Neutrino Physics
Neutrino mass and mixing
No neutrinoless double beta decay
K. Nishikawa
＠XXXIV International Meeting
on Fundamental Physics
April 3-7,2006
Neutrinos are Everywhere
• Big Bang:
– They are still left over: ~300 neutrinos per cm3
• Natural sources
– Sun :
1012 of neutrinos /sec /cm2
– Atmosphere : 103 high energy neutrinos /sec/m2
– Reactor :
1020 neutrinos/GWth
• Weak:
– Need to stack up lead shield up to three light-years to stop
them
• Light
– Twelve orders of magnitudes below Mt or weak scale10
Brief history
– 1930 Pauli’s neutrino hypothesis
– 1934 Fermi theory of weak interaction
– 1956 Neutrino observation by Reines and Cowan
• Neutrinos are left handed
q-t puzzle and parity
– 1957 Parity violation by Wu et.al.
Helicity of neutrino measured by M.Goldhaber et.al.
– 1958 V-A (Sudarshan & Marshak, Feynman & Gell-Mann) Current-current
formulation
• Intermediate Vector Boson (W) hypothesis
– 1960 Two neutrino hypothesis (Lee, Yang)
– 1968 Solar neutrino problem （Ray Davis)
• Electro-weak unification
– 1967 Weinberg, Salam, Glashow
–
‘t Hooft’s proof
– 1973 Discovery of Weak Neutral Current (Gargamelle)
– 1983 Observation of Z,W
Conclusion of this series of talks
Experimental evidences for the following
summary
• Two mass eigen-states have Dm2
~8x10-5 eV2
• Define n1, n2 such that
mn2 > mn1
• Solar n MSW in neutrino (not antineutrino)
n1 is the largest component in ne
8
• Third mass eigen-sate (n3) is
separated by Dm2 ~ ±3x10-3 eV2
• Small ne component in n3 (n3
consists of nm, nt, almost 50;50)
which is larger in nt ? (q23<p/4 ?)
• neutrino mass and charged lepton
mass ordering
• same or inverted
atm.
3x10-3eV2
Issues about neutrinos for coming years?
Neutrino-lessbb
•
What is Neutrino? Tiny mass (~x 10-10 ) of q,l±
– Majorana : Majorana and Dirac masses co-exist
• See Saw mn ～ m2/M (M~coupling unification scale)
• neutrino = antineutrino DL= 2 units
– Dirac : ~ quarks, charged leptons
• very very weakly coupled RH
NeutrinoOscillation
•
•
Different patterns of mixings in quarks and in leptons
– Masses and interactions (transitions among elementary
particles)
– Particle and anti-particle distinction, especially in pure
leptonic process
Baryon- Anti-Baryon asymmetry in Universe ?
Contents-1
• Experimental achievements
1. What are neutrinos?
2. Their interactions?
3. Imaging type water Cherenkov detector (Super-Kamiokande)
Helicity of neutrino (V-A)
Parity
P : r  -r , t  t
p  - p, s (  r  p )  s
LH
direction of motion
RH
direction of motion
P
Maximum parity violation means a possibility
direction
spinone
= direction
of state
advancement
right handed screw
whereofonly
of those
exist inofnature
Only left handed component exists
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
Anti-Neutrinos are Right-handed
• CPT theorem in quantum field
theory
– C: interchange particles &
anti-particles
– P: parity (r → -r)
– T: time-reversal (t → -t)
• State obtained by CPT from nL
must exist: nCR
• Lorenz transformed state
nR (Lorenz)
n CR = n R ?
nCR
Standard Model
Finite mass of neutrinos imply the Standard Model is
incomplete!
• Not just incomplete but probably a lot more profound
– New kind of field (Majorana : nCR=nR)
– Very small RH interaction (Cannot produced by
interaction)
Number of neutrino species
Intermediate Vector Boson and
m-decay
• Feinberg’s argument (1958)
• V-A current-current formulation suggest W± analog to g
nm  ne ?
• Pontecorvo (1959) Schwartz (1960) idea of high energy
neutrino beam
DONUT
FNAL E872 Beam dump beam
Status :
406 neutrino interaction analyzed.
7 nt CCevent detected
On-going ：
Component analysis of the prompt
neutrino beam
νe：νμ ：ντ
Interaction
Point
Decay
Point of
t
t
neutrino
Reject Low
momentum tracks
Reject passing
(114 tracks remained)
Vertex detection :
Neutrino interaction and decay
of short lived particles
through tracks
All tracks in the Scanning region
(4179 tracks)
(420 tracks remained)
Detection of ντCC in DONUT
The Number of Neutrinos
collider experiments
• most precise measurements come
from Z  e + e• invisible partial width, inv,
determined by subtracting measured
visible partial widths (Z decays to
quarks and charged leptons) from
the Z width
• invisible width assumed to be due
to Nn
• Standard Model value (n  l)SM =
1.991  0.001 (using ratio reduces
model dependence)
inv  l

