Braibant S., Giacomelli G., Spurio M. Particles and Fundamental Interactions: An Introduction to Particle Physics
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12.7 Neutrinos from the Sun and Oscillation Studies 371
the scattering amplitudes corresponds to a different refraction index of the
e
with
respect to
and
(MSW effect, from the names of the discoverers Mikheyev–
Smirnov–Wolfenstein) [12M79]. Let us consider the case of two neutrinos, that
is,
e
and
. In dense matter, the mass eigenstates
1
,
2
are not related to
the flavor eigenstates via the relations (12.40), but by linear combinations with
coefficients that depend on the electron density in matter. The effective mixing
is modified by the presence of matter and, under certain conditions, a resonant
effect can take place. For example, all the
e
could transform in the
2
mass
eigenstate. In this case, the
2
will continue to propagate as such, without further
oscillations.
This certainly seems the case for electron neutrinos with MeV energies produced
in the center of the Sun. Following the
e
on their journey to the Earth, they
first pass through 700,000 km of solar matter, then 150 million km into space.
Near the Sun’s core, the electron density is very high, but decreases by several
orders of magnitude as the neutrinos reach the Sun’s surface. Electron neutrinos
produced by nuclear fusion reactions (see Sect. 14.10) slowly oscillate, while they
are subject to charged and neutral current interactions. Because of the MSW
effect, when they pass through a solar region with appropriate density, a resonant
conversion
e
into
2
occurs. The conversion probability depends on the neutrino
energy and on the electron density in matter. Thus, a large fraction of
e
is trans-
formed into the mass eigenstate
2
. These neutrinos travel in the (almost) vacuum
space between the Sun surface and the detectors on Earth without any further
oscillations.
On Earth, the
2
interact with a certain probability as
e
;
;
; the probability
is determined by the composition of
2
in terms of flavor eigenstates (we will see
that this probability is around 33% for each state). CC interactions of
and
cannot be observed by ground detectors because they do not have enough energy to
produce the muon or tau rest mass.
12.7 Neutrinos from the Sun and Oscillation Studies
According to the Standard Solar Model, the energy emitted is due to a series of
thermonuclear reactions that occur in the center of the Sun. This “thermonuclear
reactor” is much smaller than the size of the star. The emitted photons (with MeV
energies) undergo a large number of collisions and take a very long time to reach the
Sun’s surface ( 0:2 million years). The visible light emitted by the Sun originates
from a well defined surface, the solar photosphere, which defines the visible size of
the Sun. A large fraction of the energy is emitted in the form of neutrinos produced
by the reactions illustrated in Fig. 12.11a. The corresponding energy spectrum is
showninFig.12.11b. Most of the neutrinos are produced by the pp ! de
C
e
reaction, with energies below 0.42 MeV. The few higher energy neutrinos (up to
14 MeV) come from the
8
B decay. Monochromatic neutrinos are also produced, for
instance, in the
7
Be decay.
372 12 CP-Violation and Particle Oscillations
p+p d+e
+
+ν
e
p+e
–
+p d+ν
e
p+d
3
He+ γ
3
He+α
7
Be+ γ
7
Be+e
–
7
Li+ν
e
7
Be+p
8
B+ γ
3
He+
3
He α+2p
pp-l pp-ll pp-lll
14%
0.1%
99%
86%
Flux at 1 AU (cm
–2
s
–1
MeV
–1
) [for lines, cm
–2
s
–1
]
13
N
13
O
17
F
7
Be
8
B
hep
pp
Cl
Kamiokande
Ga
Neutrino energy (MeV)
0.1 0.50.2 1 521020
pep
7
Li+p 2 α
8
B 2α+e
+
+ν
e
10
12
10
10
10
8
10
6
10
4
10
2
a
b
Fig. 12.11 (a) The main chain of nuclear reactions that occur in the center of the Sun. (b)The
energy spectrum of solar neutrinos arriving on Earth: the solid lines indicate the neutrinos coming
from the most important reactions of the pp cycle, the dashed and dotted lines indicate the neutrinos
from the CNO cycle, Sect. 14.10
Most of the dedicated experiments measure the
e
flux. The first experiment,
designed by R. Davis (Nobel laureate in 2002), began to produce data in the
early 1970s. The measured solar neutrino flux was lower than that expected from
the knowledge of astrophysics and nuclear properties of the Sun. This observed
12.7 Neutrinos from the Sun and Oscillation Studies 373
deficit had two possible interpretations. The first possibility was an astrophysical
overestimate of the solar neutrino production. The second was that on the way from
the center of the Sun to the Earth, transitions had occurred between the solar
e
to different flavor neutrinos (
,
) that could not be observed in the experiment.
