First Indication of Terrestrial Matter Effects on Solar Neutrino Oscillation
A. Renshaw, K. Abe, Y. Hayato, K. Iyogi, J. Kameda, Y. Kishimoto, M. Miura, S. Moriyama, M. Nakahata, Y. Nakano, S. Nakayama, H. Sekiya, M. Shiozawa, Y. Suzuki, A. Takeda, Y. Takenaga, T. Tomura, K. Ueno, T. Yokozawa, R. A. Wendell, T. Irvine, T. Kajita, K. Kaneyuki, K. P. Lee, Y. Nishimura, K. Okumura, T. McLachlan, L. Labarga, S. Berkman, H. A. Tanaka, S. Tobayama, E. Kearns, J. L. Raaf, J. L. Stone, L. R. Sulak, M. Goldhabar, K. Bays, G. Carminati, W. R. Kropp, S. Mine, M. B. Smy, H. W. Sobel, K. S. Ganezer, J. Hill, W. E. Keig, N. Hong, J. Y. Kim, I. T. Lim, T. Akiri, A. Himmel, K. Scholberg, C. W. Walter, T. Wongjirad, T. Ishizuka, S. Tasaka, J. S. Jang, J. G. Learned, S. Matsuno, S. N. Smith, T. Hasegawa, T. Ishida, T. Ishii, T. Kobayashi, T. Nakadaira, K. Nakamura, Y. Oyama, K. Sakashita, T. Sekiguchi, T. Tsukamoto, A. T. Suzuki, Y. Takeuchi, C. Bronner, S. Hirota, K. Huang, K. Ieki, M. Ikeda, T. Kikawa, A. Minamino, T. Nakaya, K. Suzuki, S. Takahashi, Y. Fukuda, K. Choi, Y. Itow, G. Mitsuka, P. Mijakowski, J. Hignight, J. Imber, C. K. Jung, C. Yanagisawa, H. Ishino, A. Kibayashi, Y. Koshio, T. Mori, M. Sakuda, T. Yano, Y. Kuno, R. Tacik, S. B. Kim, H. Okazawa, et al. (15 additional authors not shown)
aa r X i v : . [ h e p - e x ] M a r First Indication of Terrestrial Matter Effects on Solar Neutrino Oscillation
A. Renshaw, K. Abe,
1, 29
Y. Hayato,
1, 29
K. Iyogi, J. Kameda,
1, 29
Y. Kishimoto,
1, 29
M. Miura,
1, 29
S. Moriyama,
1, 29
M. Nakahata,
1, 29
Y. Nakano, S. Nakayama,
1, 29
H. Sekiya,
1, 29
M. Shiozawa,
1, 29
Y. Suzuki,
1, 29
A. Takeda,
1, 29
Y. Takenaga, T. Tomura,
1, 29
K. Ueno, T. Yokozawa, R. A. Wendell,
1, 29
T. Irvine, T. Kajita,
2, 29
K. Kaneyuki,
2, 29, ∗ K. P. Lee, Y. Nishimura, K. Okumura,
2, 29
T. McLachlan, L. Labarga, S. Berkman, H. A. Tanaka,
4, 31
S. Tobayama, E. Kearns,
5, 29
J. L. Raaf, J. L. Stone,
5, 29
L. R. Sulak, M. Goldhabar, ∗ K. Bays, G. Carminati, W. R. Kropp, S. Mine, M. B. Smy,
7, 29
H. W. Sobel,
7, 29
K. S. Ganezer, J. Hill, W. E. Keig, N. Hong, J. Y. Kim, I. T. Lim, T. Akiri, A. Himmel, K. Scholberg,
10, 29
C. W. Walter,
10, 29
T. Wongjirad, T. Ishizuka, S. Tasaka, J. S. Jang, J. G. Learned, S. Matsuno, S. N. Smith, T. Hasegawa, T. Ishida, T. Ishii, T. Kobayashi, T. Nakadaira, K. Nakamura,
15, 29
Y. Oyama, K. Sakashita, T. Sekiguchi, T. Tsukamoto, A. T. Suzuki, Y. Takeuchi, C. Bronner, S. Hirota, K. Huang, K. Ieki, M. Ikeda, T. Kikawa, A. Minamino, T. Nakaya,
17, 29
K. Suzuki, S. Takahashi, Y. Fukuda, K. Choi, Y. Itow, G. Mitsuka, P. Mijakowski, J. Hignight, J. Imber, C. K. Jung, C. Yanagisawa, H. Ishino, A. Kibayashi, Y. Koshio, T. Mori, M. Sakuda, T. Yano, Y. Kuno, R. Tacik,
23, 32
S. B. Kim, H. Okazawa, Y. Choi, K. Nishijima, M. Koshiba, Y. Totsuka, ∗ M. Yokoyama,
K. Martens, Ll. Marti, M. R. Vagins,
29, 7
J. F. Martin, P. de Perio, A. Konaka, M. J. Wilking, S. Chen, Y. Zhang, and R. J. Wilkes (The Super-Kamiokande Collaboration) Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan Research Center for Cosmic Neutrinos, Institute for Cosmic RayResearch, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T1Z4, Canada Department of Physics, Boston University, Boston, MA 02215, USA Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USA Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USA Department of Physics, Chonnam National University, Kwangju 500-757, Korea Department of Physics, Duke University, Durham NC 27708, USA Junior College, Fukuoka Institute of Technology, Fukuoka, Fukuoka 811-0295, Japan Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japan GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan Department of Physics and Astronomy, State University of New York at Stony