VOLUME 89, NUMBER 1 PHYSICAL REVIEW LETTERS 1 JULY 2002 Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory Q. R. Ahmad,17 R. C. Allen,4 T. C. Andersen,6 J. D.Anglin,10 J. C. Barton,11, * E. W. Beier,12 M. Bercovitch,10 J. Bigu,7 S. D. Biller,11 R. A. Black,11 I. Blevis,5 R. J. Boardman,11 J. Boger,3 E. Bonvin,14 M. G. Boulay,9,14 M. G. Bowler,11 T. J. Bowles,9 S. J. Brice,9,11 M. C. Browne,17,9 T. V. Bullard,17 G. Bühler,4 J. Cameron,11 Y. D. Chan,8 H. H. Chen,4, † M. Chen,14 X. Chen,8,11 B. T. Cleveland,11 E. T. H. Clifford,14 J. H. M. Cowan,7 D. F. Cowen,12 G. A. Cox,17 X. Dai,11 F. Dalnoki-Veress,5 W. F. Davidson,10 P. J. Doe,17,9,4 G. Doucas,11 M. R. Dragowsky,9,8 C. A. Duba,17 F. A. Duncan,14 M. Dunford,12 J. A. Dunmore,11 E. D. Earle,14,1 S. R. Elliott,17,9 H. C. Evans,14 G. T. Ewan,14 J. Farine,7,5 H. Fergani,11 A. P. Ferraris,11 R. J. Ford,14 J. A. Formaggio,17 M. M. Fowler,9 K. Frame,11 E. D. Frank,12 W. Frati,12 N. Gagnon,11,9,8,17 J. V. Germani,17 S. Gil,2 K. Graham,14 D. R. Grant,5 R. L. Hahn,3 A. L. Hallin,14 E. D. Hallman,7 A. S. Hamer,9,14 A. A. Hamian,17 W. B. Handler,14 R. U. Haq,7 C. K. Hargrove,5 P. J. Harvey,14 R. Hazama,17 K. M. Heeger,17 W. J. Heintzelman,12 J. Heise,2,9 R. L. Helmer,16,2 J. D. Hepburn,14 H. Heron,11 J. Hewett,7 A. Hime,9 M. Howe,17 J. G. Hykawy,7 M. C. P. Isaac,8 P. Jagam,6 N. A. Jelley,11 C. Jillings,14 G. Jonkmans,7,1 K. Kazkaz,17 P. T. Keener,12 J. R. Klein,12 A. B. Knox,11 R. J. Komar,2 R. Kouzes,13 T. Kutter,2 C. C. M. Kyba,12 J. Law,6 I. T. Lawson,6 M. Lay,11 H. W. Lee,14 K. T. Lesko,8 J. R. Leslie,14 I. Levine,5 W. Locke,11 S. Luoma,7 J. Lyon,11 S. Majerus,11 H. B. Mak,14 J. Maneira,14 J. Manor,17 A. D. Marino,8 N. McCauley,12,11 A. B. McDonald,14,13 D. S. McDonald,12 K. McFarlane,5 G. McGregor,11 R. Meijer Drees,17 C. Mifflin,5 G. G. Miller,9 G. Milton,1 B. A. Moffat,14 M. Moorhead,11 C. W. Nally,2 M. S. Neubauer,12 F. M. Newcomer,12 H. S. Ng,2 A. J. Noble,16,5 E. B. Norman,8 V. M. Novikov,5 M. O’Neill,5 C. E. Okada,8 R. W. Ollerhead,6 M. Omori,11 J. L. Orrell,17 S. M. Oser,12 A. W. P. Poon,8,17,2,9 T. J. Radcliffe,14 A. Roberge,7 B. C. Robertson,14 R. G. H. Robertson,17,9 S. S. E. Rosendahl,8 J. K. Rowley,3 V. L. Rusu,12 E. Saettler,7 K. K. Schaffer,17 M. H. Schwendener,7 A. Schülke,8 H. Seifert,7,17,9 M. Shatkay,5 J. J. Simpson,6 C. J. Sims,11 D. Sinclair,5,16 P. Skensved,14 A. R. Smith,8 M. W. E. Smith,17 T. Spreitzer,12 N. Starinsky,5 T. D. Steiger,17 R. G. Stokstad,8 L. C. Stonehill,17 R. S. Storey,10 B. Sur,1,14 R. Tafirout,7 N. Tagg,6,11 N. W. Tanner,11 R. K. Taplin,11 M. Thorman,11 P. M. Thornewell,11 P. T. Trent,11 Y. I. Tserkovnyak,2 R. Van Berg,12 R. G. Van de Water,9,12 C. J. Virtue,7 C. E. Waltham,2 J.-X. Wang,6 D. L. Wark,15,11,9 N. West,11 J. B. Wilhelmy,9 J. F. Wilkerson,17,9 J. R. Wilson,11 P. Wittich,12 J. M. Wouters,9 and M. Yeh3 (SNO Collaboration) 1 Atomic Energy of Canada, Limited, Chalk River Laboratories, Chalk River, Ontario K0J 1J0, Canada Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada 3 Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973-5000 4 Department of Physics, University of California, Irvine, California 92717 5 Carleton University, Ottawa, Ontario K1S 5B6, Canada 6 Physics Department, University of Guelph, Guelph, Ontario N1G 2W1, Canada 7 Department of Physics and Astronomy, Laurentian University, Sudbury, Ontario P3E 2C6, Canada 8 Institute for Nuclear and Particle Astrophysics and Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 9 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 10 National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada 11 Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom 12 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396 13 Department of Physics, Princeton University, Princeton, New Jersey 08544 14 Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada 15 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom and University of Sussex, Physics and Astronomy Department, Brighton BN1 9QH, United Kingdom 16 TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada 17 Center for Experimental Nuclear Physics and Astrophysics, and Department of Physics, University of Washington, Seattle, Washington 98195 (Received 19 April 2002; published 13 June 2002) 2 Observations of