Xing Zh., Zhou Sh. Neutrinos in Particle Physics, Astronomy and Cosmology
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X
C
ontents
3 Neutrinos beyond the
S
tandard Model ...................
61
3
.1 Ex
p
erimental Evidence for Neutrino Masses ...............
.
6
1
3.1.1 Atmospheric Neutrino Oscillations . . ................
62
3
.1.2
A
ccelerator Neutrino
O
scillations ...................
63
3.1.3 Solar Neutrino Oscillations . ......................
.
64
3
.1.4
R
eactor Neutrino
O
scillations ......................
67
3.1.5 Implications o
f
Experimental Data ................
.
69
3
.2 Dirac and Ma
j
oranaNeutrinoMass Terms................
.
6
9
3.2.1 Dirac Masses and Lepton Number Conservation . . ....
71
3.2.2 Ma
j
orana Masses an
d
Lepton Num
b
er Vio
l
ation......
73
3.2.3 H
y
brid Mass Terms and Seesaw Mechanisms . . . ......
75
3
.3
C
, P and T Properties o
f
FermionFields .................
.
79
3.3.1
C
, P and T Trans
f
ormations o
fSp
inor Bilinears . .....
79
3.3.2 CP Violation in
Q
uark and Le
p
tonSectors .........
.
81
3
.4 Electroma
g
netic Properties o
f
MassiveNeutrinos ...........
86
3.4.1 Electroma
g
neticFormFactors ..................... 8
6
3.4.2 Magnetic an
d
E
l
ectric Dipo
l
eMoments..............
89
3.4.3 Radiative Deca
y
so
f
MassiveNeutrinos..............
92
3.4.4 Electroma
g
netic Neutrino-electron Scatterin
g
........ 94
3
.5 Lepton Flavor Mixing and CP Violation . . . ................
97
3
.
5
.1
C
lassi
fi
cation o
f
Di
ff
erentParametrizations ..........
97
3.5.2 Democratic and Tri-bimaximal Mixin
g
Patterns ......
1
0
0
3.5.3 Rep
h
asing Invariants an
d
Unitarity Triang
l
es .......
.
103
3.5.4 F
l
avor Pro
bl
ems in Partic
l
eP
hy
sics................
.
105
3
.6 Running Behaviors of Neutrino Mass Parameters . . . .......
.
1
0
8
3.6.1 One-loop Renormalization-groupEquations..........
109
3.6.2 Evolution o
f
Ma
j
orana Neutrino Mass Parameters . . . .
111
3.6.3 EvolutionofDiracNeutrinoMassParameters........
1
1
6
R
e
f
erences ................................................
.
119
4S
eesaw Mechanisms of Neutrino Masse
s
.
.................
125
4.1 How to Generate Tiny Neutrino Masses ..................
.
1
2
5
4
.1.1 N
o
n-
seesaw
M
echa
ni
s
m
s
...........................
126
4
.1.2
S
eesaw Mechanisms . . .............................
1
2
8
4
.1.3 TheWeinbergOperator..........................
.
1
2
9
4.2
O
nthe
S
cales o
fS
eesaw Mechanisms . .....................
133
4
.2.1
S
eesaw-induced Hierarch
y
Problem .................
1
3
3
4
.2.2
S
eesaw-induced Naturalness Problem . ..............
13
4
4.
3S
eesaw Mechanisms at the Te
VS
cale .....................
135
4
.3.1 T
y
pe-I Seesaw Mechanism . . .......................
1
3
5
4
.3.2 Type-II Seesaw Mechanism . . . .....................
137
4
.3.3 Type-
(
I+II
)
Seesaw Mechanism . ...................
138
4
.3.4 T
y
pe-III Seesaw Mechanism . . . ....................
1
4
0
4
.
3
.
5
Inverse
S
eesaw Mechanism . . .......................
1
4
1
4.4 Multiple
S
eesaw Mechanisms . ...........................
.
142
C
ontents XI
4
.4.1 Two
C
lasses o
f
Multiple
S
eesaw Mechanisms ........
.
143
4
.4.2 Char
g
ed-current Interactions......................
.
1
4
7
4.5 Non-unitary Neutrino Mixing and CP Violation . . ..........
150
4
.5.1 Jarlsko
g
Invariants o
fC
PViolation................