Brook, NY 11794-3800, USA Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, SK, S4SOA2, Canada Department of Physics, Seoul National University, Seoul 151-742, Korea Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka, 425-8611, Japan Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), TodaiInstitutes for Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Department of Physics, University of Toronto, 60 St., Toronto, Ontario, M5S1A7, Canada Institute of Particle Physics, Canada, University of Toronto, 60 Saint George St., Toronta, ON, M5S1A7, Canada TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T2A3, Canada Department of Engineering Physics, Tsinghua University, Beijing, 100084, China Department of Physics, University of Washington, Seattle, WA 98195-1560, USA National Centre For Nuclear Research, 00-681 Warsaw, Poland (Dated: August 27, 2018)
We report an indication that the elastic scattering rate of solar B neutrinos with electrons in theSuper-Kamiokande detector is larger when the neutrinos pass through the Earth during nighttime.We determine the day/night asymmetry, defined as the difference of the average day rate and averagenight rate divided by the average of those two rates, to be ( − . ± . ± . σ . Since the elastic scattering process is mostly sensitive to electron-flavored solar neutrinos, a non-zero day/night asymmetry implies that the flavor oscillations ofsolar neutrinos are affected by the presence of matter within the neutrinos’ flight path. Super-Kamiokande’s day/night asymmetry is consistent with neutrino oscillations for 4 × − eV ≤ ∆ m ≤ × − eV and large mixing values of θ , at the 68% C.L. Neutrino flavor oscillations occur when the phase dif-ference of a superposition of massive neutrinos changes.Such phase changes occur while neutrinos are propagat-ing in vacuum (vacuum oscillations). Wolfenstein [1] real-ized that the neutrino-electron elastic forward-scatteringamplitude introduces additional phase shifts. As a con-sequence, neutrinos propagating in matter will oscillatedifferently than neutrinos propagating through vacuum.These matter effects are a fundamental prediction of thepresent theory of neutrino oscillations. In this letter, wereport an indication of the existence of such matter ef-fects.Vacuum oscillations cannot easily explain a solar neu-trino electron-flavor survival probability P ee which ismeasured to be significantly below one half [2–8], in theenergy region of ∼ < P ee from the MSW resonance tovacuum oscillations (near 3 MeV) were so far unsuccess-ful [8, 11]. Moreover, these previous observations implymatter effects only indirectly, since there is no “controlbeam” of solar neutrinos that only propagates in vac-uum. Atmospheric neutrino experiments can probe theexistence of matter effects within the Earth in a simi-lar fashion, and while there is currently no significantdeparture of present atmospheric data [12, 13] from thevacuum oscillation predictions, these effects will serve todetermine the mass hierarchy and CP phase in futureatmospheric and long baseline experiments.The cleanest and most direct test of matter effects onneutrino oscillations is the comparison of the daytimeand the nighttime solar neutrino interaction rates (solarday/night effect). In this comparison, the solar zenith an-gle controls the size and length of the terrestrial matterdensity through which the neutrinos pass, and therebythe oscillation probability and the observed interactionrate. An increase in the nighttime interaction rates im-plies a regeneration of electron-flavor neutrinos. Othersolar neutrino measurements [3, 8, 14] have found no sig-nificant day/night differences. Here, we report a 2.7 σ indication of a non-zero solar neutrino day/night effect. Super-Kamiokande (SK) is a 