 2 p
im12 t / 2 p
im32 t / 2 p
U 3Um 3 e
U 3Um 3 e
*
*
im32 t / 2 p
im32 t / 2 p
2
 im 2 t / 2 p

im
t
/
2
p
3
 e sin   e 1
 e



i
36

When is 3-flavor important?
n  n m ,t
2

U*iUmiUjUm*j
e


i mi2  m 2j t / 2 p
i, j


  2e U*iUmiUjUm*j sin
2
2
m

m
j
2 i
4p
i, j


 m U*iUmiUjUm*j sin
i, j
mi2  m 2j
2p
t
t
When all masses significantly different
Anti-neutrinos: UU*, the last term flips sign
Possible CP violation
37
MNS matrix
• Standard parameterization of MakiNakagawa-Sakata matrix for 3 generations
UMNS
 Ue1 Ue2

  U m1 U m 2

 U 1 U 2
Ue3 

Um 3 

U 3 
1
  c13



c23 s23  


i
 s23 c23   s13e
atmospheric
s13e i   c12

1
  s12

c13  
???
s12
c12




1
solar
38
Three-generation
• Solar & atmospheric n oscillations easily accommodated
within three generations
• sin2223 near maximal, m2atm ~ 310–3eV2
• sin2212 large, m2solar ~ 310–5eV2?
• sin2213 < 0.05 from CHOOZ, Palo Verde
• Because of small sin2213, solar & atmospheric n
oscillations almost decouple
• Need to know the solar situation,
• sin2213, and mass hierarchy
39
CP Violation
P(n e  n m ) 
2
P(n e  n m )  16s12 c12 s13 c13 s23 c23
 m2   m 2   m 2 
sin  sin  12 L sin  13 L sin  23 L
 4E   4E   4E 
• Possible only if:
– m122, s12 large enough (LMA)
– 13 large enough
40
superbeam
• Existing proposals of neutrino superbeam
(Debbie Harris@Snowmass2001)
Name
Start
Year
Proton Proton Neutrino Baseline
Power Energy Energy
(km)
Years of
Running
CP
sin 2 13
phase
kton
(3)
 (3)
JHF to
2008?
SuperK
0.77
MW
50GeV 0.7GeV
350km
5 yrs n
JHF to
2013?
HyperK
4MW
50GeV 0.7GeV
350km
2 yrs n
6 yrs n
1000 0.0025  15o
CERN
2011
to UNO
4MW
2.2GeV 250MeV
130km
2 yrs n
10 yrs n
400 0.0025  40o
50
0.016
none
41
High-energy superbeam
• Higher E, longer L  Can study matter
effect to determine the mass hierarchy
(Barger, Marfatia, Whisnant@Snowmass2001)
Baseline
(km)
Neutrino sin 2  Reach (3)
13
Energy
n
nbar
(GeV)
Sign
(m232)
CP phase
 (3)
350
1
.0013
.0016
–
20
730
2.1
.0017
.0026
–
24
1290
3.7
.0020
.0052
.04
32
1770
5
.0022
.0092
.02
40
2900
8.2
.0025
.037
.01
76
42
Solar Neutrinos
How the Sun burns
• The Sun emits light because nuclear fusion
produces a lot of energy
2 Lsun
1
10
1
2
n 

7
10
sec
cm
25MeV 4p (1AU) 2
44
45
SuperK sees the Sun
46
Solar Neutrino Spectrum
p  p  d  n e  e
p  e  p
 d  ne
7
Be  p8 B
8 Be  e + n e
8

7
Be  e 7 Li + n e
Be  2a
3

He  p
 He + n47e  e
4

We don’t get enough
48
Why?
1. Astrophysics is wrong
–
–
pp neutrino flux tied to solar luminosity
Change 7Be, 8B arbitrarily  can’t fit the data
2. Some of the data are wrong
–
–
Even if only one experiment correct, the
puzzle remains
Need both 1. & 2. to explain the situation
3. Something is wrong with neutrinos
49
Astrophysics wrong?
Fit data with arbitrary
7Be, 8B
Best fit needs negative 7Be
Remember 8B is a product of 7Be!
50
Astrophysics wrong?
• Helioseismology data agree well with the SSM
51
52
Josh Klein, Lepton Photon 2001
SNO comes to the rescue
• SNO: ne
6
2
1
n  1.75  0.07 0.12

0.0510
cm
sec
0.11
• SuperK: ne+nm,/7
6
2
1
n  2.32  0.030.08
10
cm
sec
0.07
3.3 difference
nm, are coming from the Sun!
53
SNO result
• Total 8B flux:
(5.440.99)10-9cm-2s-1
• BP2000 calculation
(5.05+0.1-0.8)10-9cm-2s-1
Remarkable agreement!
54
Wrong Neutrinos
• Only ne produced in the Sun
• Wrong Neutrinos nm, are coming from the Sun!
• Somehow some of ne were converted to nm, on
their way from the Sun’s core to the detector
 neutrino oscillation!
SNO is further studying
neutral current reaction
 ne+nm+n
Expect result in April!
55
Conclusions
• Evidence for oscillation in atmoshperic
neutrino very strong
• More cross-checks with man-made beams
• Eventually to more powerful long-baseline
oscillation experiments, aiming at CP
violation
• Solar neutrino problem clearly not due to
astrophysics
56