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First Indication of Terrestrial Matter Effects on Solar Neutrino Oscillation
A. Renshaw,7,† K. Abe,1,29 Y. Hayato,1,29 K. Iyogi,1 J. Kameda,1,29 Y. Kishimoto,1,29 M. Miura,1,29 S. Moriyama,1,29
M. Nakahata,1,29 Y. Nakano,1 S. Nakayama,1,29 H. Sekiya,1,29 M. Shiozawa,1,29 Y. Suzuki,1,29 A. Takeda,1,29 Y. Takenaga,1
T. Tomura,1,29 K. Ueno,1 T. Yokozawa,1 R. A. Wendell,1,29 T. Irvine,2 T. Kajita,2,29 K. Kaneyuki,2,29,* K. P. Lee,2
Y. Nishimura,2 K. Okumura,2,29 T. McLachlan,2 L. Labarga,3 S. Berkman,4 H. A. Tanaka,4,31 S. Tobayama,4 E. Kearns,5,29
J. L. Raaf,5 J. L. Stone,5,29 L. R. Sulak,5 M. Goldhabar,6,* K. Bays,7 G. Carminati,7 W. R. Kropp,7 S. Mine,7 M. B. Smy,7,29
H. W. Sobel,7,29 K. S. Ganezer,8 J. Hill,8 W. E. Keig,8 N. Hong,9 J. Y. Kim,9 I. T. Lim,9 T. Akiri,10 A. Himmel,10
K. Scholberg,10,29 C. W. Walter,10,29 T. Wongjirad,10 T. Ishizuka,11 S. Tasaka,12 J. S. Jang,13 J. G. Learned,14 S. Matsuno,14
S. N. Smith,14 T. Hasegawa,15 T. Ishida,15 T. Ishii,15 T. Kobayashi,15 T. Nakadaira,15 K. Nakamura,15,29 Y. Oyama,15
K. Sakashita,15 T. Sekiguchi,15 T. Tsukamoto,15 A. T. Suzuki,16 Y. Takeuchi,16 C. Bronner,17 S. Hirota,17 K. Huang,17
K. Ieki,17 M. Ikeda,17 T. Kikawa,17 A. Minamino,17 T. Nakaya,17,29 K. Suzuki,17 S. Takahashi,17 Y. Fukuda,18 K. Choi,19
Y. Itow,19 G. Mitsuka,19 P. Mijakowski,35 J. Hignight,20 J. Imber,20 C. K. Jung,20 C. Yanagisawa,20 H. Ishino,21
A. Kibayashi,21 Y. Koshio,21 T. Mori,21 M. Sakuda,21 T. Yano,21 Y. Kuno,22 R. Tacik,23,32 S. B. Kim,24 H. Okazawa,25
Y. Choi,26 K. Nishijima,27 M. Koshiba,28 Y. Totsuka,28,* M. Yokoyama,28,29 K. Martens,29 Ll. Marti,29 M. R. Vagins,29,7
J. F. Martin,30 P. de Perio,30 A. Konaka,32 M. J. Wilking,32 S. Chen,33 Y. Zhang,33 and R. J. Wilkes34(The Super-Kamiokande Collaboration)
1

Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada
5
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
6
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
7
Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697-4575, USA
8
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
9
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
10
Department of Physics, Duke University, Durham North Carolina 27708, USA
11
Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan
12
Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan
13
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
14
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
15High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
16
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan17
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan18
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
19
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan20
Department of Physics and Astronomy, State University of New York at Stony Brook, New York 11794-3800, USA
21
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
22
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
23
Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan S4SOA2, Canada
24
Department of Physics, Seoul National University, Seoul 151-742, Korea
25
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka 425-8611, Japan
26
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
27
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
28
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
29
Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study,
University of Tokyo, Kashiwa, Chiba 277-8582, Japan30
Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S1A7, Canada
31
Institute of Particle Physics, Canada, University of Toronto, 60 Saint George Street, Toronta, Ontario M5S1A7, Canada
32
TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T2A3, Canada
33
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
34
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
35
National Centre For Nuclear Research, 00-681 Warsaw, Poland(Received 18 December 2013; published 7 March 2014)