.
151
4
.5.2 Mixin
gA
n
g
les and CP-violatin
g
Phases .............
1
5
2
R
eferences ................................................
.
155
5 Phenomenology of Neutrino Oscillations
.
.................
159
5
.1 Neutrino Oscillations and Matter Effects . . ...............
.
1
5
9
5
.1.1 Neutrino
O
scillations in
V
acuum ..................
.
160
5.1.2
A
diabatic Neutrino Oscillations in Matter . .........
.
1
6
4
5.1.3 Non-adiabatic Neutrino Oscillations in Matter . .....
.
1
6
8
5
.1.4 T
h
e
3
×
3
N
eutrino
M
ixing
M
atrix in
M
atter ........
171
5.1.5 Leptonic Unitarity Trian
gl
esinMatter.............
.
1
7
4
5
.2 Neutrino Oscillations and
Q
uantum Coherence ............
.
177
5
.2.1 A Paradox of Neutrino
O
scillations . . ..............
.
178
5.2.2 The Wave-
p
acket
App
roach........................
1
8
2
5
.2.
3C
oherence of
C
osmicNeutrinos ....................
18
4
5
.3 Density Matrix Formu
l
ation .............................
187
5.3.1 Two-
fl
avor Neutrino
O
scillations ...................
1
8
8
5
.
3
.2 Three-flavor Neutrino
O
scillations ..................
193
5.3.3 Non-
l
inear Evo
l
utionEquations ...................
.
195
5
.4 Future Lon
g
-baseline Neutrino Oscillation Facilities . .......
.
2
0
1
5.4.1 Prospects of Accelerator Neutrino Experiments.......
201
5.4.2 Prospects of Reactor
A
ntineutrinoExperiments ......
206
R
eferences ................................................
.
2
0
9
6Neutrinos
f
rom Stars
.
....................................
213
6
.1
S
tellar Evolutionin aNutshell ...........................
213
6.1.1 Distance, Luminosit
y
andMass ....................
2
1
3
6.1.2 BasicEquationsofStellar Evolution ...............
.
218
6.1.3 Ener
g
y
S
ources o
fS
tars ..........................
.
223
6.1.4 The Mass-Luminosit
y
Relation.....................
2
2
6
6
.2 Neutrinos from the
S
un .................................
2
2
7
6.2.1 The
S
tandard
S
olar Model........................
.
2
2
8
6.2.2 Proton-protonChain and CNOCycle ..............
.
230
6
.2.
3S
olar NeutrinoFluxes............................
.
232
6
.3 Ex
p
erimental Detection o
fS
olar Neutrinos................
.
2
3
3
6
.
3
.1
R
adiochemicalMethods ..........................
.
233
6
.
3
.2
W
ater
C
herenkov Detectors.......................
.
237
6.3.3 Future Solar Neutrino Ex
p
eriments................
.
2
4
0
6
.4
S
olar Neutrino
O
scillations . . . ..........................
.
2
4
1
6
.4.1 The
S
olar NeutrinoProblem......................
.
241
6.4.2 TheMSWMatterEffects.........................
.
242
6.4.3 ConstraintsonNeutrino Properties ................
.
2
44
XII
C
ontents
R
e
f
erences ................................................
.
245
7Neutrinos
f
rom Su
p
ernovae
.
.............................. 249
7.1 StellarCoreCollapsesand SupernovaNeutrinos...........
.
2
4
9
7
.1.1 De
g
enerate
S
tars ................................
.
250
7
.1.2 Core-colla
p
se Su
p
ernovae.........................
.
2
5
2
7
.1.3 Supernova Neutrinos.............................
.
25
4
7.2 Lessons from the Supernova 1987
A
......................
.
256
7
.2.1 Discoveriesofthe NeutrinoBurst...................
2
5
7
7
.2.2 Constraints onNeutrinoProperties ................
.
259
7
.2.3 The Di
ff
use
S
upernova Neutrino Back
g
round.........
260
7
.2.4 Future Su
p
ernova Neutrino Ex
p
eriments ...........
.
2
6
2
7.3 Matter EffectsonSupernova Neutrinos...................
.
263
7
.3.1 Neutrino Fluxes and Ener
g
y
S
pectra...............
.
