# History of Solar Neutrino Observations

Masayuki Nakahata
Kamioka Observatory Institute for Cosmic Ray Research  University of Tokyo
456 Higashi-Mozumi  Kamioka-cho  Hida-shi  Gifu 506-1205  Japan
Kavli Institute for the Physics and Mathematics of the Universe (WPI)
The University of Tokyo Institutes for Advanced Study  University of Tokyo
Kashiwa  Chiba 277-8583  Japan<EMAIL_ADDRESS>
###### Abstract

The first solar neutrino experiment led by Raymond Davis Jr. showed a deficit
of neutrinos relative to the solar model prediction, referred to as the “solar
neutrino problem” since the 1970s. The Kamiokande experiment led by Masatoshi
Koshiba successfully observed solar neutrinos, as first reported in 1989. The
observed flux of solar neutrinos was almost half the prediction and confirmed
the solar neutrino problem. This problem was not resolved for some time due to
possible uncertainties in the solar model. In 2001, it was discovered that the
solar neutrino problem is due to neutrino oscillations by comparing the Super-
Kamiokande and Sudbury Neutrino Observatory results, which was the first
model-independent comparison. Detailed studies of solar neutrino oscillations
have since been performed, and the results of solar neutrino experiments are
consistent with solar model predictions when the effect of neutrino
oscillations are taken into account. In this article, the history of solar
neutrino observations is reviewed with the contributions of Kamiokande and
Super-Kamiokande detailed.

C43, F21

##  1 Introduction

The main energy source of the sun is thermonuclear reactions inside the core.
Considerable amounts of electron-type neutrinos (${\nu}_{\rm e}$s) are
produced through nuclear fusion reactions, and solar neutrino experiments
provide direct surveys of the deep interior of the sun. Prof. R. Davis
established the Homestake experiment to identify the main fusion reactions in
the 1960s. However, the observed flux was much smaller than that predicted by
the standard solar model, and this was referred to as the “solar neutrino
problem”. The Homestake experiment used a radiochemical method that collected
argon atoms produced by neutrino reactions. Because of the unconventional
technique of the experiment, it did not convince people whether the solar
neutrino problem could be attributed to properties of neutrinos themselves or
errors in the standard solar model.

The Kamiokande experiment was undertaken in 1983 under the leadership of Prof.
Masatoshi Koshiba. The original purpose of Kamiokande was to search for proton
decay. Proton decays were not observed and Prof. Koshiba proposed upgrading
the detector for solar neutrino measurements a few months after data
collection was started. In 1988, the Kamiokande experiment succeeded in
observing solar neutrinos. This was the first measurement with a real-time
detection method. The observed solar neutrino flux was about 50 % of the
prediction and confirmed the solar neutrino problem. Although the Homestake
and Kamiokande experiments observed a deficit in the solar neutrino flux, they
could not determine the cause of the discrepancy because of large
uncertainties in the model predictions.

In the early 1990s, gallium experiments (SAGE and GALLEX) were started to
measure low-energy solar neutrinos. These experiments also observed a flux
smaller than the prediction, enhancing the possibility of neutrino
oscillations as the solution of the solar neutrino problem.

In 1996, Super-Kamiokande, which had 30 times more fiducial volume than
Kamiokande, started collecting data. It detected about 22,400 solar neutrino
events by 2001 and the 8B solar neutrino flux was measured with an accuracy of
3% using neutrino–electron scattering. In 2001, the SNO group announced a 8B
flux measurement using charged-current neutrino–deuteron interactions, and
comparisons between the Super-Kamiokande and SNO results gave direct evidence
for model-independent solar neutrino oscillations. The evidence was further
strengthened by neutral-current measurements from SNO. In 2002, combining the
results of the solar neutrino experiments, global analyses showed that the
most suitable oscillation parameter is the large mixing angle (LMA; a solution
with a mass squared difference $\Delta m^{2}_{21}(=m_{2}^{2}-m_{1}^{2})$ of
$10^{-5}-10^{-4}$ eV2 and a mixing angle ($\theta$) of
$\sin^{2}(2\theta)=0.5-1$)111Details of the oscillation parameters will be
described in Sections 5 and 9.. In 2008, the Borexino experiment measured the
flux of 7Be solar neutrinos and further confirmed the existence of neutrino
oscillations.

In this article, results from solar neutrino experiments are reviewed with
detailed descriptions of Kamiokande and Super-Kamiokande. In Section 2, the
standard solar model and its neutrino flux predictions are described. The
results of the Homestake experiment are described in Section 3 and the
observations from Kamiokande are described in Section 4. In Section 5, the
status of understanding of the solar neutrino problem just before the start of
Super-Kamiokande and SNO is summarized, including results from the SAGE and
GALLEX experiments. Solar neutrino measurements by Super-Kamiokande, SNO and
Borexino are described in Sections 6, 7 and 8, respectively. Solar neutrino
oscillations are discussed in Section 9 and a conclusion and future prospects
are given in Section 10.

##  2 Standard Solar Model

It is important to develop precise standard solar models in order to discuss
neutrino oscillations. In the standard solar model (SSM)SOLBP2001 ; SOLBP2004
; SSM2017 , the time evolution of the temperature and pressure at each
position in the sun is solved using equations of hydrostatic equilibrium, mass
continuity, energy conservation and energy transport by radiation or
convection. The boundary conditions for solving the model are the mass,
radius, age and luminosity of the sun at present. The input parameters for the
SSM include nuclear fusion cross sections, the initial chemical composition of
the sun (elements other than H and He) and the opacity to photons. The SSM
assumes that the current surface chemical composition reflects the initial
chemical composition, and photo-spectroscopic measurements of the surface are
used to estimate its chemical composition.

The SSM predicts that 99% of the energy production in the sun is due to the
$pp$ nuclear reaction chain and the remaining 1% is due to the CNO cycle, as
shown in Fig.1.

Figure 1: $pp$ chain and CNO cycle reactions

In the figure, the reactions marked with double borders produce neutrinos, and
the neutrinos from these reactions are named depending on the reaction: $pp$,
${}^{7}{\rm Be}$, ${}^{8}{\rm B}$, $hep$, ${}^{13}{\rm N}$, ${}^{15}{\rm O}$
and ${}^{17}{\rm F}$ neutrinos. The fluxes of each neutrino type from the
latest SSMSSM2017  are shown in Table 1.

source | flux (/cm2/s)
---|---
| GS98 | AGSS09met
$pp$ | 5.98 $\times 10^{10}(1\pm 0.006)$ | 6.03 $\times 10^{10}(1\pm 0.005)$
${}^{7}{\rm Be}$ | 4.93$\times 10^{9}(1\pm 0.06)$ | 4.50$\times 10^{9}(1\pm 0.06)$
$pep$ | 1.44$\times 10^{8}(1\pm 0.01)$ | 1.46$\times 10^{8}(1\pm 0.009)$
${}^{8}{\rm B}$ | 5.46$\times 10^{6}(1\pm 0.12)$ | 4.50$\times 10^{6}(1\pm 0.12)$
$hep$ | 7.98$\times 10^{3}(1\pm 0.30)$ | 8.25$\times 10^{3}(1\pm 0.30)$
${}^{13}{\rm N}$ | 2.78$\times 10^{8}(1\pm 0.15)$ | 2.04$\times 10^{8}(1\pm 0.14)$
${}^{15}{\rm O}$ | 2.05$\times 10^{8}(1\pm 0.17)$ | 1.44$\times 10^{8}(1\pm 0.16)$
${}^{17}{\rm F}$ | 5.29$\times 10^{6}(1\pm 0.20)$ | 3.26$\times 10^{6}(1\pm 0.18)$
Table 1: Solar neutrino flux predicted by SSMSSM2017 . The second and third
columns show the flux predictions using the chemical composition from GS98GS98
and AGSS09metAGSS09 , respectively.

