Xing Zh., Zhou Sh. Neutrinos in Particle Physics, Astronomy and Cosmology
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6 1 Neutrinos: Past, Present an
d
Futur
e
1
946
)
. The cross section of this reaction was precisely computable and its
ener
g
y threshol
d
E
(
ν
e
)
0
.
814 MeV was low enou
g
h to make the mea
-
s
urement sensitive to so
l
ar
8
B
neutrinos. It was John Bahcall who carefully
c
alculated the
fl
ux o
f
solar neutrinos and the capture rate o
f
8
Bneutrinos
,
d
emonstrating that Pontecorvo’s idea was experimentally feasible
(
Bahcall
,
1
964
)
. In the middle of 1960’s, Raymond Davis and his team built a 1
0
5
-ga
ll
o
n
Chlorine-
A
r
g
on neutrino detector in the Homestake Gold Mine to detect so
-
l
ar neutrinos
(
Davis, 1964
)
. The final result of their experiment came out i
n
1968
: the measured flux of solar
8
B neutrinos was only about one third of
the value predicted by the standard solar model
(
SSM
)(
Davis
et al
.
, 1968
;
Bahcall and Shaviv, 1968
)
. This was just the famous solar neutrino problem,
which was actually caused by the
fl
avor conversion o
f
solar
ν
e
neut
rin
os o
n
their wa
yf
rom the core o
f
the
S
un to the detector on the Earth. Davis re-
c
eived the Nobel Prize in Physics in 2002, at the age of 88, for his discover
y
of so
l
a
rn
eut
rin
os a
n
dt
h
e
ir
defic
i
t.
I
n the 1960’s, another burnin
g
question was whether the neutrinos emit
-
ted from the primary decay modes o
f
π
±
m
esonswerethesameasthosefro
m
the beta decay. I
f
they were the same particles, the branchin
g
ratio o
f
th
e
l
epton-flavor-violatin
g
deca
y
μ
→
e
+
γ
w
ould be of
O
(
1
0
−
5
)
, several orders of
m
agnitude larger than the experimental upper bound
(
Lee and Yang, 1960
)
.
I
f
there were onl
y
one neutrino species, electrons and muons would be equall
y
p
roduced from the collision between a neutrino beam of several GeV and a
n
ucleon. The situation was clarified by Leon Lederman, Melvin Schwartz and
J
ack
S
teinber
g
er, who did the
fi
rst hi
g
h-ener
g
y accelerator neutrino experi-
m
ent at the Brookhaven National
A
ccelerator Laborator
y
in 1962. In their
experiment t
h
ec
h
arge
d
pions were pro
d
uce
db
y
b
om
b
ar
d
ing t
h
emeta
lb
ery
l
-
l
ium tar
g
et with protons, while the muons emitted
f
rom the decayin
g
pions
were stopped by ionization loss in the shield. The events of single muon track
i
n the spark chamber were observed, providin
g
the robust evidence
f
or the
e
xi
ste
n
ce of t
h
e
m
uo
nn
eut
rin
o
ν
μ
(
Danby
et al.
, 1962
)
. The tau neutrin
o
ν
τ
was naturally expected to exist, after the tau lepton was discovered and th
e
m
issin
g
ener
g
y
f
rom its decay was observed by Martin Perl and his team i
n
1
975
(
Perl
et al
., 1975
)
.Butthe
ν
τ
-
induced interactions were not directl
y
observed until the end of 2000 at the Fermilab
(
Kodama
e
ta
l.
,
2001
)
.A
picture of three lepton families, including three charged leptons
(
e
,
μ
,
τ
)
and
three neutrinos
(
ν
e
,ν
μ
,ν
τ
)
, was therefore completed in the SM
.
1.2 Neutrinos in
A
stronomy and Cosmolog
y
N
eutrinos were made in astonishin
g
numbers at the time o
f
the Bi
g
Ban
g
an
d
took part in the evolution of the Universe from its very beginning. Neutrino
s
c
an also be produced in sta
gg
erin
g
numbers
f
rom nuclear burnin
g
o
f
stars,
violent ex
p
losions o
f
su
p
ernovae, interactions between the cosmic microwav
e
background
(
CMB
)
radiation and ultrahigh-energy cosmic rays, annihilation
1.2 Neutrinos in Astronomy and Cosmology 7
o
f
dark matter, and a variety o
f
distant astrophysical sources such as
g
amma
ray bursts and active
g
alactic nuclei. Only the neutrinos emitted from the
Sun and Supernova 1987A have been observed. Hence neutrino astronomy
i
s still very much in its in
f
ancy, so is neutrino cosmolo
g
y. We shall
g
ive a
s
hort account of astroph
y
sical neutrinos in this section. Detailed discussions
a
bout hot and important topics of neutrino astronomy and cosmology wil
l
be presented in the second part o
f
this book,
f
rom
C
hapter 6 to
C
hapter 11
.
1.2.1 Neutrinos
f
rom Stars and Supernova
e
In t
h
e 1930
’
s, it was unc
l
ear w
h
et
h
er neutrinos
h
a
d
somet
h
ing to
d
owit
h
w
h
y
the
S
un was shinin
g
. Bethe did not include neutrinos into solar nuclear
f
usion
c
hains when he published his seminal paper on the ener
g
y production in star
s
i
n 1939
(
Bethe, 1939
)
. One year later, George Gamow and Mario Sch¨onber
g
pointed out that neutrinos would take away a certain part o
f
stellar ener
g
ie
s
a
nd their role was particularl
y
important in a collapsed star because of the
h
igh temperature and density in its interior
(
Gamow and Sch¨onberg, 1940,
1
941
)
. Today we know that solar neutrinos take away a few percent of th
e
total energy of the Sun.