265
7
.3.2 Matter Effects in the Su
p
ernova...................
.
265
7
.
3
.
3
Matter E
ff
ectsinthe Earth.......................
.
269
7.4
C
ollective Neutrino Flavor
C
onversions...................
.
2
7
2
7
.4.1 E
q
uationsof Motion.............................
.
272
7
.4.2
S
ynchronized Neutrino
O
scillations . . . .............
.
275
7
.4.3 Bi
p
olar Flavor
C
onversions .......................
.
2
7
7
7
.4.4 NeutrinoSpectral Splits..........................
.
280
7
.4.
5
E
ff
ects o
f
ThreeNeutrino Flavors...................
283
R
eferences ................................................
.
2
8
5
8Ultrahi
g
h-ener
g
y Cosmic Neutrino
s
.......................
289
8
.1 Possible
S
ources o
fU
HE
C
osmicNeutrinos ................
289
8.1.1 TheGZKCutoff and UHENeutrinos ...............
2
9
0
8.1.2 AstrophysicalSourcesofUHE Neutrinos ............
292
8.1.3 Top-
d
own Mo
d
e
l
san
d
UHENeutrinos ..............
297
8
.2 Detection ofUHE CosmicNeutrinos .....................
.
2
9
8
8
.2.1 A k
m
3
-
sca
l
e UHE Neutrino Te
l
escope ..............
.
299
8.2.2 Identi
fi
cation o
f
UHENeutrinoFlavors.............
.
300
8.2.3 Other Wa
y
sto Detect UHE Neutrinos ..............
3
0
3
8
.
3
Flavor Distribution of
U
HE
C
osmicNeutrinos.............
.
305
8.3.1 Flavor Issues o
f
UHENeutrinos ....................
3
0
5
8.3.2 Flavor EffectsinNewPhysics Scenarios .............
309
8
.4 Neutrinos and Multi-messen
g
er Astronomy ...............
.
313
8.4.1
C
osmic Neutrinos and
Z
-bu
r
sts
...................
.
3
1
3
8.4.2 CosmicNeutrinos and GammaRays ................
3
1
5
8
.4.
3
Neutrinos and
G
ravitational
W
aves ................
.
318
R
eferences ................................................
.
3
1
9
C
ontents XIII
9B
i
gBangNucleosynthes
i
sandRel
i
cNeutr
i
nos ...........
323
9
.1 Neutrinos in the Earl
y
Universe .........................
.
3
2
3
9.1.1 Hu
bbl
e
’
sLawan
d
t
h
eFrie
d
mannEquations ........
.
3
24
9.1.2 The Ener
g
y Density o
f
theUniverse ................
325
9.1.3 The
Ag
eandRadiusoftheUniverse................
3
2
7
9.1.4 Ra
d
iation in t
h
eEar
l
yUniverse ...................
.
329
9.1.5 Neutrino Decoup
l
in
g
.............................
.
332
9
.2 Big BangNucleosynthesis ..............................
.
3
3
5
9.2.1 T
h
eNeutron-to-protonRatio .....................
.
336
9.2.2
S
ynthesis o
f
the Li
g
ht Nuclei......................
.
3
3
7
9.2.3 The Bar
y
on Densit
y
andNeutrinoSpecies...........
3
4
0
9
.3 Possi
bl
e Ways to Detect Re
l
icNeutrinos...................
342
9.3.1
C
osmic Neutrino Back
g
round ......................
342
9
.
3
.2 Direct Detection of
R
elicNeutrinos.................
3
4
3
R
e
f
erences ................................................
.
347
10 Neutrinos and
C
osmological
S
tructures ................... 3
49
1
0.1 The CosmicMicrowave Background......................
.
3
4
9
10.1.1 Matter-ra
d
iation Equa
l
ity ........................
.
349
10.1.2 Formation o
f
the
C
MB...........................
.
3
5
1
10.1.3 AnisotropiesoftheCMB .........................
.
353
10.1.4 Neutrino
S
pecies and Masses .......................
357
1
0.2 Lar
g
e-scaleStructures andDarkMatter ..................
.
3
5
9
10.2.1 Inflationand DensityFluctuations.................
.
360
1
0
.2.2 L
SS
andDarkMatter............................
.