The second and third columns in the table show the flux predictions using
chemical compositions obtained by GS98GS98  and AGSS09metAGSS09 ,
respectively. GS98 is based on a one-dimensional model of the solar atmosphere
that was released in 1998. AGSS09met, released in 2009, is based on a three-
dimensional model and uses the most up-to-date atomic and molecular data, and
should therefore be more reliable than the GS98-based solar model. However,
the GS98-based solar model can reproduce various observations inside the sun,
such as the sound speed profile, depth of the convective zone and the helium
abundance, while the AGSS09met based solar model’s predictions have large
discrepancies with observations. Therefore, the flux predictions of both are
given here.

The energy spectrum of solar neutrinos predicted by the SSM is shown in Fig.2.

Figure 2: Solar neutrino energy spectrum expected from the SSMSOLBP2001 ;
SOLBP2004 . The solid and dashed curves show neutrinos in the $pp$ chain and
CNO cycle, respectively.

The most energetic neutrino is the 8B neutrino and it was the main neutrino
source for the Homestake, Kamiokande, Super-Kamiokande and SNO experiments,
though its intensity is only about 0.01% of the total solar neutrino flux. The
most abundant source is the $pp$ neutrino but its maximum energy is only 0.42
MeV. The gallium experiments were sensitive to $pp$ neutrinos.

##  3 Homestake experiment

The Homestake experiment was located in the Homestake gold mine at a depth of
1480 metersSOLDAVIS . The experiment was started around 1970 and data were
obtained until 1994. The target for the solar neutrinos was ${}^{37}{\rm Cl}$
atoms in 615 tons of ${\rm C}_{2}{\rm Cl}_{4}$. The neutrino energy threshold
of the reaction ${}^{37}{\rm Cl}+\nu_{e}\rightarrow^{37}{\rm Ar}+e^{-}$ is
0.814 MeV and it is mainly sensitive to 8B neutrinos. This radiochemical Cl-Ar
method of solar neutrino detection was proposed by B. Pontecorvo in
1946PONT1946 . The expected event rate from the SSMSOLBP2004  was 8.5$\pm$1.8
SNU, where one SNU is $10^{-36}$captures/atom/s. The contribution from each
neutrino source is 6.6 SNU from ${}^{8}{\rm B}$ neutrinos, 1.2 SNU from 7Be
neutrinos, 0.22 SNU from $pep$ neutrinos and the remainder from CNO cycle
neutrinos. The produced ${}^{37}{\rm Ar}$ atoms were collected once every
60–120 days and the decay of ${}^{37}{\rm Ar}$ was counted using a low
background proportional counter. Figure 3 shows the observed production rate
of ${}^{37}{\rm Ar}$ in each collection cycleSOLDAVIS .

Figure 3: Data from the Homestake experimentSOLDAVIS . Each data point shows
the ${}^{37}{\rm Ar}$ production rate measured in each collection cycle (run).
The scale of the right hand side is in SNU. The time averaged rate is shown to
the right of the main data.

The average event rate observed by the Homestake experiment was

$\displaystyle\phi(Homestake)=2.56\pm 0.16(stat.)\pm 0.16(sys.)~{}~{}{\rm
SNU}$

The observed event rate was only about 30% of the SSM prediction, leading to
the so-called solar neutrino problem.

##  4 Kamiokande

The Kamiokande detector was constructed in 1983 to search for proton decay.
The detector had a 2340 ton water volume, located 1000 meters underground in
the Kamioka Mine in Japan. The water volume was viewed by 1,000 20-inch
diameter photomultipliers (PMTs) mounted on a 1-m grid on the inner surface.
Data collection was started on July 6, 1983 and tens of proton decay events
within a few months were expected if the original idea of the grand unified
theoryGGGUT  is correct. However, no proton decay events were found. Since the
primary purpose of the detector was to observe events with $\sim$1 GeV total
energy, low-energy events such as solar neutrinos were not triggered in the
first stage of the Kamiokande experiment as the electronics at that time read
out only the integrated charge information for each PMT. The total sum signal,
which is the sum of analog signals from all PMTs, was used to trigger the
readout electronics, and the trigger energy threshold was about 30 MeV for
electrons, which is much higher than the energy of solar neutrino signals. The
total sum signal was recorded by a transient digitizer (R7912, Tektronix),
which records a digitized oscilloscope image in order to detect
$\mu\rightarrow e$ decay signals from stopping muons. There were several
hundred cosmic ray stopping muons per day in the Kamiokande detector. Figure 4
shows the pulse height distribution of $\mu\rightarrow e$ signals.

Figure 4: Pulse height distribution of $\mu\rightarrow e$ signals of stopping
cosmic ray muons at the early stage of Kamiokande.

The distribution showed that the Kamioka detector had the potential to detect
low-energy neutrinos down to $\sim$10 MeV, and Prof. Koshiba proposed
upgrading the detector for ${}^{8}{\rm B}$ solar neutrino measurements in the
fall of 1983.

In order to detect solar neutrinos, two major upgrades were required. First,
an anti-counter system had to be constructed to reduce environmental
background signals such as gamma rays from radioactivity in the surrounding
rock. Second, a new set of electronics to read out the timing and charge
information of each individual PMT was necessary. Precise determination of the
position where an event occurred, called the vertex position, is crucial for
solar neutrino measurements. The gamma rays from the rock which remained after
passing through the anti-counter tended to have a vertex position near the
wall of the detector. High-energy cosmic rays produce hadronic cascade showers
by spallation and generate short-life radioactive nuclei. The event rate of
the beta decays of those nuclei was more than one order of magnitude higher
than the expected rate of ${}^{8}{\rm B}$ solar neutrino signals. Those
spallation products were produced along the track of the originating cosmic
ray muons and could be removed using the vertex information.

The anti-counter was constructed from September 1984 through March 1985. 123
20-inch PMTs were mounted in the anti-counter to work as an active veto. The
bottom PMT plane of the inner-counter was lifted by 1.2 m to allow PMTs to be
inserted for the bottom anti-counter. The PMTs for the top anti-counter were
mounted 0.8 m above the top inner-counter. Additional water was added to the
tank to submerge these PMTs. The Kamiokande tank was constructed in a newly
excavated cavern, and rubber-asphalt was sprayed on the surface of the cavern
to make it water-tight so that water could be filled between the cavern wall
and the Kamiokande tank. PMTs were mounted in this newly prepared layer, which
functioned as the barrel part of the anti-counter. A schematic view of the
Kamiokande detector after the upgrade is shown in Fig.5.

Figure 5: Schematic view of the Kamiokande detector after the upgrade.

Prof. Koshiba gave a talk on the possibility of detecting ${}^{8}{\rm B}$
solar neutrinos in Kamiokande at ICOBAN’84 (International Conference On BAryon
Non-conservation, Park City, Utah, 1984) and asked the participants to
collaborate on the electronics upgrade. Soon after this workshop, the Univ.
Pennsylvania group led by Prof. A.K. Mann expressed interest in producing the
new electronics. The electronics system, included timing and charge readouts
and a trigger system using number-of-hit PMTs, was installed in the fall of
1985.