Over the years, the second interpretation of the measured deficit was found to be
correct.
The Davis experiment was a radiochemical underground experiment located in
the Homestake mine in South Dakota. A large tank containing 680 t of organic
liquid (perchloroethylene) was used as a target. The nuclear transmutation induced
by solar neutrinos was
e
C
37
Cl !
37
Ar Ce
. The radioactive
37
Ar is a gas which
was extracted from the target, purified and counted. For this reason, the experiment
was denoted as “radiochemical.” The reaction has an energy threshold of 814 keV.
Therefore, only neutrinos from the
8
B decay and from the electron capture in
7
Be
can be detected (see Fig. 12.11). The experimental results with the
37
Cl showed a
e
flux equal to about one third of that predicted by the Standard Solar Model. This
was the beginning of the solar neutrino problem.
In the early 1990s, two different radiochemical experiments (GALLEX at Gran
Sasso in Italy, and SAGE in Russia) started operation: both used the
71
Ga and
were sensitive to neutrinos with energies above 233 keV, through charged current
interaction
e
C
71
Ga !
71
Ge Ce
.The
71
Ge was extracted from the liquid target
in the gaseous form GeCl
4
, chemically purified, and converted to GeH
4
gas for
counting. The detection of solar neutrinos with E
> 233 keV includes the neutrinos
produced in the p Cp ! d Ce
C
C
e
reaction. The results showed without a doubt
that in the Sun’s core, a “fusion power plant” is active. These two radiochemical
experiments also reported a significant deficit of solar neutrinos.
A different detection strategy which confirmed the deficit was used by the
Kamiokande experiment (and after by SuperKamiokande) in Japan: neutrinos
interacting via elastic scattering on electrons
x
e
!
x
e
were detected in a
large water tank. Their energy threshold was about 7 MeV, corresponding to the
neutrinos coming from the
8
B(Fig.12.11).
The combined results indicate that there are “missing” neutrinos from the Sun,
when data are compared to theoretical models. However, not one of the experiments
mentioned above was able to conclusively prove that the lack of solar electron
neutrinos was due to the oscillation phenomenon. They were all
e
disappearance
experiments. Neutrino appearance experiments should be able to observe neutrinos
of flavor different from
e
.The
(or
) appearance through charged current (CC)
interactions produces the corresponding charged lepton. Nevertheless, the muon (or
tau) rest mass is much larger than the energy corresponding to solar neutrinos, and
the CC reaction cannot occur. The problem was solved by the SNO experiment,
which measured the fraction of
C
in the neutrino flux from the Sun using their
neutral current (NC) interactions.
The SNO experiment. The Sudbury Neutrino Observatory (SNO) in Canada
recorded data from 1999 until 2006. It was able to detect Cherenkov light emitted by
charged particles crossing the detector, filled with 1,000 t of heavy water (D
2
O) and
374 12 CP-Violation and Particle Oscillations
surrounded by 1,500t of normal water used for screening purpose. The reactions
that occur in normal water are:
1. The elastic scattering on electron (ES), as in SuperKamiokande:
ES W
x
C e
!
x
C e
: (12.58)
The ES occurs through a Z
0
exchange for all neutrino flavors, and through a W
˙
exchange in the case of
e
(see Fig. 12.10). The ES is sensitive to neutrinos of
any flavor but the cross-section for nonelectronic neutrinos is largely reduced:
.