363
10.2.3 Constraints on Neutrino Masses ....................
3
6
5
1
0
.2.4
S
terile Neutrinos as DarkMatter..................
.
369
R
e
f
erences ................................................
.
372
11 Cosmolo
g
ical Matter-antimatter
A
symmetry ............. 375
1
1.1 BaryonAsymmetry ofthe Universe......................
.
375
11.1.1 Constraints from
A
ntimatterSearches...............
376
11.1.2 ObservationsfromtheCMB andBBN ..............
3
7
8
1
1.2 Typical Mechanisms ofBaryogenesis ......................
379
11.2.1
S
akharov
C
onditions.............................
.
3
7
9
11.2.2 Electroweak Baryogenesis .........................
380
11.2.3
G
UT Baryo
g
enesis ..............................
.
386
11.2.4 Th
eA
ffl
ec
k-Din
e
M
ec
h
a
ni
s
m.......................
3
8
7
11.2.5
L
eptogenesis....................................
.
389
1
1.3
B
aryo
g
enesis via
L
epto
g
enesis...........................
.
390
11.3.1 Thermal or Non-thermalProduction...............
.
3
9
0
11.3.2 CP-violatingAsymmetries.........................
392
11.3.3 Bo
l
tzmann Equations ............................
.
398
11.3.4 Bar
y
on Number
A
s
y
mmetr
y
....................... 40
5
1
1.4 Recent Deve
l
opmentsin Leptogenesis ..................... 4
08
XI
VC
ontents
11.4.1 Trip
l
et Lepto
g
enesis .............................
.
408
11.4.2 Resonant Lepto
g
enesis ............................
412
11.4.3 SoftLeptogenesis................................
.
41
3
11.4.4 Fl
avo
rE
ffects
...................................
.
4
1
5
R
eferences ................................................
.
41
7
I
n
de
x ......................................................... 421
1
N
eutr
i
nos: Past, Present and Futur
e
E
lusive neutrinos have been playin
g
a special and important role in nuclea
r
p
h
ysics, partic
l
ep
h
ysics, astronomy an
d
cosmo
l
ogy. T
h
ey exist everyw
h
er
e
i
nt
h
eUniversean
d
are Nature
’
s mysterious messen
g
ers. In t
h
is c
h
apter w
e
s
hall
g
ive a broad but brief overview of the history of neutrino physics and
the present situation of neutrino astrophysics. The prospects of neutrino as
-
tronomy an
d
neutrino cosmo
l
o
g
ywi
ll
a
l
so
b
e
d
escri
b
e
d
.
1.1 Neutrinos in Nuclear and Particle Ph
y
sics
The histor
y
o
f
neutrino ph
y
sics can be traced back to 4 December 1930, whe
n
Wolfgang Pauli wrote his famous letter to the “Dear radioactive ladies and
g
ent
l
emen
”
w
h
o
h
a
dg
at
h
ere
d
in T¨u
b
in
g
en
1
.Int
h
is
l
etter Pau
l
i conjecture
d
the existence o
f
neutrinos as a desperate remedy
f
or the ener
g
y crisis observe
d
i
nt
h
e
b
eta
d
ecay
b
ecause t
h
eenergyan
d
momentum conservation
l
aws
,
w
h
ic
hh
a
db
een re
g
ar
d
e
d
to
b
e very sacrosanct, were severe
l
yc
h
a
ll
en
g
e
d
by the continuous ener
g
y spectrum of the beta ray. Based on the neutrino
h
ypothesis, Enrico Fermi put forward an effective quantum theory of the
beta decay in 1933, throu
g
h which people made the
fi
rst acquaintance wit
h
a
new force in nature — the weak interaction. Soon after the ex
p
erimenta
l
d
iscovery of electron antineutrinos in 1956, the space-inversion symmetr
y
(
or parity conservation
)
was found to be maximally violated in a number o
f
p
rocesses of weak interactions. Hence neutrinos were assumed to be massles
s
Weyl particles with only two components: left-handed neutrinos and right-
h
an
d
e
d
antineutrinos. T
h
e
y
were natura
lly
inc
l
u
d
e
d
into t
he
V
−
A
theor
y
o
f
weak interactions in 1958 and into the standard model
(
SM
)
of electroweak
i
nteractions in 1967. The latter was experimentally veri
fi
ed in 1974 thanks
1
S
ee, e.g., Pauli’s lecture given in 1957 in Z¨urich: “Zur ¨alteren und neueren
Geschichte des Neutrinos”
(
i.e., “On the Earlier and More Recent History of the
Neutrino”), which was published in 1984 (Pauli, 1984)
.