A further consideration was radon in the tank water, which is the most
significant source of background noise in solar neutrino measurements. The
concentration of radon, especially ${}^{222}{\rm Rn}$, was two or more orders
of magnitude higher in the air and water in the mine than in the usual
environment outside the mine. A daughter of ${}^{222}{\rm Rn}$, ${}^{214}{\rm
Bi}$, emits beta rays with an end-point energy of 3.27 MeV, which mimics a
solar neutrino signal. When Kamiokande started collecting data after the
installation of anti-counters, fresh water was being constantly supplied to
the tank. The trigger rate in the lower energy threshold mode was several
hundred events per second, while the goal was at most only about one solar
neutrino event per day. Figure 6 shows the change in trigger rate after a
modification was made to recirculate water rather than supplying fresh water.
The decrease in the trigger rate was consistent with the decay of
${}^{222}{\rm Rn}$ with a half life of 3.8 days.

Figure 6: Change in trigger rate after changing to recirculated water without
supplying fresh water.

Various efforts were made to further reduce radon in the tank water in 1986,
including air-tightening of buffer tanks in the water purification system. The
detector was almost ready for solar neutrino measurements in early 1987.

Prof. Koshiba noted that the following three features are necessary to perform
“neutrino astronomy”:

  * •

Directionality

  * •

Real-time measurement

  * •

Energy spectrum measurement

In Kamiokande, solar neutrino signals were observed based on the Cherenkov
radiation of recoil electrons from neutrino–electron scattering. Since the
energy of ${}^{8}{\rm B}$ solar neutrino is much larger than the mass of an
electron, the direction of a scattered electron is strongly correlated with
the direction from the sun to the earth. In addition, since Kamiokande
observed images of the Cherenkov ring pattern, the direction of the electron
could be observed. Kamiokande was a real-time detector and events were
observed at the time when they happened. The energy spectrum of the neutrinos
could be deduced from the spectrum of the scattered electrons. Thus, the
observations at Kamiokande satisfied the criteria for neutrino astronomy.

Figure 7 shows the angular distribution to the sun for the events that passed
the criteria for solar neutrino event selection. The plot was obtained with
initial 450-day data taken from January 1987 to May 1988SOLKAMIOKANDE1 .

Figure 7: Angular distribution to the direction of the sun in
KamiokandeSOLKAMIOKANDE1 . The plot shows data from the first 450 days of data
taken from January 1987 to May 1988. The solid histogram shows the prediction
from the SSM.

A clear excess of events was observed in the direction of the sun but the
observed rate was about 50% of the prediction from the SSM (solid histogram in
the figure). This observation confirmed the solar neutrino problem.

The Kamiokande detector observed $\sim$600 solar neutrino events by February
1995SOLKAMIOKANDE2  and the obtained flux of 8B neutrino was

$\displaystyle\phi(^{8}{\rm B})_{Kamiokande}$ $\displaystyle=$ $\displaystyle
2.80\pm 0.19(\mbox{stat.})\pm 0.33(\mbox{sys.})$ $\displaystyle\times
10^{6}/cm^{2}/s~{}.$

The observed flux was 48$\pm$3(stat.)$\pm$6(sys.) % of the prediction from the
SSM. The energy spectrum of recoil electrons normalized by the predicted
spectrum is shown in Fig.8,

Figure 8: Energy spectrum of recoil electrons normalized by the predicted
spectrum from the 2079-day dataset of Kamiokande. The hatched area shows the
range of systematic uncertainty.

consistent with a flat spectrum, i.e. no hint of neutrino oscillations was
given in the spectrum. In order to proceed to investigate possibility of
neutrino oscillations, high statistics measurements with Super-Kamiokande was
necessary.

##  5 Status just before the start of Super-Kamiokande and SNO

This section describes other experiments that have been performed and how we
enhanced our understanding of the solar neutrino problem before the Super-
Kamioakande/SNO era.

SAGE and GALLEX were radiochemical experiments using gallium targets conducted
since the early 1990s. The SAGE experimentSAGE1994 ; SAGE2001 ; SAGE2009  was
conducted at the Baksan Observatory and the GALLEX experiment GALLEX94 ;
GALLEX95 ; GALLEX96  (later changed to GNOSOLGNO ) was conducted at the Gran
Sasso Laboratory. The energy threshold of the gallium reaction (${}^{71}{\rm
Ga}+\nu_{e}\rightarrow^{71}{\rm Ge}+e^{-}$) is 0.233 MeV and is mainly
sensitive to low-energy solar neutrinos. The expected event rate from the
SSMSOLBP2004  is 131${}^{+12}_{-10}$ SNU, with contributions of 69.6 SNU from
$pp$ neutrinos, 34.8 SNU from 7Be neutrinos, 13.9 SNU from ${}^{8}{\rm B}$
neutrinos, 2.9 SNU from $pep$ neutrinos and the remainder from CNO cycle
neutrinos. SAGE used 50 tons of gallium in metallic form and GALLEX/GNO used
30 tons of gallium in a GaCl${}_{3}\cdot$HCl solution. The lifetime of 71Ge is
16.5 days and a typical exposure time for one run was 28 days. By the middle
of 1990s, a deficit of solar neutrinos had been observed at SAGE and GALLEX,
where the predicted event rate was mainly coming from robust sources such as
$pp$ and 7Be neutrinos. The final results of the gallium experiments are shown
here but the conclusion had not been changed since the middle of the 1990s.
The average event rates observed by SAGE and GALLEX/GNO were

$\displaystyle\phi(SAGE)=65.4^{+3.1}_{-3.0}(stat.)^{+2.6}_{-2.8}(sys.)~{}{\rm
SNU}$
$\displaystyle\phi(GALLEX)=73.1^{+6.1}_{-6.0}(stat.)^{+3.7}_{-4.1}(sys.)~{}{\rm
SNU}$
$\displaystyle\phi(GNO)=62.9^{+5.5}_{-5.3}(stat.)^{+2.5}_{-2.5}(sys.)~{}{\rm
SNU}~{}.$

Combining these resultsSAGE2009 , the flux measured by the gallium experiments
was

$\displaystyle\phi(gallium)=66.1\pm 3.1~{}~{}{\rm SNU}$

The observed flux is 50% of the expectation from the SSMSOLBP2004 .

Since it was difficult to attribute the deficits of the neutrino event rates
at the Homestake, Kamiokande and SAGE/GALLEX experiments to potential problems
in the SSM, the possibility of solar neutrino oscillations was extensively
discussed in the mid 1990s. Assuming two types of neutrinos, the relation
between the mass eigenstates of the two neutrinos ($\nu_{1}$ and $\nu_{2}$)
and their interaction eigenstates($\nu_{e}$ and $\nu_{X}$(X=$\mu,\tau$)) is
expressed as

$\displaystyle\left(\begin{array}[]{c}\nu_{e}\\\ \nu_{X}\\\
\end{array}\right)$ $\displaystyle=$
$\displaystyle\left(\begin{array}[]{cc}\cos\theta&\sin\theta\\\
-\sin\theta&\cos\theta\\\ \end{array}\right)\left(\begin{array}[]{c}\nu_{1}\\\
\nu_{2}\\\ \end{array}\right)~{},$ (7)

where $\theta$ is the mixing angle. Solving the time evolution of the neutrino
wave function, the probability that produced as electron-type neutrinos are
observed as eletron-type neutrinos is

$\displaystyle P(\nu_{e}\rightarrow\nu_{e})$ $\displaystyle=$ $\displaystyle
1-\sin^{2}2\theta\times\sin^{2}\left(1.27\times\Delta
m^{2}\frac{L}{E}\right)~{},$

where $\Delta m^{2}$ is the mass squared difference ($m_{2}^{2}-m_{1}^{2}$) in
units of eV2, $L$ is the neutrino travel length in meters, and $E$ is neutrino
energy in MeV. If the argument of the last sine function, $1.27\times\Delta
m^{2}\frac{L}{E}$, is much larger than $2\pi$, it averages out and the
survival probability becomes :