50,000 metric ton cylin-drical water Cherenkov detector. The optically separated32,000 ton inner detector (ID), viewed by ∼ ∼ B and hep solar neutrinos produce recoil elec-trons of sufficiently high energy to be detected in SK.Neutrino-electron elastic scattering is mostly sensitive toelectron-flavored neutrinos, because the cross section for ν µ,τ scattering is six times smaller, since only the elec-troweak neutral-current interaction channel contributes.The scattering vertex is reconstructed using the timingof the Cherenkov light, while the direction and energy ofthe recoil electrons are determined from the light patternand intensity. For 10 MeV electrons in SK-IV, the ver-tex resolution is 52 cm, the directional resolution is 25 ◦ (limited by multiple Coulomb scattering), and the energyresolution is 14.0% (dominated by Poisson fluctuations ofthe number of photons detected with ∼ ∼ This is consistent with the strong limits of [14] using 861 keVmono-energetic neutrinos, an energy where presently-preferredneutrino oscillation parameters predict no day/night effect. subtracted 0.5 MeV) while [4–6] use total energy. In [11],the observed solar neutrino signal at lower recoil electronenergies is used for the flux and spectrum analysis.At the time of each event, the solar zenith angle θ z is determined. This is the angle between the vectorfrom the solar position to the event vertex and the ver-tical detector ( z ) axis. The precision of the cosine ofthis angle is much better than 10 − , the bin width usedin the following analysis. The accuracy of this angleis limited only by SK’s absolute time precision (a few100 ns) and basic astronomy. The SK elastic scatter-ing rate as a function of the solar zenith angle r (cos θ z )is used to search for a day/night difference in the in-teraction rate. The expected change in the interactionrate due to the varying Sun-Earth distance (inducedby the eccentricity of Earth’s orbit) is taken into ac-count throughout this paper. The most straight-forwardmethod to look for a day/night effect is to define sep-arate day (cos θ z ≤
0) and night (cos θ z >
0) samples.Based on r D ( r N ), the average scattering rate of the day(night) sample, we define the SK day/night asymmetryas A DN = ( r D − r N ) / ( r D + r N ). Therefore, A DN = 0implies no terrestrial matter effect on solar neutrino os-cillations.To increase sensitivity, [16] first introduced an un-binned maximum likelihood fit of the solar zenith an-gle distribution of the rate r (cos θ z ) to the day/nightvariation amplitude α . This was done using “shapes”of such variations expected from neutrino oscillationcalculations. By construction, α scales the calculatedday/night asymmetry A calcDN while leaving the average rateunchanged, giving the measured day/night asymmetry A fitDN = A calcDN × α . This more sophisticated method, re-ferred to as the “amplitude fit”, was also used in [4]. Thecalculated oscillation shapes ignore the SK daytime over-burden, which can be up to a few kilometers dependingon the solar zenith angle.We refer to the angle between the solar and recon-structed recoil electron candidate directions as θ sun . Thesolar neutrino interaction rate is extracted by an ex-tended maximum likelihood fit [4] to the cos θ sun distri-bution. [16] expands the signal likelihood to allow for atime-dependent solar neutrino-electron elastic scatteringrate, parameterized by the amplitude scaling variable α .The best-fit α , multiplied with A calcDN , defines a best-fit A fitDN . In this manner the day/night asymmetry is mea-sured more precisely statistically. It is also less vulner-able to some key systematic effects, such as directionalvariation of the energy scale (the frequency of which islimited by SK’s angular resolution, ∼ ◦ ).Because the