Nn 
l  n


SM
Nn = 2.984 0.008
Neutrinos
How they interact
Charged current interaction
Transformation between pair of particles, differ by unit charge
t3=1/2
neL nmL ntL
uL cL tL
(nR nR nR)
uR cR tR
dR sR bR
eR mR tR
dL sL bL
mixing exist (CKM)
•Coupling constant(GF) is universal for all particles
•Left-handed particles form weak isospin-doublets
•All right-handed particles have no charged current interaction
(even if they exist in nature) iso-singlets
• Interaction is mediated by W intermediate vector boson
t3=-1/2
GF
g2

2
2 8M W
eL mL tL
GF =
g
2 2
W
GF ~ 1.17 10 -5 GeV - 2
GF : Fermi coupling constant
d
GF ( s - ml2 ) 2

d CM (2p) 2
s
2
nl+e → ne+l
nl
g
l
W
e
g
nl + n → l(-) + p
nl + p → l(+) +n
ne
2g 2

8M W2
isotropic in cms
~10-41・En cm2
En th~10GeV for m
s  2me En
En
g
2me En
ｌ：Forward peak
qn-e small
d
GF ( s - mN2 ) 2

 FF
2
d CM (2p)
s
2
s  2mN En  mN2
~10-38・En cm2
Complication by
free, almost free nucleons
form factors, Nuclear effect(Pauli blocking) H2O D2O CH
Quasi-elastic scattering cross-sections
• Two form factors
nm
•MV fixed by e.m. (CVC)
10-38cm2
•Axial V form factor
mfA , fV 
W
p
n
1
2 

q
1 
2


M
A
,
V


2
/En (10-38cm2/GeV)
Cross-section (nm)
magenta Old MC
red
new MC
1
10
100 GeV
Data on charged current processes
• Not well
known
• Especially 2~3
GeV
• must be
determined
internally
Neutral current interaction
nl
gL,R
nl
Z
e(N)
e(N)
gL,R
neL nmL ntL
eL mL tL
uL cL tL
(nR nR nR)
eR mR tR
uR cR tR dR sR bR
dL sL bL
g=T3 - sin2qW·Q
Iso-doublet
gL
Iso-singlet
gR
eL mL tL
-1/2 + sin2qW
eR mR tR
sin2qW
neL nmL ntL
+1/2
neR nmR ntR
0
uL cL tL
1/2 - 2/3sin2qW
uR cR tR
-2/3sin2qW
dL s L b L
-1/2 +1/3 sin2qW
dR sR bR
1/3sin2qW
Neutrino mass and oscillation
Neutrino oscillation
n1
nm
n m  cos q  n1  sin q  n 2
n2
phase difference 
nt
( m22  p 2 - m12  p 2 )i (ct )
 Dm 2 / 2 p  i (ct )
 Dm 2  L / 2 p  i
n1  cos q  n m - sin q  n t
n t  - sin q  n1  cos q  n 2 n 2  sin q  n m  cos q  n t
• Inteferometry (i.e., Michaelson-Morley)
– Coherent source
– Interference (i.e., large mixing angles)
– Need long baseline for small Dm2
• Neutrino mass must be non-zero, if oscillation occurs
The Hamiltonian
• The Hamiltonian of a freely-propagating massive neutrino
H
2
m
p2  m 2  p 
2p
• But in quantum mechanics, mass is a matrix in general. 22
case:
 m 211
M2   2
 m 21
2 
m 12