$\displaystyle P(\nu_{e}\rightarrow\nu_{e})$ $\displaystyle=$ $\displaystyle
1-{1\over 2}\sin^{2}2\theta~{}.$

In the case of solar neutrino oscillation, the effect of matter in the sun and
the earth must be considered. The matter effect was originally discussed by L.
WolfensterinSOLMSWW  in 1978. P. Langacker, J. P. Leveille and J. Sheiman
corrected a sign mistake in the Wolfensterin’s paper in 1983LLS1983 . Then in
1985, S. P. Mikheyev and A. Y. Smirnov pointed out that the significant
deficit of the event rate in Homestake, especially much less than the half of
the expectation, can be explained by the matter effectSOLMSWMS . As you can
see in the upper equation, the $P(\nu_{e}\rightarrow\nu_{e})$ cannot be less
than 0.5, but the matter effect can make it much less than 0.5 if $\Delta
m^{2}>0$, i.e. $m_{2}>m_{1}$. Thus, the mass ordering of $m_{2}$ and $m_{1}$
was determined by the solar neutrino observations. In 1993, global analyses
had been performedKRAPET1993 ; HATALANG1993  and a typical contour plot of the
oscillation parameters at that time is shown in Fig.9.

Figure 9: Global analysis performed by Hata and Langacker in 1993HATALANG1993
.

The two solutions shown in the figure are called the SMA (small mixing angle)
and LMA (large mixing angle) solutions for $\sin^{2}2\theta\sim 10^{-2}$ and
$\sin^{2}2\theta\sim 0.6$, respectively.

To obtain information about neutrino oscillations, it was necessary to measure
something that is independent of solar models. Possibilities were the shape of
the energy spectrum and the time variation of solar neutrino event rates, such
as the day/night difference. Another possibility, which is more robust, was a
comparison between event rates measured with charged current and neutral
current interactions, which are sensitive to only ${\nu}_{\rm e}$ and all
neutrino types, respectively. Regarding the shape of the energy spectrum and
the day/night difference, Fig.10 shows the neutrino survival probability as a
function of energy for each solution.

Super-Kamiokande aimed to measure the energy spectrum shape distortion, which
is expected for SMA, and the day/night difference, which is expected for LMA
with smaller $\Delta m^{2}$. As will be described in Section 9, the first
model-independent discovery of neutrino oscillations was in a comparison
between a charged current measurement by SNO (i.e. ${\nu}_{\rm e}$ flux
measurement) and an electron-scattering measurement by Super-Kamiokande (which
had contributions from $\nu_{\rm\mu}$ and ${\nu}_{\rm\tau}$).

Figure 10: Neutrino survival probability as a function of energy for typical
oscillation parameters in each solution. The top plot is the predicted solar
neutrino spectrum from the SSM.

##  6 Super-Kamiokande

The Super-Kamiokande (SK) detector is a 50,000-ton water Cherenkov detector
located 1000 meters underground in the Kamioka Mine in Japan. Yoji Totsuka led
the detector construction and initial analyses of SK data. The detector has an
inner active volume (32,000 tons) viewed by 11,146 20-inch diameter
photomultipliers (PMTs). The fiducial volume for the solar neutrino
measurement is 22,500 tons, defined by the volume more than 2 m from the
surface of the PMTs. A schematic view of the SK detector is shown in Fig.11.

Figure 11: Schematic view of the Super-Kamiokande detector.

SK has measured ${}^{8}{\rm B}$ neutrinos using neutrino–electron scattering
in the same manner as Kamiokande. The main difference between Super-Kamiokande
and Kamiokande is the 30 times larger fiducial volume and increased fraction
of photo-sensitive coverage by a factor of 2, which enabled the energy
threshold to be lowered below 5 MeV.

To measure the ${}^{8}{\rm B}$ solar neutrino flux energy spectrum with high
precision, special care was taken in SK. The absolute energy of the detector
was calibrated using an electron linear accelerator (LINAC)LINACPAP  installed
at the detector site. The LINAC system could generate mono-energetic electrons
and inject them at various positions in the detector. The LINAC system
provided a very precise energy scale calibration, but it is only accurate for
vertical downward-going events. To calibrate the angular dependence of the
energy scale, a 16N radioactive sourceSKN16  was used. 16N atoms are produced
by fast neutron capture by oxygen nuclei in water. Neutrons were generated by
a commercially built deuteron–tritium generator which produced 106 14.2-MeV
neutrons per pulse. The main decay mode of 16N is an electron with a 4.3-MeV
maximum energy coincident with a 6.1-MeV gamma ray. A setup of the DT
generator was deployed in the SK tank, and it is raised by about 2 m after it
emits neutrons in order to avoid shadowing of the Cherenkov light. Because of
the precise energy calibration by the LINAC and DT systems, the absolute
energy scale of the SK detector was calibrated with an accuracy of 0.64% (rms)
in the first phase of the SK detector (SK-I) and was improved to 0.53 % in the
fourth phase.

SK-I ran for 1496 live-days from May 1996 to July 2001SOLSK2001 ; SOLSKFULL ;
SOLSK2002 . In November 2001, a chain reaction implosion destroyed more than
half of the PMTs, such that the second phase (SK-II) ran for 791 live-days
from December 2002 to October 2005, using 5,182 ID PMTs with 19% photocathode
coverageSOLSK2008 . Since SK-II the ID PMTs have been covered in fiber-
reinforced plastic cases with an acrylic window to prevent similar accidents.
The detector was fully reconstructed from October 2005 to July 2006 and the
third phase (SK-III) ran for 548 live-days from October 2006 to August
2008SOLSK2010 . The readout electronics were replaced in September 2008 and
the fourth phase (SK-IV) ran for 2970 live-days until May 2018SOLSK2020 . The
SK tank was refurbished to make it leak-tight for a future upgrade (as
explained later) from June 2018 to January 2019. The fifth phase (SK-V) ran
from February 2019 through June 2020 with pure water. 13 tons of
Gd2(SO4)${}_{3}\cdot$H2O was loaded into the tank water to make a 0.01 %wt Gd
solution from July to August in 2020 and the sixth phase (SK-VI) is running
with a neutron tagging capability. Solar neutrino data analyses were performed
for all SK phases and were completed by SK-IV. Figure 12 shows the angular
distribution of solar neutrino candidates with respect to the direction of the
sun from SK-IV. Solar neutrino events are clearly seen above the flat
background distribution.

Figure 12: Angular distribution with respect to the direction of the sun in
Super-Kamiokande phase IVSOLSK2020 .

Table 2 shows live-times, energy thresholds, measured fluxes, ratios compared
with a Monte Carlo simulation (in which ${}^{8}{\rm B}$ flux of 5.25$\times
10^{6}$/cm2/s is assumed) and the numbers of extracted signals for each SK
phase, and combined results.

Phase | Livetime | Threshold | Measured Flux | DATA/MC | # of signals
---|---|---|---|---|---
| (days) | (MeV) | ($10^{6}$/cm2/s) |  | ($\pm$stat. only)
SK-I | 1496 | 4.5 | 2.38$\pm 0.02\pm 0.08$ | 0.453$\pm 0.005^{+0.016}_{-0.014}$ | 22443${}^{+227}_{-225}$
SK-II | 791 | 6.5 | 2.41$\pm 0.05^{+0.16}_{-0.15}$ | 0.459$\pm 0.010\pm 0.030$ | 7210${}^{+153}_{-151}$
SK-III | 548 | 4.0 | 2.40$\pm 0.04\pm 0.05$ | 0.458$\pm 0.007\pm 0.010$ | 8148$\pm 133$
SK-IV | 2970 | 3.5 | 2.33$\pm 0.01\pm 0.03$ | 0.443$\pm 0.003\pm 0.006$ | 63890${}^{+381}_{-379}$
Combined | 5805 | - | 2.35$\pm 0.01\pm 0.04$ | 0.447$\pm 0.002\pm 0.008$ | More than
|  |  |  |  | 100k events
Table 2: Summary of flux measurements at Super-Kamiokande.