amplitude fit depends on the shape of theday/night variation, given for each energy bin in [16](and also in [4]), it necessarily depends on the assumedoscillation parameters. Vacuum oscillations depend onthe neutrino energy, the length of the flight path L andthe oscillation parameters; the difference of the squared cos q z F l u x ( x / c m / s ) A ll D a y N i gh t FIG. 1. SK combined solar zenith angle dependence of the B solar neutrino flux. Solid red (dashed blue) gives the pre-diction based on oscillation parameters from a fit to SK datawhile constraining the flux (solar+KamLAND fit) and thedashed-dotted line gives the total average flux. masses of the mass eigenstates ∆ m ij ( i = 1 , , , ... ) andthe mixing of the mass eigenstates with the flavor eigen-states (mixing angles θ ij ). If the neutrinos propagatethrough matter, then the density of the matter will ef-fectively change the oscillation parameters. It was shownanalytically by [17–19] that r (cos θ z ) − r D oscillates withthe vacuum frequency ∆ m E L , if L ≈ R cos θ z denotesnow the path length of the neutrino inside the Earth ( R being the Earth radius). Although the dependence ofmatter effects on the mixing angles (in or near the largemixing angle solutions and for θ values consistent withreactor neutrino measurements [20]) is quite small, thedependence on ∆ m is more noticeable. The fit is runfor solar oscillation parameter sets which predict vari-ous matter effects (10 − eV ≤ ∆ m ≤ − eV and10 − ≤ sin θ ≤ θ between 0.015and 0.035.Fig. 1 combines the data from all four SK phases toshow the measured zenith angle distribution of the fluxassuming no oscillations. The expected zenith variationassuming best-fit oscillation parameters [11] from a globalfit based on solar neutrino data [2, 4–6, 8, 10, 11] is over-laid in solid red. The dashed blue line also includes reac-tor anti-neutrino data [22]. The day and night flux val-ues given in the left portion of Fig. 1 imply a day/nightasymmetry of A DN = ( − . ± . ∼ A DN . We be-lieve this is a statistical flucuation, accounted for by thequoted statistical uncertainties. The result A fit DN comingfrom the unbinned maximum likelihood fit is less prone tothese types of flucuations. To calculate the total system-atic uncertainty, the individual systematic uncertainties TABLE I. Day/night asymmetry for each SK phase, comingfrom separate day and night rate measurements (middle col-umn) and the amplitude fit (right column). The uncertaintiesshown are statistical and systematic. The entire right columnassumes the SK best-fit point of oscillation parameters. A DN ± (stat) ± (syst) A fitDN ± (stat) ± (syst)SK-I ( − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . − . ± . ± . of the four phases (for values see [4–6, 11]) are assumed tobe uncorrelated, since the dominant contributions comefrom the energy-scale uncertainty (tuned independentlyfor each phase) and the background directional distribu-tion shape uncertainty (evaluated from detector zenithangle data distributions and limited by statistical fluctu-ations). The measured day/night asymmetry when us-ing this simple method is shown in the middle column ofTable I, along with the statistical and systematic uncer-tainties. SK measures the day/night asymmetry in thissimple way as A DN = ( − . ± . ± . σ .Fig. 2 shows the combined SK-I/II/III/IV day/nightamplitude fit as a function of recoil electron energy. Ineach recoil electron energy bin e , the day/night varia-tion is fit to an amplitude α e . The displayed day/nightasymmetry values are the product of the fit amplitude α e with the expected day/night asymmetry A e DN , calc (red),when using the SK best-fit point of oscillation parame-ters (∆ m = 4 . +1 . − . × − eV , sin θ = 0 . +0 . − . [11] and sin θ = 0 . ± .