A
nother example is the Supernova 1987
A
explosion,
i
n which about 99
%
of the energy was taken away by neutrinos
.
T
he
S
un shines as a result o
f
nuclear
f
usion in its core. The
pp
a
nd
C
N
O
chains of hydrogen fusion in the Sun can be expressed as 4
p
4
+2
e
−
→
4
He
+
2
ν
e
+
(
2
6
.
7
MeV
)
,soabout98
%
of the energy radiates in the form of ligh
t
a
nd only 2% of the ener
g
y is taken away by neutrinos. Soon after the
V
−
A
theory of weak interactions emerged in 1958, Pontecorvo realized that th
e
bremsstrahlun
g
radiation o
f
neutrinos
f
rom the
S
un was also possible to take
place
(
Pontecorvo, 1959
)
. But the energy of this kind of solar neutrinos must
be very low because it is subject to the Sun’s temperature
(
T
TT
∼
1
0
7
K
∼
1
keV
)
. In comparison, those neutrinos emitted from nuclear reactions insid
e
the Sun are more ener
g
etic and their typical ener
g
ies are o
f
O
(
1
)
MeV.
S
olar neutrinos were first observed by Davis in Homestake — the firs
t
ra
d
ioc
h
emica
l
experiment w
h
ic
h
was sensitive to so
l
ar
8
B
neutrinos
(
Davis
et al
.
,
1968
)
. The subsequent radiochemical experiments, GALLEX
/
GNO i
n
Gran Sasso
(
Hampel
et al
.
,
1999; Altmann
,
et al.
, 2005
)
andSAGEinBaksan
(
Abdurashito
v
et al.
,
2002
)
, employed the reaction
7
1
G
a
+
ν
e
→
7
1
G
e
+
e
−
to detect solar neutrinos. The energy threshold of this reaction is as low as
E
(
ν
e
)
0
.
233 MeV, and hence more than half of the
ν
e
-
in
duced eve
n
ts
in
the GALLEX
/
GNO or SAGE experiment are attributed to sola
r
pp
neut
r
i
n
os
emitted from the nuclear reaction
p
+
p
→
D
+
e
+
+
ν
e
inside the Sun. Th
e
n
eutrino
fl
ux measured in either o
f
these two
g
allium experiments was onl
y
a
bout one hal
f
o
f
that predicted by the
SS
M, implyin
g
that the solar neutrin
o
a
nomaly revealed by the Homestake experiment might be a real proble
m
i
ndependent o
f
the uncertainties o
f
the
SS
M itsel
f
.
S
uch an anomaly was also
observed in the Kamiokande and Super-Kamiokande
(
SK
)
experiments wit
h
the hel
p
of water Cherenkov detectors, where sola
r
8
Bneutrinos
(
emitted
8 1 Neutrinos: Past, Present an
d
Futur
e
f
rom the deca
y
8
B
→
8
B
e
+
e
+
+
ν
e
)
an
d
h
e
p
n
eutrinos
(
emitted from th
e
react
i
on
3
He
+
p
→
4
He
+
e
+
+
ν
e
)
were measured via the elastic neutrino
-
e
l
ectron scattering proces
s
ν
e
+
e
−
→
ν
e
+
e
−
(
Fukud
a
et a
l
.
,
1996
;
Fu
k
u
d
a
et
al.
,
2001
)
. The simplest solution to this solar neutrino problem was based on
the assum
p
tion that sola
r
ν
e
neutrinos mi
g
ht have converted into other type
s
o
fn
eut
rin
os w
hi
c
h
we
r
eu
n
detectab
l
e
in
t
h
e detecto
r
s
l
ocated o
n
t
h
e
E
a
r
th
(
Wolfenstein, 1978; Mikheyev and Smirnov, 1986
)
. A decisive experiment wa
s
d
one in 2001 at the Sudbury Neutrino Observatory
(
SNO
)
,wheresola
r
8
B
n
eutrinos were
d
etecte
d
via t
h
ec
h
arge
d
-current process
ν
e
+
D
→
p
+
p
+
e
−
,
t
h
eneutra
l
-current proces
s
ν
α
+D
→
p
+
n
+
ν
α
an
d
t
h
ee
l
astic scatterin
g
p
r
ocess
ν
α
+
e
−
→
ν
α
+
e
−
for
α
=
e
,
μ
an
d
τ
(
Ahmad et al
.
,
2001
)
. The tota
l
n
eutrino
fl
ux measured in the
S
N
O
experiment was in a
g
reement with tha
t
predicted b
y
the
SS
M. Furthermore, the
S
N
O
experiment con
fi
rmed the
SK
result and gave very convincing evidence for
ν
e
→
ν
μ
a
nd ν
e
→
ν
τ
transitions.
These important results point to solar neutrino oscillations. The theory o
f
n
eutrino oscillations will be described in
C
ha
p
ter 5, and the
p
ro
p
erties o
f
s
tellar neutrinos will be discussed in Chapter 6
.
T
he observation of neutrinos arisin
g
from the Supernova 1987
A
explosio
n
was another milestone in neutrino astronom
y
.
A
t 07:35:41 UT on 23 Februar
y
1
987, the burst of neutrinos from a supernova explosion in the Large Mag-
ellanic
C
loud at a distance o
f
about 50 kpc was recorded b
y
three neutrino
telescopes on the Earth: Kamiokande-II led b
y
Masatoshi Koshiba in Japa
n
(
Hirata
et al
.