Z.-Z. Xing et al., Neutrinos in Particle Physics, Astronomy and Cosmology
© Zhejiang University Press, Hangzhou and Springer-Verlag Berlin Heidelberg 2011
2 1 Neutrinos: Past, Present an
d
Futur
e
to the discover
y
o
f
neutral-current interactions — a neutrino could interact
with another particle and remained to be a neutrino.
A
lthou
g
h the SM ha
s
s
o far passed almost all experimental tests, it must be incomplete because it
does
n
ot allow
n
eut
rin
os to be
m
ass
i
ve
.
S
ince 1998, a lot of robust ex
p
erimental evidence has
p
ointed to the fac
t
t
h
at neutrinos can osci
ll
ate — a pure quantum p
h
enomenon w
h
ic
h
can ta
k
e
place only i
f
neutrinos have
fi
nite masses. This
g
reat breakthrou
g
hisopenin
g
a
n important window towards new ph
y
sics be
y
ond the SM. In this section we
s
hall follow the historical line to briefly address the role played by neutrino
s
i
n the development o
f
nuclear and particle ph
y
sics.
S
ome particular attention
will be paid to the following three aspects:
(
1
)
the background for Pauli to
c
onjecture the existence of neutrinos;
(
2
)
the establishment of th
e
V
−
A
the-
ory of weak interactions; and
(
3
)
the discovery of neutrinos. An introduction
to the ex
p
erimental and theoretical as
p
ects of neutrino oscillations will b
e
presented in
S
ection 3.1 and
C
hapter 5
.
1.1.1 Pauli’s Neutrino H
y
pothesi
s
The ultimate goal of particle physics is to explore the fundamental buildin
g
blocks of matter and the fundamental forces between them, and to discover
the basic laws
g
overnin
g
how Nature works as it does. In the early sta
g
eo
f
th
e
2
0th century electrons and protons were commonly regarded as the elemen
-
tary particles and thus the unique in
g
redients o
f
atoms, which made up the
m
atter. This picture encountered some serious di
ffi
culties, amon
g
which th
e
m
ost important two were the “wrong statistics” problem and the continuous
ener
g
y spectrum o
f
the beta decay
.
A
t that time the nitro
g
en nucleus
14
N
was ex
p
ected to contain 14
p
roton
s
a
nd 7 electrons. Hence the s
p
in of
1
4
N should be half-integral and obey th
e
F
ermi-Dirac statistics. T
h
e experiments,
h
owever, in
d
icate
d
t
h
a
t
14
N
actua
lly
f
ollowed the Bose-Einstein statistics
(
Kronig, 1928; Heitler and Herzberg
,
1
929; Rasetti, 1930
)
. This was just the “wrong statistics” problem
.
T
he continuous ener
g
y spectrum o
f
the beta decay was
fi
rst discovered b
y
J
ames Chadwick in 1914
(
Chadwick, 1914
)
. After a longtime debate it was
finally established. But the final state of the beta decay of an unstable nucleu
s
was assumed to consist o
f
only two particles: the dau
g
hter nucleus and th
e
electron.
A
simple kinematic anal
y
sis of this two-bod
y
deca
y
mode led to th
e
c
onc
l
usion t
h
at t
h
e emitte
d
e
l
ectron must
b
emonoenergetic.T
h
ere were tw
o
c
onflicting viewpoints on the observed continuous spectrum at that time:
(
1
)
the energy spectrum was originally monochromatic, but it was subsequentl
y
broadened due to the energy loss of electrons in nuclei;
(
2
)
the electrons
f
rom the individual decay modes carried various ener
g
ies that distributed
c
ontinuously. In order to verify or falsify either point, one had to measure the
ener
g
y released in the beta decay as accurately as possible.