003 [20]). These parametersare chosen when using SK’s spectral and time variationdata along with constraints on the B solar neutrino fluxand θ . When all energy bins are fit together and thesame oscillation parameters assumed, the resulting SK-measured day/night asymmetry coming from the ampli-tude fit is A fitDN = ( − . ± . − .
3% expected by numerical calculations (see [16] fordetails).Originally the systematic uncertainties on the SK-I andII day/night amplitude measurements (see [16]) were con-
TABLE II. Day/night amplitude fit systematic uncertaintiesby SK phase. The total is found by adding the contributionsfor each phase in quadrature.SK-I SK-II SK-III SK-IVEnergy Scale 0.8% 0.8% 0.2% 0.05%Energy Resolution 0.05% 0.05% 0.05% 0.05%Background Shape 0.6% 0.6% 0.6% 0.6%Event Selection — — 0.2% 0.1%Earth Model [21] 0.01% 0.01% 0.01% 0.01%Total 1.0% 1.0% 0.7% 0.6%
Recoil Electron Kinetic Energy (MeV) D a y / N i gh t A sy mm e t r y ( % ) -40-20020 5 10 15 FIG. 2. SK day/night amplitude fit as a function of re-coil electron kinetic energy (unlike [16] which uses total en-ergy), shown as the measured amplitude times the expectedday/night asymmtery, for oscillation parameters chosen bythe SK best-fit. The error bars shown are statistical uncer-tainties only and the expected dependence is shown in red. servatively assigned to be the same as that of the sim-ple day/night asymmetry measurement (see [4, 5]). Be-cause [4, 5] only give total systematic uncertainties andnot those for each of the components, we have now re-estimated the systematic uncetainties of the day/nightamplitude fit of the first two SK phases, using similarmethods as for SK-III and IV. The methods for estimat-ing the systematic uncertainties of the amplitude fit inSK-III and IV are detailed in [11] (see Section 9.3). Asummary of the various components of the systematicuncertainty on the day/night amplitude fit, as well asthe total, is given in Table II for each SK phase.During the SK-I and II phases, the largest contributionto the systematic uncertainty came from the directionaldependence of the energy scale. From the beginning ofthe SK-III phase, a depth-dependent water transparencyparameter was introduced into the MC simulation pro-gram. This corrects for the depth-dependence of the wa-ter absorption coefficient and greatly reduces the direc-tional dependence of the energy scale. The further reduc-tion seen from SK-III to SK-IV comes from an improve-ment in the comparison between data and MC timing,the result of the electronics upgrade prior to SK-IV. Thelargest contribution to the systematic uncertainty nowcomes from the expected background shapes, which arederived from fits to the detector’s zenith and azimuthalangle distributions after statistical subtraction of the so-lar neutrinos. The accuracy of these shapes are limitedby statistics.The additional contribution to the systematic uncer-tainty during SK-III and IV, coming from the event se-lection, is the result of the combination of the externalevent and tight fiducial volume cuts (see [6, 11]). Thetight fiducial volume cut introduced at the start of SK-III is asymmetric in the z direction, causing the externalevent cut to have different selection efficiencies duringthe day and night times. As for the case of the simpleday/night asymmetry measurement, the total systematicuncertainty of each SK phase is assumed to be uncorre-lated, and is added in quadrature to the statistical uncer-tainty of the corresponding phase before combining theresults of each phase together.The right column of Table I lists the measuredday/night asymmetry coming from the amplitude fit toeach phase, as well as the combined fit, for oscillations pa-rameters at the SK best-fit point. The combined fit takesinto account energy threshold and resolution. The equiv-alent SK day/night asymmetry coming from the ampli-tude fit is A fitDN = ( − . ± . ± . , which differs from zero by 2.7 σ . The measured valueof the day/night asymmetry agrees with − . ± . A predDN = ( − . ± . . Combining SK and SNO datayields A fitDN = ( − . ± . σ . The expected SK day/night asym-metry for these oscillation parameters is − . m to 7 . × − eV and sin θ to 0.31 (moti-vated by KamLAND data [22]) changes the SK-measuredday/night asymmetry to ( − . ± . ± . σ .Fig. 3 shows the ∆ m dependence of the equivalentday/night asymmetry of the SK combined amplitude fitfor sin θ = 0 .