,
1987
)
, IMB in the United States
(
Biont
a
et al.
,
1987
)
an
d
Baksan in Russia
(
Aleksee
v
et al.
, 1987
)
. This burst lasted less than 13 sec
-
onds. Totall
y
24 events of electron antineutrinos were detected in the above
observatories
(
11 at Kamiokande-II, 8 at IMB and 5 at Baksan
)
,andtheir
a
vera
g
eener
g
y was around 10 MeV.
A
bout 2.5 hours later, the visible li
g
ht
emitted from this su
p
ernova ex
p
losion reached the Southern Hemis
p
here an
d
was observed by three independent groups
(
Arnet
t
et al.
, 1989
)
. Koshiba wo
n
the Nobel Prize in Ph
y
sics in 2002
f
or his detection o
f
supernova neutrinos.
T
he
p
icture of a su
p
ernova ex
p
losion and the burst of su
p
ernova neutrino
s
c
an be sketched as follows
(
Bethe and Wilson, 1985; Bethe, 1990
)
:
(
a
)
whe
n
theironcoreo
f
a star reaches the
C
handrasekhar mass limit, the
g
ravitationa
l
c
ollapse occurs;
(
b
)
after the inner core exceeds the nuclear density, the in
-
f
alling outer core bounces and a shock forms;
(
c
)
the shock wave propagates
outward and loses energies by disintegrating the Fe nuclei;
(
d
)
the inner cor
e
becomes a protoneutron star by releasing the gravitational binding energy o
f
O
(
10
53
)
erg in the form of neutrinos;
(
e
)
neutrinos exchange energies wit
h
m
atter via the reactions
ν
e
+
n
p
+
e
−
an
d
ν
e
+
p
n
+
e
+
;and
(
f
)
the shock receives energies from these processes and revives to make the fi-
n
al explosion.
A
lthou
g
h only the Supernova 1987
A
neutrinos were observed,
they have greatly improved our understanding of the stellar evolution and
exp
l
osion mec
h
anisms. T
h
is o
b
servation
h
as a
l
so
b
een use
d
to constrain neu
-
trino masses, lifetimes and magnetic dipole moments
(
Raffelt, 1996, 1999
)
.
1.2 Neutrinos in Astronomy and Cosmology 9
It is there
f
ore important to stud
y
supernova neutrinos so as to probe the
dy
namics of stars and supernovae and to learn about the intrinsic propertie
s
of neutrinos themselves. We shall elaborate these points in Chapter 7
.
1.2.2 Hi
g
h-ener
g
y Cosmic Neutrinos
The study o
f
hi
g
h-ener
g
y cosmic neutrinos is well motivated because thei
r
s
ources must be associated with the astrophysical sources of high-energy o
r
u
ltrahigh-energy cosmic rays
(
Gaisser, 1991; Stanev, 2004
)
. It has been foun
d
that the most ener
g
etic cosmic ray particles can have kinetic ener
g
ies up t
o
10
21
eV, but where and how they are accelerated remain unknown. Neutrinos
a
re expected to play an important role in searchin
gf
or cosmic accelerators
f
o
r
two simple reasons:
(
a
)
they are electrically neutral and thus their trajectories
c
annot be bent by interstellar magnetic fields;
(
b
)
they do not interact with
the
C
MB and hence they can travel very lon
g
distances,
f
rom some distan
t
a
strophysical sources to the Earth. So hi
g
h-ener
g
y cosmic neutrinos shoul
d
be a unique cosmic messenger complementary to photons and protons. If
there exists an astroph
y
sical ob
j
ect responsible
f
or the production o
f
bot
h
c
osmic ra
y
s and neutrinos, then a successful measurement of the neutrinos
(
e.g., their direction, energy and flavor distribution
)
will allow us to prob
e
w
h
ere t
h
is astrop
hy
sica
l
source is
l
ocate
d
an
dh
ow it acce
l
erates cosmic ra
y
s.
T
here are a number of possible candidates for the sources of high-energ
y
c
osmic neutrinos, inc
l
u
d
ing active ga
l
actic nuc
l
ei, gamma ray
b
ursts an
d
su
-
pernova remnants
(
Halzen and Hooper, 2002
)
. In such a violent astrophysica
l
s
ource protons are likely to be accelerated to extremely high energies, lead
-
i
ng to high-energy proton-proton
(
pp
)
and proton-photon
(
pγ
)
collisions fro
m
which vast quantities o
f
pions and kaons can be produced. Hi
g
h-ener
g
yneu-
trinos can subsequently be produced from the primary and secondary decay
s
of
π
±
a
n
d
K
±
m
esons. Another possible source of hi
g
h-ener
g
y cosmic neutri
-
n
os is related to the so-called Greisen-Zatsepin-Kuzmin
(
GZK
)
cutoff in th
e
energy spectrum of cosmic rays. Given the existence of the CMB, the cosmic
rays wit
h
ener
g
ies
h
i
gh
er t
h
a
n
E
th
E
E
=5
×
10
19
eV
wou
ld
interact wit
h
t
he
back
g
round photons via the
Δ
-r
eso
n
a
n
ce p
r
ocess
p
+
γ
C
M
B
→
Δ
+
→
p
+
π
0
or
n
+
π
+
.T
h
is imp
l
ies t
h
at t
h
e extraga
l
actic cosmic rays wit
h
E
E
th
EE
sh
ou
ld
n
ot travel more than 50 Mpc and thus never reach the Earth
(
Greisen, 1966;
Zatsepin and Kuzmin, 1966
)
. Some recent observational data have indicated
that the GZK cutoff seems to exist
(
Abbas
i
et al
.