20031-9007=14=112(9)=091805(6)091805-1© 2014 American Physical Society

PRL 112, 091805 (2014)

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We report an indication that the elastic scattering rate of solar 8 B neutrinos with electrons in the SuperKamiokande detector is larger when the neutrinos pass through Earth during nighttime. We determine the
day-night asymmetry, defined as the difference of the average day rate and average night rate divided by theaverage of those two rates, to be ½−3.2  1.1ðstatÞ  0.5ðsystÞ%, which deviates from zero by 2.7σ. Since
the elastic scattering process is mostly sensitive to electron-flavored solar neutrinos, a nonzero day-night
asymmetry implies that the flavor oscillations of solar neutrinos are affected by the presence of matterwithin the neutrinos’ flight path. Super-Kamiokande’s day-night asymmetry is consistent with neutrino
oscillations for 4 × 10−5 eV2 ≤ Δm221 ≤ 7 × 10−5 eV2 and large mixing values of θ12 , at the 68% C.L.
DOI: 10.1103/PhysRevLett.112.091805

PACS numbers: 14.60.Pq, 26.65.+t, 96.50.sf

Neutrino flavor oscillations occur when the phase difference of a superposition of massive neutrinos changes. Suchphase changes occur while neutrinos are propagating in
vacuum (vacuum oscillations). Wolfenstein [1] realized thatthe neutrino-electron elastic forward-scattering amplitudeintroduces additional phase shifts. As a consequence,neutrinos propagating in matter will oscillate differently
than neutrinos propagating through vacuum. These matter
effects are a fundamental prediction of the present theory ofneutrino oscillations. In this Letter, we report an indicationof the existence of such matter effects.
Vacuum oscillations cannot easily explain a solar neutrino electron-flavor survival probability Pee which ismeasured to be significantly below one half [2–8], in theenergy region of ∼8 to 18 MeV. Mikheyev and Smirnov [9]explained this experimental fact as the adiabatic transformation of the neutrinos through the varying solar density
causing a resonant conversion to the second mass eigenstate inside the Sun (MSW resonance). Lower energy(< 2 MeV) solar neutrino data [10] are still described well
as averaged vacuum oscillations. However, searches for thetransition of Pee from the MSW resonance to vacuum
oscillations (near 3 MeV) were, so far, unsuccessful [8,11].
Moreover, these previous observations imply matter effects
only indirectly, since there is no “control beam” of solar
neutrinos that only propagates in vacuum. Atmospheric
neutrino experiments can probe the existence of matter
effects within the Earth in a similar fashion, and while there
is currently no significant departure of present atmospheric
data [12,13] from the vacuum oscillation predictions, theseeffects will serve to determine the mass hierarchy and CP
phase in future atmospheric and long baseline experiments.
The cleanest and most direct test of matter effects onneutrino oscillations is the comparison of the daytime andthe nighttime solar neutrino interaction rates (solar daynight effect). In this comparison, the solar zenith angle
controls the size and length of the terrestrial matter density
through which the neutrinos pass, and, thereby, the oscillation probability and the observed interaction rate. An
increase in the nighttime interaction rates implies a regeneration of electron-flavor neutrinos. Other solar neutrino
measurements [3,8,14] have found no significant day-nightdifferences. Here, we report a 2.7σ indication of a nonzero
solar neutrino day-night effect. (This is consistent with thestrong limits of [14] using 861 keV monoenergetic neutrinos, an energy where presently preferred neutrino oscillation parameters predict no day-night effect.)
Super-Kamiokande (SK) is a 50 000 metric ton cylindrical water Cherenkov detector. The optically separated
32 000 ton inner detector (ID), viewed by ∼11 100 50 cm
diameter photomultiplier tubes (PMTs), is surrounded by
an 18 000 ton active veto shield, viewed by ∼1900 20 cm
diameter PMTs. The detector is described in detail in [15].
SK detects recoil electrons coming from the elastic scattering of solar neutrinos with electrons. Only 8 B and hep solar
neutrinos produce recoil electrons of sufficiently highenergy to be detected in SK. Neutrino-electron elastic
scattering is mostly sensitive to electron-flavored neutrinos,
because the cross section for νμ;τ scattering is six times
smaller, since only the electroweak neutral-current interaction channel contributes. The scattering vertex is reconstructed using the timing of the Cherenkov light, while thedirection and energy of the recoil electrons are determinedfrom the light pattern and intensity. For 10 MeVelectrons in
SK-IV, the vertex resolution is 52 cm, the directional
resolution is 25° (limited by multiple Coulomb scattering),
and the energy resolution is 14.0% (dominated by Poisson
fluctuations of the number of photons detected with ∼6
photoelectrons per MeV). More details are given in[4–6,11].
There are four distinct phases of SK. Initially, SK-I had
11 146 ID PMTs and used 1496 live days between 1996
and 2001 for low-energy analysis [4]. In 2001, an accident
during maintenance destroyed ∼7000 ID PMTs. 5182
surviving and spare ID PMTs were then deployed for
SK-II [5], running between 2002 and 2005, with a total
low-energy analysis live time of 791 days. After fullreconstruction of the detector, SK-III [6] took data between
2005 and 2008, acquiring 548 live days for the low-energy
analysis, with 11 129 ID PMTs. Since 2008, SK-IV has
been running with an upgraded electronics and dataacquisition system. In this Letter, data from SK-I, SK-II,
SK-III, and 1306 live days of SK-IV are used [11]. The daynight analysis uses recoil electrons above 4.5 MeV in SK-I,
III, and IV and 7 MeV in SK-II. The energy range of the
SK-I-III day-night analysis is identical as in [4–6]; however, here, it is quoted as kinetic energy (we simply
subtracted 0.5 MeV) while [4–6] use total energy. In