314 and sin θ = 0 . m where the measured day/nightamplitude is α = 1. Superimposed are the 1 σ allowedranges in ∆ m from the solar global fit [11] (green) andfrom the KamLAND experiment [22] (blue). The ampli-tude fit has negligible dependence on the values of θ (within the large mixing angle region of oscillation pa-rameters) and θ (0 . ≤ sin θ ≤ . × − eV ≤ ∆ m ≤ SNO actually models the night/day asymmetry of the survivalprobability as a + a ( E ν −
10 MeV) and fits the coefficients a i [8]. We scale the expected coefficients (based on ∆ m =4 . × − eV ) by an amplitude α SNO and minimize the SNO χ with respect to it. SNO data then implies a = (3 . ± . a = (4 . ± . ) eV -5 (10 m D D a y / N i gh t A sy mm e t r y ( % ) -5-4-3-2-101 FIG. 3. Dependence of the measured day/night asymme-try (fitted day/night amplitude times the expected day/nightasymmetry (red)) on ∆ m , for sin θ = 0 .
314 andsin θ = 0 . σ statistical uncertainties are givenby the light gray band. The additional dark gray width tothe band shows the inclusion of the systematic uncertainties.Overlaid are the 1 σ allowed ranges from the solar global fit(solid green) and the KamLAND experiment (dashed blue). × − eV (as shown in Fig. 3). Aside from the am-plitude of the day/night asymmetry, another handle to∆ m is the day/night variation frequency. Although theamplitude of the day/night variation is too small (com-pared to present uncertainties) to measure the frequency,some frequencies are favored by about 2 σ over others.Even so, the neutrino flux-independent solar neutrinooscillation analysis of [16] uses frequency and amplitudeof the day/night variation as well as spectral information.We calculate the log likelihood ratio between α = 1 and α = 0, multiply by −
2, and then add it to the χ valuesof the fit to the recoil electron spectrum (see [11]). Fig. 4shows the flux-independent SK-I/II/III/IV contours of68% (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 theday/night variation data are highlighted in gray. In thecase of 68% C.L., those regions closely match the twolower ∆ m
68% contours shown in the figure. The blackasterisk marks the parameters selected by all solar neu-trino [8, 10, 11, 23] and KamLAND data [22], includingthis work. The SK flux-independent contours agree withthose parameters within two sigma. The previously sug-gested low (small mixing angle) solution of neutrino os-cillation parameters is excluded at more than four (five)sigma .In conclusion, we find an indication of electron-flavorregeneration in solar neutrino oscillations due to the pres- The Low and small mixing angle solution parameters can be seenin [8] and [24], respectively. D m i n e V -9 -8 -7 -6 -5 -4 -3 tan ( q )10 -4 -3 -2 -1 FIG. 4. Contours at 68% (solid thin line), 95% (solid thickline), three sigma (dashed-dotted line), and five sigma (dashedgray line) of the flux-independent SK solar neutrino oscillationanalysis. The shaded gray area indicates regions preferred bythe day/night variation data for the 95% case. The best-fitparameters resulting from a fit to all solar neutrino [8, 10, 11,23] and KamLAND [22] data is shown by the black asterisk. ence of