neutral-current n interactions on deuterium in the Sudbury Neutrino Observatory are reported. Using the neutral current (NC), elastic scattering, and charged current reactions and assuming the standard 8 B shape, the ne component of the 8 B solar flux is 10.09 6 22 21 fe 苷 1.7610.05 s for a kinetic energy threshold of 5 MeV. The non-ne 20.05 共stat兲20.09 共syst兲 3 10 cm 10.45 10.48 component is fmt 苷 3.4120.45 共stat兲20.45 共syst兲 3 106 cm22 s21 , 5.3s greater than zero, providing 011301-1 0031-9007兾02兾 89(1)兾011301(6)$20.00 © 2002 The American Physical Society 011301-1 VOLUME 89, NUMBER 1 PHYSICAL REVIEW LETTERS 1 JULY 2002 strong evidence for solar ne flavor transformation. The total flux measured with the NC reaction is 10.46 6 22 21 s , consistent with solar models. fNC 苷 5.0910.44 20.43 共stat兲20.43 共syst兲 3 10 cm DOI: 10.1103/PhysRevLett.89.011301 The Sudbury Neutrino Observatory (SNO) detects 8 B solar neutrinos through the reactions: ne 1 d ! p 1 p 1 e2 共CC兲 , nx 1 d ! p 1 n 1 nx 共NC兲 , nx 1 e 2 ! nx 1 e2 共ES兲 . The charged current (CC) reaction is sensitive exclusively to electron-type neutrinos, while the neutral current (NC) reaction is equally sensitive to all active neutrino flavors 共x 苷 e, m, t兲. The elastic scattering (ES) reaction is sensitive to all flavors as well, but with reduced sensitivity to nm and nt . Sensitivity to these three reactions allows SNO to determine the electron and nonelectron active neutrino components of the solar flux [1]. The CC and ES reaction results have recently been presented [2]. This Letter presents the first NC results and updated CC and ES results from SNO. SNO [3] is a water Cherenkov detector located at a depth of 6010 m of water equivalent in the INCO, Ltd. Creighton mine near Sudbury, Ontario, Canada. The detector uses ultrapure heavy water contained in a transparent acrylic spherical shell 12 m in diameter to detect solar neutrinos. Cherenkov photons generated in the heavy water are detected by 9456 photomultiplier tubes (PMTs) mounted on a stainless steel geodesic sphere 17.8 m in diameter. The geodesic sphere is immersed in ultrapure light water to provide shielding from radioactivity in both the PMT array and the cavity rock. The data reported here were recorded between 2 November 1999 and 28 May 2001 and represent a total of 306.4 live days, spanning the entire first phase of the experiment, in which only D2 O was present in the sensitive volume. The analysis procedure was similar to that described in [2]. PMT times and hit patterns were used to reconstruct event vertices and directions and to assign to each event a most probable kinetic energy, Teff . The total flux of active 8 B solar neutrinos with energies greater than 2.2 MeV (the NC reaction threshold) was measured with the NC signal (Cherenkov photons resulting from the 6.25 MeV g ray from neutron capture on deuterium). The analysis threshold was Teff $ 5 MeV, providing sensitivity to neutrons from the NC reaction. Above this energy threshold, there were contributions from CC events in the D2 O, ES events in the D2 O and H2 O, capture of neutrons (both from the NC reaction and backgrounds), and low energy Cherenkov background events. A fiducial volume was defined to accept only events which had reconstructed vertices within 550 cm from the detector center to reduce external backgrounds and systematic uncertainties associated with optics and event reconstruction near the acrylic vessel. The neutron response and systematic uncertainty was calibrated with a 252 Cf 011301-2 PACS numbers: 26.65. +t, 14.60.Pq, 95.85.Ry source. The deduced efficiency for neutron captures on deuterium is 29.9 6 1.1% for a uniform source of neutrons in the D2 O. The neutron detection efficiency within the fiducial volume and above the energy threshold is 14.4%. The energy calibration was updated from [2] with the 16 N calibration source [4] data and Monte Carlo calculations. The energy response for electrons, updated for the lower analysis threshold, was characterized as a Gaussian p function with resolution sT 苷 20.0684 1 0.331 Te 1 0.0425Te , where Te is the true electron kinetic energy in MeV. The energy scale uncertainty is 1.2%. The primary backgrounds to the NC signal are due to low levels of uranium and thorium decay chain daughters (214 Bi