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the mixing of the mass eigenstates with the flavor eigenstates (mixing angles θij ). If the neutrinos propagate
through matter, then the density of the matter will effectively change the oscillation parameters. It was shown,
analytically, by [17,18] that rðcos θz Þ − rD oscillates withthe vacuum frequency ðΔm221 =4EÞL, if L ≈ 2R cos θz now
denotes the path length of the neutrino inside Earth (Rbeing Earth’s radius). Although the dependence of matter
effects on the mixing angles (in or near the large mixing
angle solutions and for θ13 values consistent with reactor
neutrino measurements [19]) is quite small, the dependence
on Δm221 is more noticeable. The fit is run for solar
oscillation parameter sets which predict various matter
effects (10−9 eV2 ≤ Δm221 ≤ 10−3 eV2 and 10−4 ≤ sin2 θ12≤ 1), for values of sin2 θ13 between 0.015 and 0.035.
Figure 1 combines the data from all four SK phases toshow the measured zenith angle distribution of the flux
assuming no oscillations. The expected zenith variation
assuming best-fit oscillation parameters [11] from a global
fit based on solar neutrino data [2,4–6,8,10,11] is overlaid
in solid red. The dashed blue line also includes reactor
antineutrino data [21]. The day and night flux values givenin the left portion of Fig. 1 imply a day-night asymmetry of
ADN ¼ ½−4.2  1.2ðstatÞ%. The ninth data point in theright panel of Fig. 1 shows an ∼2 sigma deviation,enhancing the resulting ADN . We believe this is a statisticalfluctuation, accounted for by the quoted statistical uncertainties. The result Afit
DN coming from the unbinned maximum likelihood fit is less prone to these types offluctuations. To calculate the total systematic uncertainty,
the individual systematic uncertainties of the four phases(for values see [4–6,11]) are assumed to be uncorrelated,since the dominant contributions come from theenergy-scale uncertainty (tuned independently for each
2.6