S
uch a precisio
n
m
easurement was done by makin
g
use o
f
the calorimetry o
f
heat
g
eneration
,
a
nd its result showed that the mean disintegration energy was consisten
t
1.1 Neutrinos in Nuc
l
ear an
d
Partic
l
eP
h
ysics
3
with the energy of electrons averaged over the continuous spectrum
(
Ellis
a
nd Wooster, 1927
)
. How to resolve the energy crisis observed in the beta
d
ecay
b
ecame a great c
h
a
ll
enge to many important t
h
eorists in t
h
e 1920
’
s
.
S
omeexoticideasemer
g
ed, althou
g
h they sounded unima
g
inable. In 1929,
f
or instance
,
Niels Bohr even considered to abandon the conservation laws of
energy an
d
momentum in an in
d
ivi
d
ua
l
su
b
atomic process.
I
n Decem
b
er 1930, Pau
l
ipostu
l
ate
d
t
h
at t
h
e
b
eta
d
ecay mi
gh
t
b
eat
h
ree
-
body decay mode in which an electrically neutral and extremely light particle
of spin 1
/
2 was also emitted from the decaying nucleus. He also conjecture
d
t
h
at t
h
is new partic
l
es
h
ou
ld h
ave a sma
ll
ma
g
netic moment suc
h
t
h
at i
t
c
ould be bounded in the decaying nucleus. The consequences of Pauli’s hy-
pothesis are obvious:
(
a
)
in the final state of the beta decay the electron has
to share the available ener
g
y with the new particle, and hence its ener
gy
s
pectrum must be continuous;
(
b
)
because each electron is accompanied b
y
a
new particle of spin 1
/
2, the spin o
f
14
Nmust
b
eaninte
g
er an
d
o
b
eys t
h
e
B
ose
-Ein
ste
in
stat
i
st
i
cs
2
.
In 1932, Chadwick discovered the neutron
(
Chad-
wick, 1932
)
— the counterpart of the proton in a nucleus
(
Heisenberg, 1932
)
.
Then Fermi named Pauli’s neutral particle as the “neutrino” and
f
ormulated
a
n effective quantum theory of the beta decay
(
Fermi, 1933
)
.
1.1.2 Weak Interactions and Neutrinos
By combining Pauli’s neutrino hypothesis, Dirac’s idea about the creation o
f
particles and Heisenber
g
’s isospin concept
f
or neutrons and protons in a co
-
h
erent way, Fermi proposed the effective Hamiltonian
H
β
H
=
g
(
pγ
μ
n
)(
e
γ
μ
ν
e
)
to account for the beta deca
y
n
→
p
+
e
−
+
ν
e
,w
h
ere t
h
e vector-current in
-
teraction
f
orm was analo
g
ous to the second-order electroma
g
netic interactio
n
(
Fermi, 1933, 1934
)
. This effective theory allowed Fermi to show the correc
t
energy spectrum of the beta decay. He even suggested that an accurate mea-
s
urement o
f
the continuous ener
g
y spectrum’s endpoint be able to pin down
the rest mass of the neutrino. However
,
it turned out that
H
β
H
itself was too
s
elective to explain all the beta decays. This un
f
ortunate situation motivated
other theorists to postulate di
ff
erent selection rules
f
or the deca
y
so
f
nucle
i
(
Gamow and Teller, 1936
)
. The most general Lorentz-invariant form of th
e
e
ff
ective Hamiltonian responsible
f
or the beta deca
y
should contain the scala
r
1
(
S
)
, vecto
r
γ
μ
(
V
)
, tensor
σ
μν
(
T
)
, pseudoscala
r
γ
5
(
P
)
and pseudovecto
r
γ
μ
γ
5
(
A
)
interactions. Historically, it took a long time for experimentalists
to clarify the form of weak interactions
(
Franklin, 2000
).
T
he breakthrou
g
h took place in 1956 and 1957. Questionin
g
the validity
of parity conservation in weak interactions, Tsung-Dao Lee and Chen Ning
2
I
n 1931, Pauli gave up the idea that his neutral particles were the necessary
ingredients of nuclei because it was in conflict with the nuclear mass relations.
It was actua
ll
yt
h
eneutront
h
at
h
a
dl
ater
b
een emp
l
oye
d
to reso
l
ve t
h
e“wron
g
statistics” problem of the nitrogen nucleus
.