;
e !
;
e/ ' .
e
e !
e
e/=6:5. In practice, the ES is dominated by
e
interactions and the measured solar neutrino flux is .
e
/ CŒ.
;
/=6:5
2. The
e
CC interaction on proton (inverse ˇ-decay), see Sect. 8.6.1:
CC W
e
C p ! e
C n (12.59)
which only occurs for
e
through a W
˙
exchange.
In addition, in the heavy water, the following NC reaction also take place:
3. Deuterium dissociation through a Z
0
exchange:
NC W
x
C d !
x
C p C n;
x
D
e
;
;
: (12.60)
A 2 MeV photon is emitted as a result of the d dissociation in p Cn. A salt which
increases the probability of neutron capture was dissolved in the detector (as for
the Cowans and Raines experiment, see Sect. 8.5). The 8 MeV emitted after the
neutron capture produces an e
C
e
pair, which emits Cherenkov light that can be
detected.
In all cases, the neutrino energy is of the order of a few MeV; also for SNO,
the neutrino flux from the reaction involving the
8
B is measured. The total incident
neutrino flux
e
C
C
was obtained through the reactions (12.60). This number
is independent from any kind of oscillations. The
e
flux was measured using the
reaction (12.59). SNO reported for the ratio is R D[(.
e
/)/(
tot
D .
e
C
C
/)], that is,
R D
.
e
/
.
e
C
C
/
D 0:340 ˙ 0:023
stat
˙ 0:030
syst
: (12.61)
This result clearly indicates that .
C
/ is nonzero, providing a definitive proof
that some of the solar electron neutrinos, on their way to the Earth, changed flavor.
On the other hand, the total number of solar neutrinos is conserved. The Standard
Solar Model [B89] provides a neutrino flux from the Sun due to the reaction
of
8
B:
tot
./
SSM
D 5:49
C0:95
0:89
10
6
cm
2
s
1
(12.62)
12.7 Neutrinos from the Sun and Oscillation Studies 375
(to be compared with 6:5 10
10
cm
2
s
1
due to the sum of all the nuclear reactions
inside the Sun). The total number of neutrinos measured by SNO via the reaction
(12.60)is
.
e
C
C
/
SNO
D 4:94 ˙ 0:21
stat
˙ 0:36
syst
10
6
cm
2
s
1
: (12.63)
The results from all the experiments mentioned above indicate that the flux of
electron neutrinos is reduced by a factor from 2/3 to 1/2. This is due to the fact
that in addition to the neutrino oscillation in vacuum from the Sun’s surface to the
Earth, the matter effect plays a significant role for high energy solar neutrinos, like
those from
8
B decay, with energies larger than 8MeV.
The KamLAND and Borexino experiments. The results obtained using solar
neutrinos were confirmed by the KamLAND experiment in Japan. The detector
had 1,000 t of liquid scintillator, and was located in the same Kamioka mine as
the SuperKamiokande experiment. The KamLAND was a long baseline experiment
(see Sect. 12.8.1) detecting
e
produced by a large number of nuclear reactors in the
central region of Japan (the experiment was located, on average, 180 km from the
reactors). Most of the electric power in Japan (more than 60 GW) is generated by
nuclear power plants. Nuclear reactors produce
e
in the ˇ
decay of neutron-rich
fission fragments. The flux and the energy spectrum of antineutrinos depend on the
reactor power and on the isotopic composition of the fissile material. KamLAND
was a
e
disappearance experiment which studied the flux and the energy spectrum
of positrons produced in the interaction. Their results in terms of neutrino oscillation
parameters (in this case, the
e
oscillations occur almost in vacuum) are in good
agreement with the results obtained using solar neutrinos (Fig. 12.12).
The operation of the Borexino experiment at the Gran Sasso Laboratory in Italy
began in 2007. The Borexino detector detects the monochromatic neutrinos (E
D
0:862 MeV) from the electron capture of
7
Be in the Sun. It uses liquid scintillator
and the detection of neutrinos is performed through the elastic scattering (ES) on
electrons.