and 208 Tl) in the detector materials. These activities generate free neutrons in the D2 O, from deuteron photodisintegration (pd), and low energy Cherenkov events. Ex situ assays and in situ analysis of the low energy (4 –4.5 MeV) Cherenkov signal region provide independent uranium and thorium photodisintegration background measurements. Two ex situ assay techniques were employed to determine average levels of uranium and thorium in water. Radium ions were directly extracted from the water onto either MnOx or hydrous Ti oxide (HTiO) ion exchange media. Radon daughters in the U and Th chains were subsequently released, identified by a spectroscopy, or the radium was concentrated and the number of decay daughter b-a coincidences determined. Typical assays circulated approximately 400 tonnes of water through the extraction media. These techniques provide isotopic identification of the decay daughters and contamination levels in the assayed water volumes, presented in Fig. 1(a). Secular equilibrium in the U decay chain was broken by the ingress of long-lived (3.8 day half-life) 222 Rn in the experiment. Measurements of this background were made by periodically extracting and cryogenically concentrating 222 Rn from water degassers. Radon from several tonne assays was subsequently counted in ZnS(Ag) scintillation cells [5]. The radon results are presented [as mass fractions in g共U兲兾g共D2 O兲] in Fig. 1(b). Independent measurements of U and Th decay chains were made by analyzing Cherenkov light produced by the radioactive decays. The b and b-g decays from the U and Th chains dominate the low energy monitoring window. Events in this window monitor g rays that produce photodisintegration in these chains 共Eg . 2.2 MeV兲. Cherenkov events fitted within 450 cm from the detector center and extracted from the neutrino data set provide a time-integrated measure of these backgrounds over the same time period and within the fiducial volume of the neutrino analysis. Statistical separation of in situ Tl and Bi events was obtained by analyzing the Cherenkov signal isotropy. Tl decays always result in a b and a 2.614 MeV g, while in this energy window Bi decays are dominated 011301-2 VOLUME 89, NUMBER 1 PHYSICAL REVIEW LETTERS FIG. 1 (color). Thorium (a) and uranium (b) backgrounds (equivalent equilibrium concentrations) in the D2 O deduced by in situ and ex situ techniques. The MnOx and HTiO radiochemical assay results, the Rn assay results, and the in situ Cherenkov signal determination of the backgrounds are presented for the period of this analysis on the left-hand side of frames (a) and (b). The right-hand side shows timeintegrated averages including an additional sampling systematic uncertainty for the ex situ measurement. by decays with only a b, and produce, on average, more anisotropic hit patterns. Results from the ex situ and in situ methods are consistent with each other as shown on the right-hand side of Figs. 1(a) and 1(b). For the 232 Th chain, the weighted mean (including additional sampling systematic uncertainty) of the two determinations was used for the analysis. The 238 U chain activity is dominated by Rn ingress which is highly time dependent. Therefore the in situ determination was used for this activity as it provides the appropriate time weighting. The average rate of background neutron production from activities in the D2 O region is 1.0 6 0.2 neutrons per day, leading to 4418 29 detected background events. The production rate from 10.4 neutrons per day, which leads external activities is 1.320.5 to 27 6 8 background events since the neutron capture efficiency is reduced for neutrons born near the heavy water boundary. The total photodisintegration background corresponds to approximately 12% of the number of NC neutrons predicted by the standard solar model from 8 B neutrinos. Low energy backgrounds from Cherenkov events in the signal region were evaluated by using acrylic encapsulated 011301-3 1 JULY 2002 sources of U and Th deployed throughout the detector volume and by Monte Carlo calculations. Probability density functions (pdfs) in reconstructed vertex radius derived from U and Th calibration data were used to determine the number of background Cherenkov events from external regions which either entered or misreconstructed