2
m 22 
M 2 1  m12 1
M 2 2  m22 2
Two-Neutrino Oscillation
• When produced (e.g., p+m+nm), neutrino is of a particular
type
• At time t
22
22
-im
t
/
2
p
-im
t
/
2
p
-im
t
/
2
p
|
1
2
1
2
n m ,t,t  1 cos q ee
 2 sin q e
• No longer 100% nm, partly nt!
• “Survival probability” for nm after t

P  n m nm ,t

2
2 4

Dm
c GeV ct 
2
2

 1 - sin 2q sin 1.27
2 c p km
eV


Three Flavor Mixing in Lepton Sector
Weak eigenstates
m1
ne
n e 
n 1 
 
 
CP
n m   U MNS VM n 2 
n 
n 
 t
 3
nm
nt
U PMNS
1

 0
0

0   c13

 s23  0
 c23  - s13e i
0
 c23
- s23
0
1
0
mass eigenstates
m2
m3
 s13e - i   c12

0
 - s12
 c13  0
 s12
 c12
0
cij = cosqij, sij=sinqij
V
CP
M
 e i 1

  0
 0

0
e
i 2
0
0

0
1
q12, q23, q13
+  (+2 Majorana phase)
Dm122, Dm232, Dm132
0

0
1 
Matter effect MSW effect
• Neutrinos propagate in matter receive a refractive effect due to
their interaction (extra energy V, the energy E, momentum k’)
with matter
'2
E  k  m V
2
The refractive index n is defined by
  exp( i  n  k x - iEt )
E2=k2+m2 the dispersion relation in vacuum and k’=nk
n=1-EV/k2
n e : V  2GF ( 1  2 sin 2 qW )  ne
2
n m ,t : V  2GF (- 1  2 sin 2 qW )  ne
2
ne electron density
MSW effect (II)
n e (CC  NC ) : Ve   2GF ( 1  2 sin 2 qW )  ne
2
n m,t ( NC )
: Ve   2GF (- 1  2 sin 2 qW )  ne
2
- for anti-neutrino
Dn=1-n ~7.6 x 10-19 (r/100g cm-3)(E/10MeV)-1 for ne small for nm,t
velocity changes == effective mass changes in matter
(r100g/cc at the center of Sun)
Active neutrinos by interaction with p,n
n e ,m , t
: Vn   2GF ( 1 - 2 sin 2 qW )  n p  2GF 1 nn
2
2
n e ,m , t
Can distinguish ‘active’ and ‘sterile’ neutrinos
effective mass
in matter
L
GF
[n e g m (1 - g 5 )n e ][eg m (1 - g 5 )e] , V e 2G F N e
2
Schrodinger eq.
n e 
 n1 
 cos q sin q 
d n e 
i    H    HU   , U  

n
n
sin
q
cos
q
dt n x 


 2
 x
Hamiltonian
E
H 
0
0  1 m12

U

E  2E  0
0  -1 Ve  Vn 0 
U 

2
0
V
m2 
n

2
2
1
0

A
D
m
cos
2
q
D
m
sin 2q 


1 2
1
2

  
2 EH  (m1  m2  A)
2
2
2
- A  Dm cos 2q 
 0 1  2  Dm sin 2q
1
m 2  (m12  m22  A)  (Dm 2 cos 2q - A) 2  (Dm 2 sin 2q) 2
2
A  2 2GF Ne E Ares  2 2GF Ne E  Dm2 cos 2q
Effective mass difference of ne and nm,t in matter by Ve
Dm 2 matter  (Dm 2 cos 2q - A) 2  (Dm 2 sin 2q) 2
Mass difference and mixing angle in matter
sin 2qm 
sin 2 2q
2
 2Ve  En