7
Be neutrinos leave the Sun with an energy of 0.862MeV. For such low
energies, the matter effect is almost negligible, and the oscillation probability of
these neutrinos is described, as in vacuum, by Eq. 12.49 (replacing with e). In
practice, it is expected that for
7
Be neutrinos, P.
e
!
e
/ D 0:6. The first Borexino
data [12B08], taken with a 100ton target, reported 47 ˙7
stat
˙12
syst
counts per day.
Assuming neutrino oscillations with the reduction factor mentioned above, 49 ˙ 4
counts per day are expected; this number is in good agreement with the measured
value (even if the experimental uncertainties are still large).
Discussion of the Solar Neutrino Results. The formula for neutrino oscillations
in vacuum (12.49) depends on two unknown parameters (m
2
and ), which, in
principle, can be zero (in this case, there are no oscillations). The formula depends
on two other parameters (the distance L between the neutrino production and
observation points and the neutrino energy) which can be estimated or measured
by experiments. Since the characteristics of solar neutrino experiments and of
376 12 CP-Violation and Particle Oscillations
10
–1
1
10
–4
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
best fit
Δm
2
(eV
2
)
tan
2
θ
Fig. 12.12 Compendium of the current situation for the oscillations of solar neutrinos. The
contour plots are shown in the parameter space (tan
2
ˇ
, m
2
ˇ
) where the x-axis is the square
of the tangent of the mixing angle and the y-axis is the mass difference squared. The combination
of solar neutrinos experiments and the KamLAND results [P08] are shown separately
KamLAND meet those for the neutrino with a dominant mass discussed above,
the formula that describes the oscillations is (12.57), with m
2
12
D m
2
ˇ
and
12
D
ˇ
. The experimental results presented as contour plots in the (tan
2
ˇ
,
m
2
ˇ
) parameters space are shown in Fig. 12.12. The results of the combination
of solar neutrino experiments and of KamLAND are shown separately. There is
an overlap region allowed by all experiments. The combined analyses provide the
preferred values (point indicated as best fit in the figure)
m
2
ˇ
D .7:59 ˙ 0:21/ 10
5
eV
2
I tan
2
ˇ
D 0:47 ˙ 0:06: (12.64)
12.8 Atmospheric
Oscillations and Experiments
Cosmic rays [G90] are protons and heavier atomic nuclei coming from outer
space and constantly bombarding the Earth’s upper atmosphere where they interact,
producing secondary particles. A fraction of these secondary particles decay, giving
rise to
and
e
in a ratio of about two to one (see Fig.12.13a). These atmospheric
neutrinos have energies > 100 MeV and are produced in the atmosphere 10–20 km
above the ground. Below 100 TeV, the atmospheric -flux is almost unaffected when
passing through the Earth. Experiments can detect both upward- and downward-
going neutrino-induced leptons [12C98] (neutrino from above and below in the
following). At the end of the 1980s, the IMB and Kamiokande experiments found
abnormalities in the
/
e
ratio, while other smaller size experiments found no
12.8 Atmospheric
Oscillations and Experiments 377
p, He, Fe ...
π
μ
ν
μ
ν
e
ν
μ
e
p, He, Fe ...
μ
μ
p, He, Fe ...
ν
μ
ν
μ
ab
Fig. 12.13 Atmospheric neutrinos. Cosmic rays interact in the upper atmosphere, producing
particle showers. Some decay of these secondary particles produces
and
e
. The neutrinos
originate from an atmospheric layer of 10–20 km thickness. A large underground detector can
detect neutrinos coming from above. These downward-going neutrinos have traveled tens of
kilometers and had no “time” to oscillate. Instead, neutrinos coming from the other hemisphere
(upward-going neutrinos) have traveled L ' 10
4
km and have oscillated. Only the CC
interactions are shown in (a). Interactions of
e
! e inside the detectors can also be
measured
deviations. In 1995, the MACRO experiment published experimental results on a
deficit of
from below.