2.5
2
6

2.4

2.3

2.2

All
Day
Night

[11], the observed solar neutrino signal at lower recoil
electron energies is used for the flux and spectrum analysis.
At the time of each event, the solar zenith angle θz isdetermined. This is the angle between the vector from thesolar position to the event vertex and the vertical detector(z) axis. The precision of the cosine of this angle is muchbetter than 10−3 , the bin width used in the following
analysis. The accuracy of this angle is limited only by SK’s
absolute time precision (a few 100 ns) and basic astronomy.
The SK elastic scattering rate as a function of the solar
zenith angle rðcos θz Þ is used to search for a day-nightdifference in the interaction rate. The expected change in
the interaction rate due to the varying Sun-Earth distance(induced by the eccentricity of Earth’s orbit) is taken into
account throughout this Letter. The most straightforward
method to look for a day-night effect is to define separate
day (cos θz ≤ 0) and night (cos θz > 0) samples. Basedon rD (rN ), the average scattering rate of the day (night)
sample, we define the SK day-night (DN) asymmetry
as ADN ¼ ðrD − rN Þ= 12 ðrD þ rN Þ. Therefore, ADN ¼ 0
implies no terrestrial matter effect on solar neutrino
oscillations.
To increase sensitivity, Ref. [16] first introduced an
unbinned maximum likelihood fit of the solar zenith angle
distribution of the rate rðcos θz Þ to the day-night variation
amplitude α. This was done using “shapes” of suchvariations expected from neutrino oscillation calculations.
By construction, α scales the calculated day-night
asymmetry Acalc
while leaving the average rate
DN
unchanged, giving the measured day-night asymmetry
calc
Afit
DN ¼ ADN × α. This more sophisticated method, referred
to as the “amplitude fit,” was also used in [4]. The
calculated oscillation shapes ignore the SK daytime overburden, which can be up to a few kilometers depending on
the solar zenith angle.
We refer to the angle between the solar and reconstructed
recoil electron candidate directions as θsun . The solar
neutrino interaction rate is extracted by an extended
maximum likelihood fit [4] to the cos θsun distribution.
Reference [16] expands the signal likelihood to allow for atime-dependent solar neutrino-electron elastic scattering
rate, parametrized by the amplitude scaling variable α. The
fit
best-fit α, multiplied with Acalc
DN , defines a best-fit ADN . In
this manner, the day-night asymmetry is measured more
precisely statistically. It is also less vulnerable to some key
systematic effects, such as directional variation of theenergy scale (the frequency of which is limited by SK’s
angular resolution, ∼25°).
Because the amplitude fit depends on the shape of the
day-night variation, given for each energy bin in [16] (andalso in [4]), it necessarily depends on the assumed
oscillation parameters. Vacuum oscillations depend on
the neutrino energy, the length of the flight path L andthe oscillation parameters, the difference of the squared
masses of the mass eigenstates Δm2ij (i ¼ 1; 2; 3; …), andFlux (x10 /cm /s)

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-1

0

1

cosθz

FIG. 1 (color online). SK combined solar zenith angle dependence of the 8 B solar neutrino flux. Solid red (dashed blue) gives
the prediction based on oscillation parameters from a fit to SK
data while constraining the flux (solar þ KamLAND fit) and thedashed-dotted line gives the total average flux.

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TABLE I. Day-night asymmetry for each SK phase, comingfrom separate day and night rate measurements (middle column)
and the amplitude fit (right column). The uncertainties shown are
statistical and systematic. The entire right column assumes the
SK best-fit point of oscillation parameters.