,
2008; Abraha
m
et al
.
,
2
008
)
. If such a cutoff is finally verified, it will be a “guaranteed” source o
f
u
ltrahigh-energy cosmic neutrinos since neutrons and
π
+
mesons generated
f
r
o
m
t
h
e
Δ
+
decays will definitely produce neutrinos and antineutrinos in
their subsequent deca
y
s.
T
he events of high-energy cosmic neutrinos are as rare as those of high
-
ener
g
y cosmic rays, an
dh
ence t
h
ey can on
l
y
b
e
d
etecte
db
yusin
g
extraor
d
i
-
n
arily lar
g
e neutrino detectors — the so-called neutrino telescopes. In a
g
ive
n
1
0 1 Neutrinos: Past, Present an
d
Futur
e
telescope the neutrino
fl
ux is identi
fi
ed by detectin
g
its char
g
ed-current in
-
teractions with nuclei
(
i.e.,
ν
α
+
N
→
l
−
α
+
N
an
d
ν
α
+
N
→
l
+
α
+
N
r
eact
i
o
n
sfor
α
=
e
,
μ
,τ
)
. The produced charged leptons move in the detector
m
edium so rapidly that they can emit visible Cherenkov li
g
ht.
A
noptica
l
Cherenkov neutrino telescope must satisfy the following conditions:
(
a
)
larg
e
enou
g
hthatsomeo
f
the rare
g
alactic or extra
g
alactic neutrinos can interac
t
a
stheypassby;
(
b
)
transparent enough to allow light to travel through
a
widely-spaced array of optical sensors;
(
c
)
dark enough to avoid the inter-
f
erence of natural light; and
(
d
)
deep enough below the Earth’s surface to
a
void the contamination from cosmic ra
y
s. Onl
y
dark lakes or oceans an
d
d
eep fields of ice meet all these requirements. The k
m
3
-
sca
l
eneutrinote
l
e
-
s
cope IceCube is now under construction at the South Pole
(
Ahrens
et al
.
,
2
003
)
and its possible counterpart in the Mediterranean Sea, KM3NeT, ha
s
been proposed
(
Car
r
et al
.
,
2007
)
. Such a neutrino telescope is expected t
o
b
e most sensitive to
h
i
gh
-ener
g
ymuonneutrinos,simp
l
y
b
ecause t
h
emuo
n
c
an have a long and clear track in the detector to assure excellent energy an
d
d
irection resolutions. Needless to say, a measurement of the flavor distribu
-
tion o
f
hi
g
h-ener
g
y cosmic neutrinos
f
rom a distant astrophysical source wil
l
be very helpful to probe the production mechanism of cosmic rays and to
examine the intrinsic properties o
f
massive neutrinos
.
Hi
g
h-ener
g
y cosmic neutrinos mi
g
ht also come
f
rom the annihilation o
f
d
ark matter. In addition, the origin of high-energy cosmic neutrinos might be
a
ssociated with the production o
f
hi
g
h-ener
g
y photons and even
g
ravitational
waves at an astroph
y
sical source. Such topics will be discussed in Chapter 8
.
1.2.3 Cosmic Neutrino Back
g
round
One of the greatest discoveries in the history of cosmology was Edwin Hub
-
ble’s observation that
g
alaxies were recedin
gf
rom each other at velocities
proportional to their distances
(
Hubble, 1929
)
. This observation, which wa
s
c
onsistent with Albert Einstein’s prediction for the relationship between ve-
l
ocities and distances
(
Einstein, 1915
)
, strongly indicated that the Universe
was expandin
g
and its dynamics could be correctly described by
g
eneral rel
-
a
tivity. Starting from the present-day data and allowing the equations o
f
g
eneral relativity to run backwards in time, one may immediately in
f
er that
the Universe should become increasingly hotter and denser until the Big
Bang
(
i.e., the initial singularity or a state of infinite density and temper-
a
ture
)
is finally encountered
(
Lemaitre, 1931
)
. One can then run the clock
f
orward from the Big Bang and construct a time line which orders the evolu-
tion o
f
the Universe.
S
ome important events in the evolution o
f
the Universe
i
nclude cosmolo
g
ical in
fl
ation, quark-baryon transition, Bi
g
Ban
g
nucleosyn-
thesis
(
BBN
)
, recombination, large-scale structure formation, and so on.
I
nt
h
eear
l
yUniverset
h
eener
g
y
d
ensity was
d
ominate
db
yre
l
ativisti
c
l
eptons, quarks and
g
au
g
e bosons. Within a
f
ew microseconds, the quarks
were confined to form
p
rotons and neutrons. Within about one second, soon
1.3 Knowledge and
Q
uestions on Neutrinos 1
1
af
ter neutrinos lose their contact with the thermal bath and decoupled
f
rom
the rest of matter, the synthesis of primordial nuclei
(
e.g., D
,
3
H
e
,
4
He an
d
7
Li
)
began
(
Alpher
e
ta
l
.