In 1998, SuperKamiokande (SK) [12F98], MACRO [12A98] and Soudan 2
[12S98] presented new results with definitive indications for oscillations. These
observations included the number of muon neutrinos from different directions (i.e.,
different values of the neutrino path length L); SK and Soudan 2 also measured
the ratio between the number of
and
e
. The number of electron neutrinos was
roughly in agreement with the prediction; the number of muon neutrinos coming
from below was lower, while the number of
from above was in agreement with
the expectations.
The oscillations between two neutrino flavor eigenstates (12.49) indicate that
the probability depends on the ratio L=hE
i,whereL is the distance between the
neutrino production and observation points (i.e., L 10 km for neutrinos coming
from above, L 10
4
km for neutrinos coming from below). The energy E
of a
single neutrino cannot be measured. Therefore, one uses an average energy, hE
i,
obtained from Monte Carlo simulations for a certain topology of detected neutrinos.
CC events in which the produced particles remain entirely contained in the detector
have hE
i0.5 GeV; partially contained events (typically, a few GeV muon exits
the detector) have hE
i5 GeV. The events in which the neutrino interacts below
the detector producing an upward through–going muon have hE
i50 GeV.
378 12 CP-Violation and Particle Oscillations
1.5 2 2.5 3
3.5
4
0.4
0.6
0.8
1
1.2
0.2
0
1 10
10
2
10
3
10
4
10
5
0
0.5
1
1.5
L / E (km / GeV)
Data / Monte Carlo
e-like
μ-like
ab
Fig. 12.14 (a) Ratio between the numbers of “e-like” (full circles)and“-like” (open circles)
events measured and predicted by Monte Carlo (MC) in the absence of oscillation, as a function
of L=hE
i in the SuperKamiokande experiment. The dotted lines represent the Monte Carlo (MC)
predictions assuming
!
oscillations. (b) Ratio R of the numbers of
-induced events,
measured and predicted by Monte Carlo with (line with error band) and without (dashed line at R
D 1) neutrino oscillations in MACRO. The points with error bars represent data
In agreement with the oscillation hypothesis, the ratio of the measured and
predicted numbers of
events decreases when L=hE
iincreases (see Fig. 12.14). It
can be deduced that during the journey through the Earth, a fraction of
oscillates
into neutrinos of another type.
As for solar neutrinos, atmospheric neutrino measurements provide information
on the mass difference of neutrinos involved in the oscillations. These measurements
are presented in Fig. 12.14.Forthe
e
flavor (see Fig. 12.14a), the results are
compatible with the no-oscillation hypothesis and one concludes that the
e
did
not oscillated. The results obtained for the
and
flavors instead show a clear
deficit with respect to the no-oscillation hypothesis. The
and
must therefore
have oscillated. Moreover, since m
2
atm
m
2
ˇ
,Eq.12.55 are still valid.
Information on m
2
23
D m
2
atm
and on the mixing angle
23
D
atm
were
obtained by the MACRO, Soudan 2 and SK experiments. The corresponding
parameter space allowed for neutrino oscillations is shown in Fig. 12.15.The
data indicate that the preferred values correspond to a mass difference m
2
atm
D
0:0024 eV
2
and to a maximal mixing sin
2
2
atm
D 1.
The SuperKamiokande (SK) experiment is a large cylindrical detector
containing 50,000t of water. The detector is divided into two regions; in the
inner region, 11,200 photomultipliers (PMT), 20 inches (50.8 cm) in diameter,
detect faint flashes of light produced by the Cherenkov effect from electrically
charged particles passing through. The external region offers a shielded
12.8 Atmospheric
Oscillations and Experiments 379
Fig. 12.15 Soudan2, MACRO and SK contour plots of the regions compatible with atmospheric
neutrino oscillations in the (sin
2
2
atm
, m
2
atm
) parameter space
volume for cosmic rays and is used for anticoincidence. The fiducial detector
mass is 22,500 t. SuperKamiokande is located 1,000 m underground in the
Kamioka mine in Japan. As mentioned, the experiment also measured solar
neutrinos. In 2001, an accident destroyed more than half of the PMTs. SK
came back into operation in 2003 using about 5,000 PMTs, with a slightly
lower energy resolution. Now (2011), it is once again fully efficient.