SK-I
SK-II
SK-III
SK-IV
Combined

ADN  ðstatÞ  ðsystÞ

Afit
DN  ðstatÞ  ðsystÞ

ð−2.1  2.0  1.3Þ%ð−5.5  4.2  3.7Þ%ð−5.9  3.2  1.3Þ%ð−5.3  2.0  1.4Þ%ð−4.2  1.2  0.8Þ%ð−2.0  1.7  1.0Þ%ð−4.3  3.8  1.0Þ%ð−4.3  2.7  0.7Þ%ð−3.4  1.8  0.6Þ%ð−3.2  1.1  0.5Þ%

phase) and the background directional distribution shape
uncertainty (evaluated from detector zenith angle data
distributions and limited by statistical fluctuations). The
measured day-night asymmetry when using this simple
method is shown in the middle column of Table I, alongwith the statistical and systematic uncertainties. SK measures the day-night asymmetry in this simple way as
ADN ¼ ½−4.2  1.2ðstatÞ  0.8ðsystÞ%, which deviatesfrom zero by 2.8σ.
Figure 2 shows the combined SK-I/II/III/IV day-night
amplitude fit as a function of recoil electron energy. In eachrecoil electron energy bin e, the day-night variation is fit toan amplitude αe . The displayed day-night asymmetry
values are the product of the fit amplitude αe with the
expected day-night asymmetry AeDN;calc (red), when using
the SK best-fit point of oscillation parameters−5(Δm221 ¼ 4.8þ1.8
eV2 , sin2 θ12 ¼ 0.342þ0.029−0.9 × 10−0.025 [11]2and sin θ13 ¼ 0.025  0.003 [19]). These parameters arechosen when using SK’s spectral and time variation data
along with constraints on the 8 B solar neutrino flux and θ13 .
20

Day/Night Asymmetry (%)

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0-20

When all energy bins are fit together and the same
oscillation parameters are assumed, the resulting
SK-measured day-night asymmetry coming from theamplitude fit is Afit
DN ¼ ½−3.2  1.1ðstatÞ%, with an asymmetry of −3.3% expected by numerical calculations (see[16] for details).
Originally, the systematic uncertainties on the SK-I andII day-night amplitude measurements (see [16]) wereconservatively assigned to be the same as that of the simple
day-night asymmetry measurement (see [4,5]). Because[4,5] only give total systematic uncertainties and not thosefor each of the components, we have now reestimated thesystematic uncertainties of the day-night amplitude fit of
the first two SK phases, using similar methods as for SK-III
and IV. The methods for estimating the systematic uncertainties of the amplitude fit in SK-III and IV are detailed in[11] (see Section 9.3). A summary of the various components of the systematic uncertainty on the day-night
amplitude fit, as well as the total, is given in Table II
for each SK phase.
During the SK-I and II phases, the largest contribution to
the systematic uncertainty came from the directional
dependence of the energy scale. From the beginning of
the SK-III phase, a depth-dependent water transparency
parameter was introduced into the MC simulation program.
This corrects for the depth-dependence of the water
absorption coefficient and greatly reduces the directional
dependence of the energy scale. The further reduction seenfrom SK-III to SK-IV comes from an improvement in thecomparison between data and MC timing, the result of theelectronics upgrade prior to SK-IV. The largest contribution
to the systematic uncertainty now comes from the expectedbackground shapes, which are derived from fits to thedetector’s zenith and azimuthal angle distributions after
statistical subtraction of the solar neutrinos. The accuracyof these shapes are limited by statistics.
The additional contribution to the systematic uncertainty
during SK-III and IV, coming from the event selection,is the result of the combination of the external event andtight fiducial volume cuts (see [6,11]). The tight fiducial
volume cut introduced at the start of SK-III is asymmetricin the z direction, causing the external event cut to havedifferent selection efficiencies during the day and night
TABLE II. Day-night amplitude fit systematic uncertainties by
SK phase. The total is found by adding the contributions for eachphase in quadrature.