,
1948
)
. The BBN was completed when the Uni
-
verse was about several minutes old, but the Universe itsel
f
remained to
o
h
ot for nuclei to ca
p
ture electrons and form neutral atoms. The e
p
och o
f
recom
b
ination arrive
d
a
b
out
3
×
10
5
y
ears after the Big Bang, when the ex-
pandin
g
Universe cooled to a temperature o
f
0.3 eV, allowin
g
electrons an
d
protons to combine to form neutral hydrogen atoms. This epoch marked th
e
d
ecoupling of matter and electromagnetic radiation. The relic photons finally
became the
C
MB o
f
the Universe,
j
ust like the relic neutrinos which
f
orme
d
the cosmic neutrino background
(C
ν
B)
of the Universe. In 1965, Arno Pen
-
zias and Robert Wilson succeeded in detectin
g
the existence o
f
the
C
M
B
(
Penzias and Wilson, 1965
)
. Their great discovery offered a strong suppor
t
to the model of hot Big Bang proposed by Alpher, Bethe and Gamow i
n
1
948. The avera
g
e temperature o
f
the
C
MB has been measured to an un
-
precedented accurac
y
:
T
γ
T
T
=
(2
.
72
5
±
0
.
0
01
)
K, and its spectrum fits the
blackbody radiation formula very well. The average temperature of the
C
ν
B
i
spre
d
icte
d
to
be
T
ν
TT
=
(
4
/
1
1
)
1
/
3
T
γ
TT
=
(1
.
945
±
0
.
001
)
K in the hot Bi
g
Ban
g
model, implyin
g
that the kinetic ener
g
y of relic neutrinos is only about
E
ν
∼
1
.
6
×
10
−
4
e
V
. How to detect the
C
ν
B
turns out to
b
ea
b
ig c
h
a
ll
enge
i
n modern neutrino astronomy because the cross section o
f
such a low-ener
gy
n
eutrino flux interactin
g
with matter within a detector is too small, charac-
terized by
(
G
F
E
ν
)
2
∼
1
.
4
×
10
−
63
c
m
2
.
T
he number densit
y
o
f
relic neutrinos can be computed with the Fermi
-
D
irac statistics at their present-day average temperature. It is found tha
t
t
h
ere are tota
ll
ya
b
out 336 neutrinos an
d
antineutrinos per cu
b
ic centimeter
i
nt
h
e Universe; i.e.,
n
ν
α
≈
n
ν
α
≈
56
cm
−
3
for
α
=
e
,
μ
a
n
d
τ
. In comparison
,
the cosmic background photons are slightly more numerous and their number
d
ensity is a
b
out
n
γ
≈
4
11
cm
−
3
.
R
elic neutrinos are there
f
ore the second
m
ost abundant particles in the Universe
(
Dondelson, 2003; Weinberg, 2008
).
They must contribute to the total energy density of the Universe, whic
h
g
overns how the Universe evolves. The species o
f
neutrinos must have a
ff
ected
the primordial abundances o
f
li
g
ht elements durin
g
the BBN. In addition,
the existence of the
C
ν
B
canhaveanim
p
act on the evolution of the CMB
a
nisotropy and the
g
rowth o
f
matter perturbations. We shall spell out the
c
rucial roles of neutrinos pla
y
ed in the evolution of the Universe, such as the
BBN and the structure formation, in Chapter 9 and Chapter 10
.
1.3 Knowled
g
eand
Q
uestions on Neutrinos
N
eutrinos are very elusive. A neutrino is by Pauli’s definition an electrically
n
eutral and extremely light particle of spin 1
/
2. This section will first out-
l
ine some
f
undamental knowled
g
eo
f
neutrinos that we have accumulated i
n
the past eight decades, and then list some important open questions abou
t
1
2 1 Neutrinos: Past, Present an
d
Futur
e
the properties o
f
massive neutrinos and their unique roles in the micro- and
m
acro-worlds. The prospects of neutrino ph
y
sics, neutrino astronom
y
an
d
n
eutrino cosmo
l
ogy re
l
yont
h
eextenttow
h
ic
h
t
h
ose questions wi
ll b
ean
-
s
were
d
,an
d
on new
d
iscoveries an
d
surprises on t
h
eroa
d
a
h
ea
d.
1.3.1 Present Knowled
g
eonNeutr
i
no
s
There are three neutrino species
(
ν
e
,
ν
μ
,
ν
τ
)
, consistent with the existence
of three families of charged leptons
(
e
,
μ
,
τ
)
,
Q
=+
2
/
3
quarks
(
u
,
c
,
t
)
an
d
Q
=
−
1
/
3quarks
(
d
,
s
,
b
)
. The invisible decay width of the gauge boso
n
Z
0
m
easure
d
in t
h
e LEP experiment provi
d
es t
h
e most stringent constrain
t
on the number o
f
neutrino species
:
N
ν
NN
=
2
.
984
±
0
.
0
08
(
Nakamur
a
et al
.
,
2
010
)
, which is in excellent agreement with the SM expectatio
n
N
ν
NN
=
3.
N
ote that this constraint is only valid for the active neutrinos that take
part in t
h
estan
d
ar
d
wea
k
interactions an
dh
ave masses
b
e
l
ow
M
Z
M
0
/
2
≈
45
.
6 GeV. Moreover
,
the observational data on the BBN and CMB set th
e
f
ollowing consistent but looser bounds on the number of neutrino species
:
N
ν
N
N
=3
.
14
+
0
.
70
−
0
.
65
(
BBN
)
at the 68
%
confidence level
(
Cybur
t
et al.
,
2005
)
and
N
ν
N
N
=4
.
4
±
1.5
(
CMB
)
at the same confidence level
(
Komatsu et al., 2009
)
.