terrestrial matter effects. The fit amplitude of thesolar zenith angle variation of the SK solar neutrino in-teraction rate corresponds to a day/night asymmetry of( − . ± . ± . σ . This analysis probes matter effects directly,since it compares the flavor content of the solar neutrinobeam with Earth matter to that without. Therefore,this is the first direct indication that neutrino oscillationprobabilities are modified by the presence of matter.The authors gratefully acknowledge the cooperation ofthe Kamioka Mining and Smelting Company. Super-Khas been built and operated from funds provided by theJapanese Ministry of Education, Culture, Sports, Sci-ence and Technology, the U.S. Department of Energy,and the U.S. National Science Foundation. This workwas partially supported by the Research Foundation ofKorea (BK21 and KNRC), the Korean Ministry of Sci-ence and Technology, the National Science Foundationof China (Grant NO. 11235006), the European UnionFP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442) and the State Committee for Scientific Re-search in Poland. ∗ Deceased.[1] L. Wolfenstein, Phys. Rev. D , 2369 (1978).[2] R. Davis, Jr. et al. , Phys. Rev. Lett. , 1205 (1968).[3] Y. Fukuda et al. , Phys. Rev. Lett. , 1683 (1996).[4] J. Hosaka et al. , Phys. Rev. D , 112001 (2006).[5] J. P. Cravens et al. , Phys. Rev. D , 032002 (2008).[6] K. Abe et al. , Phys. Rev. D , 052010 (2011).[7] Q. R. Ahmad et al. , Phys. Rev. Lett. , 071301 (2001).[8] B. Aharmin et al. , Phys. Rev. C , 025501 (2013).[9] S. P. Mikheyev and A. Yu. Smirnov, Sov. Jour. Nucl.Phys. , 913 (1985).[10] J. N. Abdurashitov et al. (SAGE collaboration), Phys.Rev. C , 015807 (2009); M. Altmann et al. (GALLEXCollaboration), Phys. Lett. B , 174 (2005); G. Bellini et al. (Borexino Collaboration), Phys. Rev. Lett. ,141302 (2011).[11] A. Renshaw, “First Direct Evidence for Mat-ter Enhanced Neutrino Oscillation, Using Super-Kamiokande Solar Neutrino Data”, Ph.D. Thesis, ;K. Abe et al. , “Solar Neutrino Measurements in SK-IV”,to be submitted to Phys. Rev. D (2014).[12] J. Hosaka et al. , Rhys. Rev. D , 032002 (2006).[13] R. Wendell et al. , Phys. Rev. D , 092004 (2010).[14] G. Bellini et al. , Phys. Lett. B (2012).[15] The SK Collaboration, Nucl. Insturm. Meth. A (2003).[16] M. B. Smy et al. , Phys. Rev. D , 011104(R) (2004).[17] A. N. Ioannisian and A. Y. Smirnov, Phys. Rev. Lett. ,241801 (2004).[18] M. Blennow, T. Ohlsson and H. Snellman, Phys. Rev. D , 073006 (2004).[19] E. K. Akhmedov, M. A. Tortola and J. W. F. Valle, JHEP0405, 057 (2004).[20] F. P. An et al. (Daya Bay Collaboration), Chin. Phys. C , 011001 (2013); J. K. Ahn et al. (RENO Collabo-ration), Phys. Rev. Lett. et al. (Double Chooz Collaboration), Phys. Rev. D et al. (Paticle Data Group),Phys. Rev. D , 010001 (2012).[21] A. M. Dziewonski and D. L. Anderson, Phys. EarthPlanet. Inter. , 297 (1981); J. J. Durek and G. Ek-strom, Bull. Seism. Soc. Am. , 144-158 (1996).[22] S. Abe et al. , Phys. Rev. Lett. , 221803 (2008);The KamLAND Collaboration, arXiv:1303.4667v2(2013).[23] R. Davis et al. (Homestake Experiment),Phys. Rev. Lett. , 1205 (1968);[24] M. C. Gonzalez-Garcia, Phys. Particles and Nucl.42