4 1 Neutrinos: Past, Present an
d
Futur
e
Yan
g
su
gg
ested an experiment to examine the an
g
ular distribution o
f
the
beta ra
y
s emitted from the
60
Co nuclei with spins polarized alon
g
an externa
l
m
agnetic field
(
Lee and Yang, 1956
)
— if parity were conserved, there shoul
d
be no correlation between the spin and momentum o
f
ever
y
electron emitte
d
i
n the deca
y
3
. Chien-Shiung Wu and her collaborators did this experiment
a
nd found that the electrons were almost always emitted in the directio
n
opposite to the nuclear spins — a si
g
nature o
f
maximal
parity violation
(
W
u
et al
.
,
1957
)
. More evidence for maximal parity non-conservation was later o
n
obtained by other experimental groups in different weak processes
(
Garwi
n
et
al.
,
1957; Friedman and Telegdi, 1957
)
. Soon after the observation of parit
y
violation, several important theorists independently put forward the idea that
n
eutrinos mi
gh
tsimp
l
y
b
e mass
l
ess an
d
cou
ld
natura
ll
y
b
e
d
escri
b
e
d
in terms
of the two-component Weyl spinor
(
Lee and Yang, 1957; Landau, 1957; Salam,
1
957
)
. In such a two-component neutrino theory the helicity of a neutrino
m
ust be identical with its handedness or chirality. The a
f
orementioned
60
Co
experiment indicated that the emitted electron and its accompanyin
g
electro
n
a
ntineutrino should have left
(
λ
=
−
1
/
2)
and right
(
λ
=+
1
/
2
)
helicities,
respectivel
y
. Direct helicit
y
measurements con
fi
rmed
λ
=
−
1
/
2
fo
rn
eut
rin
os
a
nd
λ
=
+1
/
2 for antineutrinos
(
Goldhabe
r
et al
.
,
1958
;
Bardon et al
.
,
1961
).
That is why neutrinos
(
antineutrinos
)
had commonly been accepted to be
exactly massless and purely left-handed
(
right-handed
)
for several decades
before the
p
henomena of atmos
p
heric and solar neutrino oscillations wer
e
firmly established at the end of the 1990’s and the beginning of the 2000’s
.
T
he discovery o
f
parity non-conservation, to
g
ether with a coherent anal
-
y
sis of man
y
other experimental data on various weak processes, led t
o
the theo
r
et
i
cal obse
r
vat
i
o
n
that weak
in
te
r
act
i
o
n
s should have the u
ni
ve
r-
sal
V
−
A
f
orm with maximal parity and charge-conjugation violation
(
Su
-
d
arshan and Marshak, 1958; Feynman and Gell-Mann, 1958
)
.Inthe
V
−
A
theory o
f
weak interactions a
f
our-
f
ermion interaction can be expresse
d
as
g
ψ
1
γ
μ
(1
−
γ
5
)
ψ
2
ψ
3
γ
μ
(
1
−
γ
5
)
ψ
4
.
H
e
n
ce
i
t
i
st
h
e effect
i
ve
H
a
mil
to
ni
an
H
β
H
=
g
pγ
μ
(
1
−
γ
5
)
n
eγ
μ
(1
−
γ
5
)
ν
e
t
hat governs the beta decay
n
→
p
+
e
−
+
ν
e
.
S
uch a current-current interaction picture actually serves
f
or a low-ener
g
y
a
pproximation o
f
the
S
Mo
f
weak interactions mediated by massive
g
au
ge
bosons
W
±
and
(
or
)
Z
0
(
Weinberg, 1967; Salam, 1968
).
1.1.3 Discoveries o
f
Neutrino
s
Since the beginning of the 1930’s, numerous experiments have been done t
o
s
earch
f
or neutrinos and measure their properties. Be
f
ore the 1950’s, however,
a
ll of the experiments were desi
g
ned to observe the ener
g
y and momentu
m
c
arried away by the neutrino in the beta decay. This kind of kinematic mea-
s
urement was actually realized by detectin
g
the recoil o
f
relevant nuclei an
d
3
Th
e corre
l
ation
b
etween spin an
d
momentum is measure
db
yt
h
e average va
l
ue
o
f
the helicit
y
λ
≡
s
·
p
/
|
p
|
=
±
1
/
2, w
h
ic
h
c
h
an
g
es si
g
nun
d
er a parity inversio
n
and thus must vanish if parity is conserved in a given process
.