Neutrinos and antineutrinos are electrically neutral fermions of spin 1
/
2;
a
nd they have left
(
λ
=
−
1
/
2)
and right
(
λ
=
+1
/
2)
helicities, respectively.
Given the electric charge conservation as a fundamental law, one may ex
-
perimentally constrain the electric char
g
eo
f
an electron antineutrino to be
e
ν
<
3
×
10
−
21
e
i
n the beta deca
y
thanks to the precision measurements o
f
the electric charges of electrons, protons and neutrons
(
Ignatiev and Joshi,
1
995
)
. The astrophysical bounds on the electric charges of neutrinos, such as
t
h
eo
n
e
e
ν
<
2
×
10
−
14
e
o
btained
f
rom the observational data on the
g
lob
-
u
lar clusters
(
Raffelt, 1999
)
, are much looser but they also point t
o
e
ν
=
0
.
G
iven the an
g
ular momentum conservation as a
f
undamental law, one may
c
onsider
π
+
→
μ
+
+
ν
μ
,
π
+
→
e
+
+
ν
e
and other weak
p
rocesses to in-
f
er that neutrinos must have spin 1
/
2. In the orbital-electron capture re
-
action
152
63
E
u+
e
−
→
152
62
S
m
∗
+
ν
e
an
d
t
h
e
d
eca
y
mo
d
e
π
−
→
μ
−
+
ν
μ
,
f
or example, the helicit
y
of the electron neutrino and that of the muon an-
tineutrino were found to be left
(
Goldhabe
r
et a
l.
,
1958
)
and right
(
Bardon
et al.
, 1961
)
, respectively. The ALEPH Collaboration measured the deca
y
m
ode
τ
−
→
l
−
α
+
ν
α
+
ν
τ
(
fo
r
α
=
e
or
μ
)
and determined the helicity of
the tau
n
eut
rin
otobe
λ
=
−
0
.
496
±
0
.
0
06
(
Heiste
r
et al
., 2001
)
, consistent
with the
S
M expectation
λ
=
−
1
/
2.
A
ll the available experiments indicat
e
that neutrinos are essentiall
y
left-handed while antineutrinos are essentiall
y
rig
h
t-
h
an
d
e
d
,event
h
oug
h
t
h
eir rest masses may not
b
eexact
l
yvanis
h
ing.
Neutrinos are actuall
y
massive but their rest masses are ver
y
tin
y
,a
t
m
ost of
O
(
1
)
eV. Since 1998, the phenomena of neutrino oscillations hav
e
c
onvincin
gl
y
b
een o
b
serve
d
in atmosp
h
eric, so
l
ar, reactor an
d
acce
l
erato
r
n
eutrino experiments
(
Nakamura
et al.
, 2010
)
. The discovery of neutrino os-
c
illations marks a great breakthrough in particle physics, because it implies
1.3 Knowledge and
Q
uestions on Neutrinos 1
3
that neutrinos have rest masses and the
S
M itsel
f
is incomplete.
C
urren
t
experimental data have revealed the ma
g
nitudes of two independent neu
-
trino mass-squared differences
:
Δ
m
2
2
1
≡
m
2
2
−
m
2
1
∼
7
.
7
×
10
−
5
eV
2
a
n
d
Δ
m
2
32
≡
m
2
3
−
m
2
2
=
±
2
.
4
×
10
−
3
eV
2
.H
e
n
ce at least two
n
eut
rin
os
m
ust be
m
assive and at least one neutrino mass must be lar
g
er tha
n
|
Δ
m
2
32
|∼
0
.
04
9
e
V
. But the absolute scale of neutrino masses cannot be determined fro
m
n
eutrino oscillations. The kinematic measurements o
f
the tritium beta deca
y
3
H
→
3
He
+
e
−
+
ν
e
and the pion and tau deca
y
shave
y
ielded some up-
per bounds on the effective masses of three neutrinos, but they are loose
r
than those obtained from the neutrinoless double-beta
(
0
ν
2
β
)
decay and th
e
c
osmological constraints
(
Fogl
i
e
tal., 2008
)
. One may conservatively expect
t
h
at t
h
eabso
l
ute
n
eut
rin
o
m
ass sca
l
es
h
ou
l
dbeof
O
(
1
)
eV or smaller
.
T
he neutrino mass eigenstates
(
ν
1
,
ν
2
,
ν
3
)
do not match the neutrin
o
flavor eigenstates
(
ν
e
,
ν
μ
,
ν
τ
)
, leading to the phenomenon of neutrino flavo
r
m
ixin
g
which is exactly analo
g
ous to that o
f
quark
fl
avor mixin
g
.Inthe
basis where the mass ei
g
enstates o
f
three char
g
ed leptons are identi
fi
ed with
their flavor eigenstates, the mismatch between mass and flavor eigenstate
s
o
f
three neutrinos can be described b
y
a
3
×
3un
i
tar
y
matr
i
x
V
—
the
s
o-called Maki-Nakagawa-Sakata
(
MNS
)
matrix
(
Mak
i
e
tal., 1962
)
or th
e
MNS-Pontecorvo matrix
(
Pontecorvo, 1968
)
, which is usually parametrized
i
n terms of three mixing angles
(
θ
1
2
,
θ
1
3
,
θ
23
)
and three CP-violating phase
s
(
δ
,
ρ
,
σ
)
. A global analysis of current neutrino oscillation data yields
θ
12
≈
34
◦
,
θ
2
3
≈
45
◦
a
n
d
θ
1
3
<
10
◦
(
Fogl
i
et al.
, 2008; Schwetz
et al
.