The energy threshold of the data analysis was 4.5 MeV (kinetic energy) in SK-I
but was lowered to 3.5 MeV in SK-IV. That was possible because the radon
background in the tank water was reduced by a stable laminar flow in the tank
given by a precise temperature control.

In addition, the systematic error was reduced by more precise calibrations and
detailed studies of the efficiencies of various cuts. When SK started data
collection in 1996, the solar activity was near the minimum. The SK data
covered almost two solar cycles until the end of SK-IV. Figure 13 shows the
measured yearly fluxes compared with the solar activity. The measured fluxes
are consistent with a flat distribution within statistical and systematic
errors and no correlation with the solar activity was observed.

Figure 13: Yearly plot of the ${}^{8}{\rm B}$ solar neutrino flux measured by
SK, shown as red points with error bars. The black dots show the number of
sunspots, from SUNSPOT .

The energy spectrum shape is important for the discussion of neutrino
oscillations. Figure 14 shows energy spectra of solar neutrino signals
observed in each SK phase compared with the expected spectrum without neutrino
oscillations. A ${}^{8}{\rm B}$ flux of 5.25$\times 10^{6}$/cm2/s is assumed
in this figure, based on the SNO neutral current measurement, consistent with
the SSM predictions.

Figure 14: Energy spectrum of the solar neutrino signal observed in each SK
phase. The vertical axis is normalized by the spectrum without neutrino
oscillations with a flux of 5.25$\times 10^{6}$/cm2/s. The blue and green
histograms show the expectations with neutrino oscillations with parameters
from the KamLAND reactor measurementKAMLAND  and solar global analysis,
respectively. The bands around the horizontal line show $\pm 1\sigma$ energy-
correlated systematic errors.

The observed energy spectrum shapes in SK-I, II and III are consistent with a
flat oscillation probability. The SK-IV spectrum shape disfavors a flat
probability with a significance of $\sim 1\sigma$, which is consistent with
the shape expected from the oscillation parameters obtained by the KamLAND
reactor measurementKAMLAND .

The day/night flux difference was evaluated by an asymmetry parameter
($A_{DN}$) defined as $\frac{(day-night)}{\frac{1}{2}(day+night)}$. The
asymmetry parameters measured by SK-ISOLSK2002 , SK-IISOLSK2008 , SK-
IIISOLSK2010  and SK-IVSOLSK2020  were

$\displaystyle A^{SK-I}_{DN}$ $\displaystyle=$ $\displaystyle-0.021\pm
0.020\mbox{(stat.)}^{+0.013}_{-0.012}\mbox{(sys.)}$ $\displaystyle A^{SK-
II}_{DN}$ $\displaystyle=$ $\displaystyle-0.063\pm 0.042\mbox{(stat.)}\pm
0.037\mbox{(sys.)}$ $\displaystyle A^{SK-III}_{DN}$ $\displaystyle=$
$\displaystyle-0.056\pm 0.031\mbox{(stat.)}\pm 0.013\mbox{(sys.)}$
$\displaystyle A^{SK-IV}_{DN}$ $\displaystyle=$ $\displaystyle-0.021\pm
0.011\mbox{(stat.)}\hskip 28.45274pt\mbox{(preliminary)}$

Since $A_{DN}$ depends on $\Delta m^{2}$, as shown by the red curve in Fig.15,
we can measure $\Delta m^{2}$ by $A_{DN}$. This is a unique method for
measuring $\Delta m^{2}$ using solar neutrinos and is likely to be the only
method for neutrinos. (Note that $\Delta m^{2}$ can be measured for anti-
neutrinos using reactor neutrinos.) To demonstrate the accuracy of the $\Delta
m^{2}$ measurement, $A_{DN}$ for SK-IV is shown in Fig.15 by black data points
with statistical errors.

Figure 15: Expected asymmetry from matter oscillation in the earth as a
function of $\Delta m^{2}_{21}$ (red curve) and SK-IV data with its
statistical error (black data points).

##  7 SNO

The Sudbury Neutrino Observatory (SNO) detector was a 1000-ton heavy water
(D2O) Cherenkov detector located 2090 meters underground in the Creighton Mine
near Sudbury, Canada. It used 9456 8-inch diameter PMTs to view heavy water
contained in an acrylic vessel. The SNO detector could measure the $\nu_{e}$
flux from 8B neutrinos and the flux of all active neutrino flavors through the
following interactions:

$\begin{array}[]{lcll}\nu_{e}+d&\rightarrow&p+p+e^{-}&\hskip
3.61371pt\mbox{(charged current (CC))}\\\
\nu_{x}+d&\rightarrow&p+n+\nu_{x}&\hskip 3.61371pt\mbox{(neutral current
(NC))}\\\ \nu_{x}+e^{-}&\rightarrow&\nu_{x}+e^{-}&\hskip
3.61371pt\mbox{(electron scattering (ES))}\\\ \end{array}$

where $\nu_{x}$ is any of $\nu_{e}$, $\nu_{\mu}$ or $\nu_{\tau}$. The first
phase of SNO data collection (SNO-I) was undertaken using a pure D2O target
over 306 days from November 1999 to May 2001SOLSNO1 . Free neutrons from the
NC interaction were thermalized and 6.25-MeV $\gamma$ rays were emitted
following their capture by deuterons. The capture efficiency was about 30%.
The measured fluxes were

$\displaystyle\phi(^{8}{\rm B})^{CC}_{SNO-I}$ $\displaystyle=$ $\displaystyle
1.76\pm 0.05\mbox{(stat.)}\pm 0.09\mbox{(sys.)}\times 10^{6}/cm^{2}/s$
$\displaystyle\phi(^{8}{\rm B})^{ES}_{SNO-I}$ $\displaystyle=$ $\displaystyle
2.39^{+0.24}_{-0.23}\mbox{(stat.)}\pm 0.12\mbox{(sys.)}.\times
10^{6}/cm^{2}/s$ $\displaystyle\phi(^{8}{\rm B})^{NC}_{SNO-I}$
$\displaystyle=$ $\displaystyle
5.09^{+0.44}_{-0.43}\mbox{(stat.)}^{+0.46}_{-0.43}\mbox{(sys.)}\times
10^{6}/cm^{2}/s~{}.$

In the second phase of the SNO experiment (SNO-II), 2 tons of NaCl were added
to the D2O target to enhance the detection efficiency of the NC channelSOLSNO2
. Thermalized neutrons were captured by 35Cl nuclei, resulting in the emission
of a $\gamma$-ray cascade with a total energy of 8.6 MeV. The CC and NC
signals were statistically separated using the isotropy of the Cherenkov light
pattern and each event’s angle to the sun. The forward peaked signal was due
to ES and the backward distribution was due to CC interactions. NC events were
isotropic with respect to the solar direction. The measured fluxes in SNO-II
were

$\displaystyle\phi(^{8}{\rm B})^{CC}_{SNO-II}$ $\displaystyle=$ $\displaystyle
1.68\pm 0.06\mbox{(stat.)}^{+0.08}_{-0.09}\mbox{(sys.)}\times 10^{6}/cm^{2}/s$
$\displaystyle\phi(^{8}{\rm B})^{ES}_{SNO-II}$ $\displaystyle=$ $\displaystyle
2.35\pm 0.22\mbox{(stat.)}^{+0.15}_{-0.15}\mbox{(sys.)}\times 10^{6}/cm^{2}/s$
$\displaystyle\phi(^{8}{\rm B})^{NC}_{SNO-II}$ $\displaystyle=$ $\displaystyle
4.94\pm 0.21\mbox{(stat.)}^{+0.38}_{-0.34}\mbox{(sys.)}\times
10^{6}/cm^{2}/s.$