2
cos
2
q

sin
2q


2
 Dm

2
Dm 2 matter  (Dm 2 cos 2q - A) 2  (Dm 2 sin 2q) 2
A  2 2GF Ne E
A change sign for anti-neutrinos
Ne= 6x1025 /cc = 6 x 10-14 /fm3 for r100g/cc
GF~10-5 GeV-2 (0.2GeV·fm)3 =8 x 10-8 GeV fm3
A =10-2 En (GeV) eV2
MSW in the Solar neutrinos
Dm 2 matter  (Dm 2 cos 2q - A) 2  (Dm 2 sin 2q) 2
2 2G F E center
Dm <
Ne
cos 2q
2
A  2 2GF N e E
Ares  2 2GF N e E  Dm 2 cos 2q
In(Dm2)
2res
Dm matter
 Dm2 sin 2q
m2
m1
A  Dm 2 cos 2q ~ 10 -4 eV 2 ( En ~ 10MeV )
In(sin2q)
Also Day Night!
‘MSW’ for sterile
n e,m,t 
 n1 
 cos q sin q 
d  n e ,m , t 
i 
 H
 HU   , U  



n
n
sin
q
cos
q
dt n sterile


 2
 s 
E
H 
0
0  1 m12

U

E  2E  0
0  -1 Vn
U 
2
m2 
0
0
0
n e ,m , t
: Vn   2GF ( 1 - 2 sin 2 qW )  n p  2GF 1 nn   2 2  nn
2
2
n e ,m , t
A  2GF Nn E Ares  2GF Nn E  Dm2 cos 2q
Dm
2
matter
 (Dm cos 2q - A)  (Dm sin 2q)
2
2
2
Large Dm2 →(E >10 GeV in earth) Dm2~A
2
matter effect in the earth for sterile neutrinos
sin 2 2qm 
sin 2 2q
2
 2Vn  E n

2
cos
2
q

sin
2q


2
 Dm

E n  20GeV  sin 2 2qm 
PC, Evis>5GeV
<Eν>～25GeV
up/down ratio
νμーνs
νμーντ
ns
Z
νμーνs
νμーντ
up through going μ
<Eν>～100GeV
vertical/horizontal ratio
ns
n
n
Detectors for Neutrino Oscillation Experiments
•
•
•
Massive
Neutrino oscillation is the oscillation between different flavors
– e, μ, τidentification by charged current interactions
– target and sensor must be combined
Only Flux(En) x (En) will be measured
– En, L must be known event-by event to get Dm2
– Two distances if possible
Nobs  F(En )  P( n   nb )  (En )
2
2
1
.
27
D
m
(
eV
)L(km)
P( n   nb )  sin 2 2q  sin 2
En (GeV)
Particle identification
•
•
•
m-ID
– minimum ionizing particle with long range
R500g/cm2/GeV
e-ID
– showering particle, large g (TRD), E/p1(with magnet)
t-ID
• short decay length
• isolated hadronic activity (charm)
• t→enn t→mnn, tnt hadrons
Super Kamikande
Inside Super-K
Kamiokande
Super-Kamiokande
４０ｍ
1996(1996)
50000ton water
11146 50cmf PMT
(40% photo coverage)
1000m underground
Min det. energy ~ 5 MeV
Inner and outer
Principle of the technique
• Cherenkov radiation: electromagnetic radiation in a medium
with refractive index n if nb>1 (b=v/c)
– cosqc = 1/nb,
q
c
dN
=
dxdl
•
•
•
•
2psin2qc
l2
– where N is the number of emitted Cherenkov photons with
wavelength l, dx is the particle’s path length, and  =1/137
– Cherenkov photons are detected with a large number of
photomultiplier tubes (PMT)
For Super-K, qC = 42deg (b = 1), good at simple geom.
N(photo e.) ~ 6 / Mev e- : about 1/1000 of scintillator
Attenuation length can be attained upto ~100m
P(threshold)~1.2 GeV/c for protons
Cherenkov light
Charged particle
Electron-like and muon-like events
e-like
e
m-like
m
Particle ID (e & m) (in single ring events)
•
An experiment with test beams
confirmed the particle ID
capability (PL B374(1996)238)
e
m
K2K 98% nm beam
near detector
m
e
Atm. data
Excellent for low
multiplicity
Low energy
Particle ID in multi ring events (p0 selection)
π0←