,
2008
)
,bu
t
three
C
P-violatin
g
phases are entirely unrestricted due to the lack o
f
relevant
ex
p
erimental information. The fact that
θ
12
an
d
θ
23
a
re remarkably large
r
than the largest quark mixing angle
(
i.e., the Cabibbo angle
ϑ
C
≈
13
◦
)
is
a
nintri
g
uin
g
puzzle, implyin
g
an intrinsic di
ff
erence between the ori
g
in o
f
l
epton flavor mixing and that of quark flavor mixing
.
Neutrinos ta
k
e part in
b
ot
h
neutra
l
-an
d
c
h
ar
g
e
d
-current wea
k
interac-
tions. The available experimental results
f
or neutrino-electron scatterin
g,
n
eutrino-nucleus scattering and quasi-elastic or inelastic neutrino-nucleo
n
s
catterin
g
are all consistent with the
S
M. Hence the
S
M remains to be th
e
s
tandard theor
y
o
f
neutrino interactions even a
f
ter neutrino oscillations have
been discovered, and it is the guiding principle of various man-made exper-
i
ments to pro
d
uce an
dd
etect neutrinos. Up to now so
l
ar neutrinos, atmo
-
sp
heric neutrinos and Su
p
ernova 1987
A
neutrinos have been observed, thank
s
to the rapid development of detector techniques, so have geoneutrino
s
5
.
T
h
e
technolo
g
yo
f
producin
g
low- and hi
g
h-ener
g
yneutrinos
f
rom reactors and
a
ccelerators has been very mature, too. We can therefore foresee a bri
g
ht fu
-
ture in experimental neutrino physics and astronomy, which will finally hel
p
brin
g
the true theory o
f
massive neutrinos to li
g
ht
.
5
G
eoneutrinos are the low-energy neutrinos created in the decays of radioactive
isotopes inside the Earth. The
y
have been detected in the KamL
A
ND and Borexino
experiments (Araki
e
ta
l
.
,
2005; Bellini et a
l.
, 2010)
.
1
4 1 Neutrinos: Past, Present an
d
Futur
e
1.3.2
O
pen
Q
uestions on Neutrinos
A
lthou
g
h we have known quite a lot about elusive neutrinos, as briefly sum-
m
arized in Section 1.3.1, we have many open questions about their intrinsic
properties and their unique roles in the Universe. The
f
ollowin
g
is a partia
l
l
ist of some immediate and important questions in neutrino ph
y
sics, neutrino
a
stronomy an
d
neutrino cosmo
l
ogy.
Question 1: are massive neutrinos the Dirac or Ma
j
orana particles
?
If
m
assive neutrinos are the Dirac particles, just like the charged leptons an
d
q
uarks, then they must be distinguishable from their antiparticles because
o
f
lepton number conservation. B
y
de
fi
nition, a Ma
j
orana neutrino is it
s
own antiparticle
(
Majorana, 1937; Case, 1957
)
. Hence the weak processes
m
e
d
iate
db
y massive Majorana neutrinos can
b
e
l
epton-num
b
er-vio
l
ating
.
A
t present the onl
y
feasible wa
y
to identif
y
the Ma
j
orana nature of three
known neutrinos is to observe the
0
ν
2
β
decays of some even-even nuclei
(
i.e.
,
N
(
A
,
Z
)
→
N
(
A
,
Z
+2
)
+2
e
−
decays
)
, which can naturally take place via the
exchan
g
eo
f
virtual Majorana neutrinos between two associated beta decays
(
Xing, 2004
)
. No convincing evidence for an occurrence of the 0
ν
2
β
deca
y
h
as so
f
ar been established, althou
g
h most theorists believe that massiv
e
n
eutrinos should be the Majorana particles and the ori
g
in of their masse
s
m
ust be different from that of charged-fermion masses
.
Question 2: what is the absolute neutrino mass scale
?
The
r
ea
r
eth
r
ee
f
easible wa
y
s to probe the absolute mass scale of three known neutrinos
.
The KATRIN experiment is the most promising next-generation direct-mass-
s
earch experiment. Its sensitivit
y
to the e
ff
ective mass o
f
the tritium
β
-d
eca
y
m
e
≡
m
2
1
|
V
e
VV
1
|
2
+
m
2
2
|
V
e
VV
2
|
2
+
m
2
3
|
V
e
VV
3
|
2
ma
y
hopefull
y
reac
h
∼
0
.
2e
V
(
Bornschei
n
et al.
, 2003
)
. If massive neutrinos are the Majorana particles
,
i
tisa
l
so possi
bl
e to constrain t
h
eir masses
b
yo
b
servin
g
t
h
e
0
ν
2
β
d
eca
y
an
d
d
etermining its effective mas
s
m
ee
≡|
m
1
V
2
e
VV
1
+
m
2
V
2
e
V
V
2
+
m
3
V
2
e
VV
3
|
.
The
p
resen
t
0
ν
2
β
e
xperiments are sensitive to
m
ee
o
f
O
(
0
.
1)
eV, while the future 0
ν
2
β
experiments are likely to have sensitivities in the meV range
(
Avignone II
I
et al., 2008
)
. In addition, one may obtain useful information on the abso
-
l
ute neutrino mass scale from cosmolo
g
y or astrophysics. A
g
lobal analysis
o
f
current cosmolo
g
ical data has provided us with a very strin
g
ent upper
bound on the sum of light neutrino masses, whose magnitude is typically o
f
O
(0
.
1
)
eV t
o
O
(
1
)
eV, but its explicit value depends on what assumptions
a
re made and which data are used
(
Seljak
et al.