-40
5

10

15

Recoil Electron Kinetic Energy (MeV)

FIG. 2 (color online). SK day-night amplitude fit as a functionof recoil electron kinetic energy (unlike [16] which uses totalenergy), shown as the measured amplitude times the expected
day-night asymmetry, for oscillation parameters chosen by the
SK best fit. The error bars shown are statistical uncertainties only,
and the expected dependence is shown in red.

Energy Scale
Energy Resolution
Background Shape
Event Selection
Earth Model [20]Total091805-4

SK-I

SK-II

SK-III

SK-IV

0.8%
0.05%
0.6%

0.01%
1.0%

0.8%
0.05%
0.6%

0.01%
1.0%

0.2%
0.05%
0.6%
0.2%
0.01%
0.7%

0.05%
0.05%
0.6%
0.1%
0.01%
0.6%

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1

-1
-2
-3
-4
2

4

6

8

10

12

14

16

18

20

22

∆m221 (10-5eV2)

FIG. 3 (color online). Dependence of the measured day-night
asymmetry [fitted day-night amplitude times the expected daynight asymmetry (red)] on Δm221 , for sin2 θ12 ¼ 0.314, andsin2 θ13 ¼ 0.025. The 1σ statistical uncertainties are given by
the light gray band. The additional dark gray width to the bandshows the inclusion of the systematic uncertainties. Overlaid are
the 1σ allowed ranges from the solar global fit (solid green) andthe KamLAND experiment (dashed blue).

day-night variation is too small (compared to present
uncertainties) to measure the frequency, some frequencies
are favored by about 2σ over others.
Even so, the neutrino flux-independent solar neutrino
oscillation analysis of [16] uses the frequency and amplitude of the day-night variation as well as spectral information. We calculate the log likelihood ratio between α ¼ 1
and α ¼ 0, multiply by −2, and then add it to the χ 2 valuesof the fit to the recoil electron spectrum (see [11]). Figure 4
-3

10

-4

10

-5

2

10

-6

10

2

which differs from zero by 2.7σ. The measured value of the
day-night asymmetry agrees with −3.2%, within 0.2%,
for all sets of oscillation parameters contained in thelarge mixing angle region. The SNO experiment also
performed a search for the day-night variation of thecharged-current interaction rate on deuterium [8]. Fromtheir result, we predict the SK day-night asymmetry to be
Apred
DN ¼ ð−2.0  1.8Þ%. [SNO actually models the nightday asymmetry of the survival probability as a0 þ a1 ðEν −10 MeVÞ and fits the coefficients ai [8]. We scale theexpected coefficients (based on Δm221 ¼ 4.84 × 10−5 eV2 )by an amplitude αSNO and minimize the SNO χ 2 withrespect to it. SNO data then implies a0 ¼ ð3.4  2.9Þ%,while SK and SNO combined is equivalent toa0 ¼ ð4.8  1.6Þ%.] Combining SK and SNO data yields
Afit
DN ¼ ½−2.9  1.0ðstat þ systÞ%, which differs from zeroby 2.9σ. The expected SK day-night asymmetry for theseoscillation parameters is −3.3%. Changing Δm221 to 7.41 ×
10−5 eV2 and sin2 θ12 to 0.31 (motivated by KamLAND
data [21]) changes the SK-measured day-night asymmetry
to ½−3.0  1.0ðstatÞ  0.5ðsystÞ%, slightly reducing thesignificance for a nonzero day-night asymmetry from 2.7
to 2.6σ.
Figure 3 shows the Δm221 dependence of the equivalent
day-night asymmetry of the SK combined amplitude fit forsin2 θ12 ¼ 0.314 and sin2 θ13 ¼ 0.025. The expected daynight asymmetry is indicated by the red curve. The point
where the best-fit crosses the expected curve represents thevalue of Δm221 where the measured day-night amplitude is
α ¼ 1. Superimposed are the 1σ allowed ranges in Δm221
from the solar global fit [11] (green) and from the
KamLAND experiment [21] (blue). The amplitude fit
has negligible dependence on the values of θ12 (within
the large mixing angle region of oscillation parameters) andθ13 (0.015 ≤ sin2 θ13 ≤ 0.035), leading to a 68% C.L.
allowed range of 4 × 10−5 eV2 ≤ Δm221 ≤ 7 × 10−5 eV2(as shown in Fig. 3). Aside from the amplitude of the
day-night asymmetry, another handle to Δm221 is the daynight variation frequency. Although the amplitude of the