In the third phase of SNO (SNO-III), 3He proportional counters were deployed
in the heavy water and the NC events were measured independentlySOLSNO3 . The
NC flux measured by SNO-III was

$\displaystyle\phi(^{8}{\rm B})^{NC}_{SNO-III}$ $\displaystyle=$
$\displaystyle
5.54^{+0.33}_{-0.31}\mbox{(stat.)}^{+0.36}_{-0.34}\mbox{(sys.)}\times
10^{6}/cm^{2}/s.$

The SNO group performed a combined analysisSOLSNOCOMB  of all three phases and
the obtained result was

$\displaystyle\phi(^{8}{\rm B})^{NC}_{SNO~{}combined}$ $\displaystyle=$
$\displaystyle 5.25\pm 0.16\mbox{(stat.)}^{+0.11}_{-0.13}\mbox{(sys.)}\times
10^{6}/cm^{2}/s.$

Compared with the ${}^{8}{\rm B}$ flux value in Table 1, the observed
${}^{8}{\rm B}$ flux with NC by SNO agrees well with the prediction within the
errors. Combining the statistical and systematic errors, the total error of
the flux observed by SNO is 3.8%, which is better than that of the SSM
prediction by a factor of 3. Therefore, the SNO value was used to make plots
of SK in the previous section and will be used in the discussion of the global
oscillation analysis in Section 9.

##  8 Borexino

Borexino is a liquid scintillator detector with an active mass of 278 tons of
pseudocumene located in the Gran Sasso Laboratory. Scintillation light is
detected via 2212 8-inch PMTs uniformly distributed on the inner surface of
the detector. Because of the high light yield of a liquid scintillator
compared with Cherenkov light, Borexino is sensitive to sub-MeV solar
neutrinos. The first 7Be solar neutrino measurement was reported in
Borexino-1st , based on 192 days of data taken from May 2007 to April 2008\.
The 0.862-MeV monoenergetic 7Be neutrinos were detected by neutrino–electron
scattering. The energy spectrum of observed events was deconvoluted using the
expected shape of the recoil electrons and possible background sources. Thus,
the extracted 7Be neutrino event rate was

$\displaystyle 49\pm 3\mbox{(stat.)}\pm 4\mbox{(sys.)}~{}{\rm counts}/({\rm
day}\cdot 100{\rm ton)},$

while the expected event rate from the SSM was $74\pm 4~{}{\rm counts}/({\rm
day}\cdot 100{\rm ton})$. The deficit of the observed 7Be neutrino event rate
is consistent with the expectation based on neutrino oscillations. Borexino
also succeeded in observing $pep$, $pp$ and CNO solar neutrinos, reported in
Borexino-pep , Borexino-pp  and Borexino-CNO , respectively. The Borexino
group corrected the effect of neutrino oscillations and obtained fluxes of
$pp$, 7Be, $pep$ and CNO neutrinos from the second phase of Borexino
asBorexino2 ; Borexino-CNO

$\displaystyle\phi(pp)^{Osc.corrected}_{Borexino}$ $\displaystyle=$
$\displaystyle 6.1\pm 0.5\mbox{(stat.)}^{+0.3}_{-0.5}\mbox{(sys.)}\times
10^{10}/cm^{2}/s$ $\displaystyle\phi(^{7}{\rm Be})^{Osc.corrected}_{Borexino}$
$\displaystyle=$ $\displaystyle 4.99\pm
0.11\mbox{(stat.)}^{+0.06}_{-0.08}\mbox{(sys.)}\times 10^{9}/cm^{2}/s$
$\displaystyle\phi(pep(HZ/LZ))^{Osc.corrected}_{Borexino}$ $\displaystyle=$
$\displaystyle 1.27/1.39\pm
0.19\mbox{(stat.)}^{+0.08}_{-0.12/-0.13}\mbox{(sys.)}\times 10^{8}/cm^{2}/s$
$\displaystyle\phi({\rm CNO})^{Osc.corrected}_{Borexino}$ $\displaystyle=$
$\displaystyle 7.0^{+3.0}_{-2.0}\mbox{(sys.)}\times 10^{8}/cm^{2}/s$

These fluxes are compared with the SSM predictions in Table 1 and are
consistent with each other within the experimental errors.

##  9 Solar Neutrino Oscillations

Precise solar neutrino measurements have shown that the solar neutrino problem
is due to neutrino oscillations. In this section, a brief history of and the
latest results for solar neutrino oscillations are discussed.

###  9.1 Evidence of solar neutrino oscillations

In March 2001, the SK collaboration released results of the precise
measurement of the ${}^{8}{\rm B}$ flux using 1258 days of SK dataSOLSK2001 .
SK measured ${}^{8}{\rm B}$ solar neutrinos using neutrino–electron scattering
(ES), in which $\nu_{\rm\mu}$ and ${\nu}_{\rm\tau}$ contribute in addition to
${\nu}_{\rm e}$ because the cross section of $\nu_{\nu/\tau}e^{-}$ scattering
is about 1/($6\sim 7$) of that for $\nu_{e}e^{-}$ scattering. In June 2001,
the SNO collaboration released the first result of the charged current (CC),
i.e. ${\nu}_{\rm e}$, measurement, including the plot in Fig.16, which
demonstrated that $\nu_{\mu/\tau}$ exist with more than 3$\sigma$
significanceSNOfirstCC . That was the first direct evidence for solar neutrino
oscillations.

Figure 16: ${\nu}_{\rm e}$ flux and $\nu_{\mu/\tau}$ flux contour obtained
from the results of SK and SNO in 2001SNOfirstCC . Each band shows the $\pm
1\sigma$ range of each measurement.

The SNO collaboration published NC current measurements, the results of which
were described above in section 7. The SK collaboration provided further data
for analysis and improved the accuracy of the ES measurement. The plot in
Fig.17 uses the latest data from SK and SNO, including NC data, showing that
the significance of $\nu_{\mu/\tau}$ had been greatly improved. The
measurements of SK and SNO are consistent with each other.

Figure 17: Latest ${\nu}_{\rm e}$ flux and $\nu_{\mu/\tau}$ flux contour
obtained from the results of SKSOLSK2020  and SNOSOLSNO1 ; SOLSNO2 ; SOLSNO3 ;
SOLSNOCOMB . Each band shows the $\pm 1\sigma$ range for each measurement.