,
2006; Kayser, 2008
)
. Not
e
that the sign of
Δ
m
2
32
has not been determined from the present neutrin
o
osci
ll
ation experiments, imp
l
yin
g
t
h
at t
h
e neutrino mass spectrum can
be
eithe
r
m
3
>
m
2
>m
1
(
normal hierarchy
)
or
m
2
>
m
1
>
m
3
(
inverted hi-
erarchy
)
. The upcoming long-baseline neutrino experiments and the future
n
eutrino
f
actor
y
or superbeam
f
acilities will be able to pin down the neutrino
m
ass hierarchy
(
Bandyopadhyay
e
tal
.
,
2009
)
.
Question 3: how small is the neutrino mixing angl
e
θ
13
?
Wh
et
h
er t
h
e
s
ma
ll
est neutrino mixin
g
an
gl
e
θ
1
3
i
s exactly vanishin
g
or not is o
fg
rea
t
1.3 Knowledge and
Q
uestions on Neutrinos 1
5
i
mportance in understandin
g
the dynamics o
f
lepton
fl
avor mixin
g
. While
θ
13
=0mi
g
ht result from a certain flavor symmetry, it is in
g
eneral unstable
d
ue to the flavor symmetry breaking or radiative corrections. The value o
f
θ
1
3
,
a
f
ter it is measured, ma
y
serve
f
or a sensitive discriminator o
f
various
n
eutrino models. There will be no CP or T violation in neutrino oscillation
s
if
θ
13
is vanis
h
ing, un
l
ess t
h
ey get invo
l
ve
d
wit
h
non-stan
d
ar
d
neutrino in-
te
r
act
i
o
n
s
.I
f
θ
13
i
s too small, it will be extremel
y
di
ffi
cult or even impossibl
e
to discover CP violation in the le
p
ton sector.
A
lesson learnt from the his
-
tory of quark flavor physics is that a determination of the smallest quark
m
ixin
g
an
gl
eisacrucia
l
turnin
g
-point in
d
oin
g
precision measurements,
d
e-
tecting CP violation and searching for new physics. It is therefore desirabl
e
to measure t
h
esma
ll
est neutrino mixin
g
an
gle
θ
13
. A number of lon
g
-baseline
a
ccelerator and reactor neutrino experiments are underwa
y
to determine o
r
c
onstrain this angle
(
Gonzalez-Garcia and Maltoni, 2008
)
. In particular, the
D
aya Bay reactor antineutrino experiment in
C
hina will probe
θ
1
3
w
i
th a
ver
yi
mpress
i
ve sens
i
t
i
v
i
t
y
:s
in
2
2
θ
13
0
.
01
(
Gu
o
et al.
,
2007
).
Question 4: is there CP violation in the lepton sector
?
W
ithin the
SM
the source of CP violation is the nontrivial Kobayashi-Maskawa
(
KM
)
phase
which resides in the 3
×
3
quark mixing matrix
(
Kobayashi and Maskawa
,
1
973
)
. The phenomena of CP violation have been observed in a number o
f
K
-
a
n
d
B
-meson decays
(
e.g., Christenson
et al
.
,
1964;
A
be
et al
.
,
2001;
A
ubert
et al
.
,
2001
)
, and all the experimental results are consistent with the KM
m
echanism
(
Nakamura
et al.
, 2010
)
. Now that neutrinos are massive an
d
l
epton
fl
avors are mixed, there should analo
g
ously exist
C
P violation in the
l
e
p
ton sector. The source of le
p
tonic CP violation is ex
p
ected to be a KM-lik
e
p
h
as
e
δ
i
nt
h
e
3
×
3
MN
S
matri
x
V
,
but two additional CP-violating phases
ou
g
ht to be taken into account i
f
massive neutrinos are the Majorana particle
s
(
Xing, 2004
)
. The most promising way to discover leptonic CP violation is
to measure an asymmetry between the probabilities o
f
ν
e
→
ν
μ
a
n
d
ν
e
→
ν
μ
transitions. Such a measurement can be done in a neutrino factory
(
Gonzalez
-
Garcia and Maltoni, 2008
)
. Note that the strength of CP violation in neutrin
o
oscillations depends both on the ma
g
nitude o
f
δ
itse
l
fa
n
do
n
t
h
eva
l
ues of
θ
12
,
θ
13
a
n
d
θ
23
,
and thus how small
θ
13
i
stu
rn
souttobec
r
uc
i
a
lin
o
r
de
r
to
j
udge whether the effect of CP violation is practically observable or not.
Question 5: are there ultrahi
g
h-ener
gy
cosmic neutrinos
?
The obse
r
vat
i
on
of solar and supernova neutrinos has initiated a new and rapidly-developin
g
s
cience — neutrino astronomy. Bot
h
so
l
ar an
d
supernova neutrinos carry
ener
g
ies o
f
O
(
1
)
MeV t
o
O
(
10
)
MeV and reach the Earth without any atten-
u
ation, offerin
g
us some
g
ood opportunities to learn about the deep interior o
f
a
star
(
Bahcall, 1989
)
. We believe that much more energetic neutrinos
(
fro
m
TeV to EeV
)
should be emitted from other astrophysical objects, such as
s
upernova remnants, active galactic nuclei and gamma ray bursts, and fro
m
the annihilation of dark matter. For the time being the k
m
3
-
scale
n
eut
rin
o
telescope Ice
C
ube is under construction at the
S
outh Pole, and it has alread
y