0-5∆m21 in eV

Afit
DN ¼ ½−3.2  1.1ðstatÞ  0.5ðsystÞ%;

Day/Night Asymmetry (%)

times. As for the case of the simple day-night asymmetry
measurement, the total systematic uncertainty of each SK
phase is assumed to be uncorrelated, and is added inquadrature to the statistical uncertainty of the corresponding phase before combining the results of each phase
together.
The right column of Table I lists the measured day-night
asymmetry coming from the amplitude fit to each phase,
as well as the combined fit, for oscillation parametersat the SK best-fit point. The combined fit takes into
account energy threshold and resolution. The equivalent
SK day-night asymmetry coming from the amplitude
fit is

-7

10

-8

10

-9

10

10

-4

-3

10

10

-2

10

-1

1

10

10

2

2

tan (θ12 )FIG. 4 Contours at 68% (solid thin line), 95% (solid thick line),
three sigma (dashed-dotted line), and five sigma (dashed grayline) of the flux-independent SK solar neutrino oscillation
analysis. The shaded gray area indicates regions preferred by
the day-night variation data for the 95% case. The best-fit
parameters resulting from a fit to all solar neutrino [2,8,10,11]
and KamLAND [21] data is shown by the black asterisk.

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shows the flux-independent SK-I/II/III/IV contours of 68%(solid thin line), 95% (solid thick line), three sigma(dashed-dotted line), and five sigma (dashed gray line)
significance. For the 95% C.L., regions preferred by the
day-night variation data are highlighted in gray. In the caseof 68% C.L., those regions closely match the two lower
Δm221 68% contours shown in the figure. The blackasterisk marks the parameters selected by all solar neutrino[2, 8,10,11] and KamLAND data [21], including this work.
The SK flux-independent contours agree with those parameters within two sigma. The previously suggested low(small mixing angle) solution of neutrino oscillation
parameters is excluded at more than four (five) sigma.
(The Low and small mixing angle solution parameters canbe seen in [8] and [22], respectively.)
In conclusion, we find an indication of electron-flavor
regeneration in solar neutrino oscillations due to thepresence of terrestrial matter effects. The fit amplitude of
the solar zenith angle variation of the SK solar neutrino
interaction rate corresponds to a day-night asymmetry of½−3.2  1.1ðstatÞ  0.5ðsystÞ%, which deviates fromzero by 2.7σ. This analysis probes matter effects
directly, since it compares the flavor content of thesolar neutrino beam with Earth matter to that without.
Therefore, this is the first direct indication that neutrino
oscillation probabilities are modified by the presence ofmatter.
The authors gratefully acknowledge the cooperation of
the Kamioka Mining and Smelting Company. Super-K has
been built and operated from funds provided by theJapanese Ministry of Education, Culture, Sports, Scienceand Technology, the U.S. Department of Energy, and the
U.S. National Science Foundation. This Letter was partially
supported by the Research Foundation of Korea (BK21 and
KNRC), the Korean Ministry of Science and Technology,
the National Science Foundation of China (Grant
No. 11235006), the European Union FP7 ITNINVISIBLES (Marie Curie Actions, Grant No. PITNGA-2011-289442) and the State Committee for
Scientific Research in Poland.

*

week ending
7 MARCH 2014

Deceased.
Corresponding author.
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