###  9.2 Determination of oscillation parameters

In the three flavor neutrino framework, the relation between the mass and
interaction eigenstates is described by

$\displaystyle\left(\begin{array}[]{c}{\nu}_{\rm e}\\\ \nu_{\rm\mu}\\\
{\nu}_{\rm\tau}\\\ \end{array}\right)$ $\displaystyle=$
$\displaystyle\left(\begin{array}[]{ccc}U_{e1}&U_{e2}&U_{e3}\\\ U_{\mu
1}&U_{\mu 2}&U_{\mu 3}\\\ U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\\\
\end{array}\right)\left(\begin{array}[]{c}\nu_{1}\\\ \nu_{2}\\\ \nu_{3}\\\
\end{array}\right)$ (17)

The unitary matrix $U$ is the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix
and can be decomposed into three angles and a phase:

$\displaystyle U$ $\displaystyle=$ $\displaystyle\begin{pmatrix}1&0&0\cr
0&{c_{23}}&{s_{23}}\cr
0&-{s_{23}}&{c_{23}}\cr\end{pmatrix}\begin{pmatrix}{c_{13}}&0&{s_{13}}e^{-i{\delta}}\cr
0&1&0\cr-{s_{13}}e^{i{\delta}}&0&{c_{13}}\cr\end{pmatrix}\begin{pmatrix}c_{21}&{s_{12}}&0\cr-{s_{12}}&{c_{12}}&0\cr
0&0&1\cr\end{pmatrix}$ $\displaystyle=$
$\displaystyle\begin{pmatrix}c_{12}c_{13}&s_{12}c_{13}&s_{13}e^{-i\delta}\cr-
s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta}&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta}&s_{23}c_{13}\cr
s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta}&-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta}&c_{23}c_{13}\cr\end{pmatrix}~{}~{},$

where $c_{ij}\equiv\cos\theta_{ij}$ and $s_{ij}\equiv\sin\theta_{ij}$. In
addition, the mass squared differences ($\Delta
m^{2}_{ij}(=m^{2}_{i}-m^{2}_{j})$) $\Delta m^{2}_{21}$ and $\Delta m^{2}_{32}$
affect the oscillations. In the solar neutrino oscillation analysis, the
oscillation probability can be calculated using three parameters,
$\theta_{12}$, $\theta_{13}$ and $\Delta m^{2}_{21}$, because $|\Delta
m^{2}_{21}|\ll|\Delta m^{2}_{32}|$.

The green contours in Fig.18 show the allowed region of the oscillation
parameters, $\theta_{12}$ and $\Delta m^{2}_{21}$, obtained from the SK data.
The total flux of ${}^{8}{\rm B}$ is constrained by the SNO NC flux
measurement ((5.25$\pm 0.20)\times 10^{6}$/cm2/s). The $\theta_{13}$ value is
constrained to $\sin^{2}(\theta_{13})=0.0219\pm 0.0014$ by the short baseline
reactor neutrino measurementsREACTOR13 . The LMA solution is more than
4$\sigma$-level more significant than the other solutions and the result is
consistent with the long baseline reactor measurement by KamLANDKAMLAND  shown
by the blue contours in the figure. The same plot on a linear scale is shown
in Fig.19.

Figure 18: Oscillation parameters obtained from SK dataSOLSK2020  compared
with the KamLAND reactor dataKAMLAND . The green contours show the allowed
region of $\theta_{12}$ and $\Delta m^{2}_{21}$ obtained from the SK data with
the ${}^{8}{\rm B}$ flux constrained by the SNO NC value((5.25$\pm 0.20)\times
10^{6}$/cm2/s). The lines show 1, 2, 3, 4 and 5$\sigma$ significance from
inside to outside. The light-blue filled area shows the KamLAND reactor
contour with 3$\sigma$ and the brown filled area shows the SK and KamLAND
combined result with 3$\sigma$. Figure 19: As for Fig.18 but the vertical axis
has a linear scale. The green, light-blue and brown regions show contours of
SK, KamLAND and the combination of SK and KamLAND, respectively.

Figure 20 shows the allowed region obtained by combining the SK and
SNOSOLSNOCOMB  data.

Figure 20: Oscillation parameters obtained from SK and SNO data compared with
the KamLAND reactor dataKAMLAND . The green contours show the allowed region
of $\theta_{12}$ and $\Delta m^{2}_{21}$ obtained from the SK and SNO data.
The lines show the 1, 2, 3, 4 and 5$\sigma$ significance from inside to
outside. The light-blue filled area shows the KamLAND reactor contour with
3$\sigma$, and the brown filled area shows the SK, SNO and KamLAND combined
contour with 3$\sigma$.

##  10 Conclusion and future prospects

The solar neutrino problem suggested by the Homestake experiment lead to some
very interesting outcomes. Owing to the insight of Prof. Koshiba, the solar
neutrino problem was confirmed by a water Cherenkov detector, Kamiokande. The
water Cherenkov technique was adopted in Super-Kamikande and SNO and precise
measurements of the ${}^{8}{\rm B}$ solar neutrino flux were conducted.
Especially, the flux difference between the neutral current and charged
current methods, which are sensitive to all types of neutrinos and only to
${\nu}_{\rm e}$, respectively, provided smoking gun evidence of neutrino
oscillations. All the results from solar neutrino experiments (Homestake,
Kamiokande, SAGE, GALLEX/GNO, Super-Kamiokande, SNO and Borexino) can be shown
to be consistent with the expectations from the standard solar model with
neutrino oscillations. That is a great accomplishment and it could not have
been done without the insight of Prof. Koshiba.

Is this the end of the story for solar neutrinos? I do not think so. The
measurements of the ${}^{8}{\rm B}$ spectrum shape and the day/night
difference are not yet precise enough to allow a proper discussion of neutrino
oscillations. Borexino succeeded in observing CNO neutrinos but without
sufficient precision to discuss the low and high metallicity models. The most
abundant solar neutrino source is $pp$ neutrinos and the SSM predicts its flux
with an accuracy of $\sim$1%. However, the experimental results are not yet
this precise. Something interesting might still be hidden in solar neutrinos.

## Acknowledgment

The author gratefully acknowledges the cooperation of the Super-Kamiokande
collaborators in providing the main contents of the SK results and oscillation
analyses. The author also wishes to thank the proposers of this special issue
(Profs. Mitsuaki Nozaki and Masashi Yokoyama) for giving me the opportunity to
write this article. The author thank Prof. S. T. Petcov for sending comments.

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# Fighting Game Adaptive Background Music for Improved Gameplay

Ibrahim Khan1, Thai Van Nguyen1, Chollakorn Nimpattanavong1, Ruck Thawonmas2
{1Graduate School, 2College} of Information Science and Engineering,
Ritsumeikan University, Japan
{gr0556vx,gr0557fv<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

This paper presents our work to enhance the background music (BGM) in
DareFightingICE by adding adaptive features. The adaptive BGM consists of
three different categories of instruments playing the BGM of the winner sound
design from the 2022 DareFightingICE Competition. The BGM adapts by changing
the volume of each category of instruments. Each category is connected to a
different element of the game. We then run experiments to evaluate the
adaptive BGM by using a deep reinforcement learning AI agent that only uses
audio as input (Blind DL AI). The results show that the performance of the
Blind DL AI improves while playing with the adaptive BGM as compared to
playing without the adaptive BGM.

###### Index Terms:

adaptive BGM, Rule-based adaptive background music, background music.

††publicationid: pubid: 979-8-3503-2277-4/23/$31.00 ©2023 IEEE

##  I Introduction

This research focuses on video game music in fighting games and how to use it
to enhance players’ experience. In fighting games, background music (BGM)
should change in response to the dynamic action, creating suspense and
excitement as the players engage in combat.

Our work is based on the DareFightingICE Competition, which has two tracks:
Sound Design Track and AI Track [1]. The competition has run at the IEEE
Conference on Games since 2022. The platform for this competition is
DareFightingICE – an enhanced version of FightingICE [2].

The goal of this research is to create an adaptive BGM by modifying the BGM of
DareFightingICE, and evaluate the performance of the adaptive BGM by using a
deep learning AI agent that only uses audio as input (Blind DL AI) [3]. Our
research focuses on giving players information about the state of the game
through the BGM. We are also the first group to use multiple instruments’
volumes in the adaptation of a BGM.

##  II Related Work

Since our research touches on the topic of adaptive fighting game music, we
describe a few fighting games that have adaptive BGM.