MACRO was a large apparatus (12 m 9:3 m 76:6 m) in the Gran Sasso
underground laboratory in Italy. It had a modular structure of six modules of
12 12 9:4 m
3
and took data from 1994 to 2000. The bottom part contained
layers of limited streamer tubes (LST) interleaved with passive material plus
two layers of liquid scintillator detectors and one plane of nuclear track
detectors. The top part of the apparatus was empty and had a “roof” with
four horizontal planes of LST and another liquid scintillator layer. Vertically,
the apparatus was surrounded by a liquid scintillator plane and six lateral
planes of LST.
12.8.1 Long Baseline Experiments
Long baseline high energy experiments are needed to probe, with well-controlled
beams, the small mass difference m
2
23
' 2 10
3
eV
2
obtained with atmospheric
neutrinos. To achieve this goal, typical values of L 1,000km and E
1GeV
are needed.
380 12 CP-Violation and Particle Oscillations
Before the discovery of neutrino oscillations in solar and atmospheric neutrinos,
two short baseline experiments were carried out at CERN: CHORUS and NOMAD.
These two detectors were exposed to a high-energy
beam, and had L 1 km.
Their goal was to search for neutrino oscillations with m
2
1 eV, by performing
disappearance and appearance measurements. The results were null, because they
were designed to explore a range of m
2
values that Nature had not chosen.
Following the results of MACRO, SK and Soudan2, several long baseline
experiments became operational. In Japan, the K2K (KEK to Kamioka) neutrino
experiment took data from 1999 to 2004: muon neutrinos were produced at the
12 GeV protosynchrotron at KEK, and were detected after a 250 km path by the
SuperKamiokande detector. In America, the MINOS experiment uses an intense
beam which is sent from Fermilab’s Main Injector to the MINOS detector
in the Soudan mine (Minnesota), located about 730 km away. The results of the
two experiments are in perfect agreement with the underground measurements of
atmospheric neutrinos. Both MINOS and K2K measure the neutrino-induced muon
energy spectrum, confirming a distortion consistent with what is expected assuming
neutrino oscillations.
Since 2008, the long baseline CERN to Gran Sasso project (CNGS) exploits the
high-intensity and high-energy
beam produced at the CERN SPS and directed
to the Gran Sasso Laboratory. The neutrino energy is fairly well-determined and
the distance is L ' 730 km. At the Gran Sasso underground laboratory, the
OPERA experiment [12A10] measures the
and (possibly) the
appearance.
The peculiarity of the CNGS project is the possibility to measure the appearance of
in a
pure beam, removing any alternative (or exotic) hypothesis different from
oscillations in
for atmospheric neutrinos.
OPERA is a hybrid, high-precision tracking detector that uses passive
nuclear emulsions and electronic devices. The detectors are distributed inside
1.3 kton of passive material, needed for a sufficient neutrino interaction rate.
Each cell consists of a thin sheet of lead (1 mm thick), alternating with
a pair of emulsion layers, each of 44 m thickness. The emulsions are
glued on opposite sides of a plastic support of 200 m thickness. The basic
element, called a brick, consists of 56 cells. Each brick has (10:2 12:7)cm
2
area and 7.5 cm thickness, followed by two scintillator planes acting as
an electronic tracker. The scintillators reconstruct the interaction vertex of
the muon neutrino with a 1 cm accuracy. This is sufficient to locate the
brick where the interaction took place. The experiment is organized in two
supermodules for a total of about 150,000 bricks. Each supermodule is
followed by a muon spectrometer, drift tubes and resistive plate chambers.
The spectrometer identifies muons, measuring the momentum and the sign of
the charge.
The
search is carried out both in the leptonic decay channels .
!
e
C
C
e
/; .
!
C
C
/ and in the hadronic channel