1.1 Neutrinos in Nuc
l
ear an
d
Partic
l
eP
h
ysics
5
the emitted electrons
(
Crane and Halpern, 1939
)
. In 1942, Kan Chang Wan
g
proposed a different idea to kinematicall
y
detect neutrinos: since th
e
β
+
-
ra
d
ioactive atom cou
ld
capture a
K
-s
h
e
ll
e
l
ectron rat
h
er t
h
an emit a positron,
the recoil ener
g
y and momentum o
f
the resultin
g
atom would merely depen
d
on the emitted neutrino
(
Wang, 1942
)
. Taking the element
7
B
e for exam
p
le
,
Wang suggeste
d
t
h
at one use t
h
e process
7
B
e
+
e
−
K
→
7
L
i
+
ν
e
+(
1MeV
)
to do the experiment. Such an experiment was soon done b
y
James
A
llen
,
who found that the recoil energy of
7
L
i was well consistent with the ex
p
ecta-
tion from a neutrino emission. So he published the result in a paper entitled
“Experimental Evidence for the Existence of a Neutrino”
(
Allen, 1942
).
However, those indirect hints had never been regarded as a real discover
y
of neutrinos
(
Crane, 1948
)
. As Hans Bethe and Robert Bacher noted, “I
t
s
eems practicall
y
impossible to detect neutrinos in the
f
ree state, i.e., a
f
te
r
they have been emitted by the radioactive atom. There is only one process
w
h
ic
h
neutrinos can certain
l
y cause. T
h
at is t
h
e inverse
b
eta process, con
-
s
istin
g
o
f
the capture o
f
a neutrino by a nucleus to
g
ether with the emissio
n
of an electron
(
or positron
)
”
(
Bethe and Bacher, 1936
)
. Hence a conclusiv
e
experiment to veri
fy
Pauli’s neutrino h
y
pothesis should detect the inverse
beta deca
y
ν
e
+
p
→
n
+
e
+
. In 1952, Cl
y
de Cowan and Frederick Reine
s
realized that a coincidence measurement of the photon signals coming bot
h
f
rom the positron annihilation and
f
rom the neutron capture on cadmium
i
n the liquid scintillator would
g
reatly reduce the back
g
round and provid
e
a
convincing signature of the inverse beta decay. They built a detector near
the nuclear reactor pile in Han
f
ord in 1953, but their experiment was unsuc-
c
essful because it suffered from the intolerable noise induced b
y
cosmic ra
y
s
.
To improve the experiment, Cowan and Reines moved the detector to th
e
S
avannah River reactor and placed it under
g
round to reduce the back
g
roun
d
f
rom cosmic rays. This time they succeeded in observing an unambiguous sig
-
n
ature o
f
the inverse beta decay and demonstrated that its cross section was
c
ompatible with the theoretical prediction
(
Cowan
et al
., 1956
)
4
.
O
n14Jun
e
1
956, Reines and Cowan sent a telegram to Pauli: “We are happy to infor
m
youthatwehavede
fi
nitely detected neutrinos
f
rom
fi
ssion
f
ra
g
ments by ob
-
s
ervin
g
inverse beta decay o
f
protons.
O
bserved cross section a
g
rees well with
expected six times ten to minus forty-four square centimeters”. They receive
d
n
orepl
yf
rom Pauli but learnt later that Pauli and some
f
riends consumed
a
c
ase of champagne in celebration of this good news
(
Reines, 1979
).
I
n 1946, Bruno Pontecorvo suggeste
d
ara
d
ioc
h
emica
l
tec
h
nique to cap
-
ture e
l
ectron neutrinos via t
h
e proces
s
3
7
C
l
+
ν
e
→
3
7
A
r+
e
−
(
Pontecorvo
,
4
N
ote that the theoretical prediction that Cowan and Reines quoted in their
experiment was based on the parity-conservin
gf
ormulation o
f
the beta decay.
G
iven
maximal parity violation discovered in 1957, th
e
V
−
A theory of weak interactions
predicted that the cross section of the inverse beta decay should be twice as large
as that reported previousl
y
.
C
owan and Reines redid their experiment and arrived
at the correct result in 1960 (Reines
e
ta
l.
,
1960).