Adaptive or dynamic, as it is called in commercial fighting games, music has
been used in a few fighting games in the past. The most prominent examples are
Killer Instinct, Tekken 7, and Them’s Fightin’ Herds. For Takken 7, many
states have a more intense version of the BGM being played for the last round.
Them’s Fightin’ Herds mixes in bits of each character’s themes depending on
who’s winning. Lastly, Killer Instinct has multiple layers to its adaptive BGM
that changes according to the movement of the players as well as the actions
of the players.

While adaptive BGM exists in fighting games, it is used to enhance the overall
gaming experience of the players, however, currently, no BGM gives information
to players such as the distance between players, and the amount of health
points (HP) remaining for both players. It is also worth noting that adaptive
music exists in games outside of fighting games as well, but since our focus
is on fighting games, we only discussed adaptive music in this genre.

##  III Rule-Based Adaptive BGM

In this research, we propose an adaptive BGM that adapts to player actions and
the players’ in-game positions. The proposed adaptive BGM consists of three
different categories of instruments playing the BGM available in the winning
sound design from the 2022 DareFightingICE competition. The BGM’s instruments
were separated using an AI service called Moises [4]. The resulting three
different instrument groups are the Drums, the Strings, and the Others
category available after the separation. The BGM adjusts by altering the
loudness of the instruments. The game elements in use are both players’ HP and
the distance between the two players (PD). The HP is the number of hits a
player can take before losing. The design of the proposed adaptive BGM is
illustrated in Fig. 1.

Figure 1: Outline of Adaptive BGM.

In Fig. 1, the strings are connected to player 1’s HP, and the others are
connected to player 2’s HP. Lastly, the drums are connected to PD.

The maximum HP for one player per round is 400, and the PD is 800 pixels
horizontally. The HP of both players and their PD are divided into different
levels to change the volumes of the different groups of instruments gradually.
The levels are empirically selected due to the lack of existing research when
it comes to adaptive BGM using volume modulation.

The levels for HP are 400, 300, 250, 200, 150, 100, and 50, which are
connected to the respective instrument group’s volume levels of 75%, 60%, 55%,
40%, 35%, 25%, and 10% respectively. For PD, the levels are 800, 600, 500,
400, 300, 60, and 0, which are connected to the drums’ volume levels of 10%,
20%, 30%, 40%, 50%, 60%, and 75%.

The adaptive BGM is created in DareFightingICE. Since there has been a recent
update to the DareFightingICE platform from version 5.2 (used in the 2022
competition) to version 6.0, we use the latest version.

##  IV Experiments

For evaluation of the adaptive BGM, we conducted an objective evaluation, the
details of which are as follows.

We use the aforementioned Blind DL AI. Our protocol for this evaluation is to
train the Blind DL AI with and without the adaptive BGM and then compare the
performances of the AI agents. We hypothesize that if the performance of the
Blind DL AI is better with the adaptive BGM then the adaptive BGM conveys
useful information. we did not compare our approach with previous approaches
since they do not exist when it comes to fighting games.

We trained the Blind DL AI for 900 rounds on DareFightingICE (1 game has 3
rounds) against MCTSAI23i, a sample agent in the 2023 competition using Monte-
Carlo tree search [5]. The same approach was used in the 2022 competition to
train the Blind DL AI.

We used similar environments as in the 2022 DareFightingICE Competition. More
specifically, six computers were used that have the same specification, i.e.,
CPU: Intel(R) Xeon(R) W-2135 CPU@ 3.70GHz 3.70 GHz, RAM: 16 GB, GPU: NVIDIA
Quadro P1000 4GB VRAM, and OS: Windows 10.

###  IV-A Results

Since the Blind DL AI had three different audio encoders [2] as an option, the
experiments were run on each encoder for both versions, i.e., one-dimensional
Convolutional Neural Network (1D-CNN), Fast Fourier Transform (FFT), and Mel-
Spectrogram (Mel-Spec).

We evaluated the performance of each trained Blind DL AI by making it fight
against the aforementioned opponent AI agent for 90 rounds. The ratio of the
number of wins111In the game, the round winner is either the one with a non-
zero HP while its opponent’s HP has reached zero or the one with the higher HP
when the round-length limit of 60 s has reached. over 90 rounds ($n=90$), Eqn.
(1), and the average HP difference at the end of round $r$ between the trained
AI agent and its opponent, Eqn. (2), are then calculated. The equations and
details above are taken from previous work [3].

$win_{ratio}=\frac{\textit{winning rounds}}{\textit{n}}$ (1)
$avgHP_{diff}=\frac{\sum_{r=1}^{r=n}(HP_{r}^{self}-HP_{r}^{opp})}{\textit{n}}$
(2)

TABLE I: Performance of the blind DL AI with winner sound design of the 2022 DareFightingICE competition in DareFighingICE 6.0. Sound design | Encoder | $win_{ratio}$ | $avgHP_{diff}$
---|---|---|---
Winner | 1D-CNN | 0.54 | 12.66
Winner | FFT | 0.52 | 27.03
Winner | Mel-spectrogram | 0.56 | 34.23
Winner Adaptive | 1D-CNN | 0.81 | 101.17
Winner Adaptive | FFT | 0.94 | 136.14
Winner Adaptive | Mel-spectrogram | 0.68 | 74.56

As shown from the results in Table I, the Blind DL AI performs better with the
adaptive BGM. For each encoder, Blind DL AI also performs better with our
adaptive BGM. This proves our hypothesis that the adaptive BGM provides useful
information with FFT being the best encoder. Example gameplay videos of blind
DL AI with each audio encoder, where the blind DL AI is player 1 and MCTSAI23i
is player 2, as well as the separated audio file of each group of instruments
and the modified code for the adaptive BGM, can be found on this link222Link
to videos and other files: https://tinyurl.com/aBGM-CoG2023. On the day of the
presentation we will ask for volunteers from the audience to test our adaptive
BGM.

##  V Conclusions And Future Work

This paper presented a rule-based adaptive background music (BGM) system that
consists of three different categories of instruments playing the BGM of the
winner sound design from the 2022 DareFightingICE Competition. The proposed
adaptive BGM adapts by changing the volumes of the different categories of
instruments. Each category is connected to a different element of the game.
The paper also showed that the performance of a deep reinforcement learning AI
agent using only audio data as its input, called Blind DL AI, improved while
playing with the adaptive BGM as compared to playing without it.

## References

  * [1] I. Khan, T. V. Nguyen, X. Dai, and R. Thawonmas, “DareFightingICE Competition: A Fighting Game Sound Design and AI Competition,” _2022 IEEE Conference on Games (CoG)_ , pp. 478–485, 2022.
  * [2] F. Lu, K. Yamamoto, L. H. Nomura, S. Mizuno, Y. M. Lee, and R. Thawonmas, “Fighting Game Artificial Intelligence Competition Platform,” _2013 IEEE 2nd Global Conference on Consumer Electronics (GCCE)_ , pp. 320–323, Oct. 2013. (https://www.ice.ci.ritsumei.ac.jp/ ftgaic/index.htm)
  * [3] T. Van Nguyen, X. Dai, I. Khan, R. Thawonmas, and H. V. Pham, “A Deep Reinforcement Learning Blind AI in DareFightingICE,” _2022 IEEE Conference on Games (CoG)_ , pp. 632–637, 2022.
  * [4] Moises Systems. 2023. Moises. [Online]. Available: https://moises.ai/
  * [5] M. Ishihara, T. Miyazaki, C. Y. Chu, T. Harada, and R. Thawonmas, “Applying and Improving Monte-Carlo Tree Search in a Fighting Game AI,” in _Proceedings of the 13th International Conference on Advances in Computer Entertainment Technology_ , pp. 1-6, Nov. 2016.