into the fiducial volume. Cherenkov event backgrounds from activities in the D2 O were evaluated with Monte Carlo calculations. Table I shows the number of photodisintegration and Cherenkov background events (including systematic uncertainties) due to activity in the D2 O (internal region), acrylic vessel (AV), H2 O (external region), and PMT array. Other sources of free neutrons in the D2 O region are cosmic ray events and atmospheric neutrinos. To reduce these backgrounds, an additional neutron background cut imposed a 250-ms dead time (in software) following every event in which the total number of PMTs which registered a hit was greater than 60. The number of remaining NC atmospheric neutrino events and background events generated by sub-Cherenkov threshold muons is estimated to be small, as shown in Table I. The data recorded during the pure D2 O detector phase are shown in Fig. 2. These data have been analyzed using the same data reduction described in [2], with the addition of the new neutron background cut, yielding 2928 events in the energy region selected for analysis, 5 to 20 MeV. Figure 2(a) shows the distribution of selected events in the cosine of the angle between the Cherenkov event direction and the direction from the Sun 共cosuØ 兲 for the analysis threshold of Teff $ 5 MeV and fiducial volume selection of R # 550 cm, where R is the reconstructed event radius. Figure 2(b) shows the distribution of events in the volumeweighted radial variable 共R兾RAV 兲3 , where RAV 苷 600 cm is the radius of the acrylic vessel. Figure 2(c) shows the kinetic energy spectrum of the selected events. In order to test the null hypothesis, the assumption that there are only electron neutrinos in the solar neutrino TABLE I. Neutron and Cherenkov background events. Source Events D2 O photodisintegration H2 O 1 AV photodisintegration Atmospheric n’s and Fission sub-Cherenkov threshold m’s 2 H共a, a兲pn 17 O共a, n兲 Terrestrial and reactor n̄’s External neutrons Total neutron background D2 O Cherenkov H2 O Cherenkov AV Cherenkov PMT Cherenkov Total Cherenkov background 18 4429 18 2728 461 ø1 2 6 0.4 ø1 113 21 ø1 78 6 12 113 2026 314 23 613 26 111 1628 118 45212 011301-3 VOLUME 89, NUMBER 1 PHYSICAL REVIEW LETTERS 1 JULY 2002 cosuØ , and 共R兾RAV 兲3 , derived from Monte Carlo calculations generated assuming no flavor transformation and the standard 8 B spectral shape [6]. Background event pdfs are included in the analysis with fixed amplitudes determined by the background calibration. The extended maximum likelihood method used in the signal decompo126.4 sition yields 1967.7161.9 260.9 CC events, 263.6225.6 ES events, 149.5 and 576.5248.9 NC events [7], where only statistical uncertainties are given. Systematic uncertainties on fluxes derived by repeating the signal decomposition with perturbed pdfs (constrained by calibration data) are shown in Table II. Normalized to the integrated rates above the kinetic energy threshold of Teff $ 5 MeV, the flux of 8 B neutrinos measured with each reaction in SNO, assuming the standard spectrum shape [6] is (all fluxes are presented in units of 106 cm22 s21 ) SNO 10.09 fCC 苷 1.7610.06 20.05 共stat兲20.09 共syst兲 , 10.24 SNO 苷 2.3920.23 共stat兲10.12 fES 20.12 共syst兲 , SNO 10.44 苷 5.0920.43 共stat兲10.46 fNC 20.43 共syst兲 . Electron neutrino cross sections are used to calculate all fluxes. The CC and ES results reported here are consistent with the earlier SNO results [2] for Teff $ 6.75 MeV. The excess of the NC flux over the CC and ES fluxes implies neutrino flavor transformations. A simple change of variables resolves the data directly into electron 共fe 兲 and nonelectron 共fmt 兲 components [9], 10.05 fe 苷 1.7620.05 共stat兲10.09 20.09 共syst兲 , 10.45 fmt 苷 3.4120.45 共stat兲10.48 20.45 共syst兲 , FIG. 2 (color). (a) Distribution of cosuØ for R # 550 cm. (b) Distribution of the volume weighted radial variable 共R兾RAV 兲3 . (c) Kinetic energy for R # 550 cm. Also shown are the Monte Carlo predictions for CC, ES, and NC 1 bkgd neutron events scaled to the fit results, and the calculated spectrum of Cherenkov background (bkgd) events. The dashed lines represent the summed components, and the bands show 61s uncertainties. All distributions are for events with Teff $ 5 MeV. flux, the data are resolved into contributions from CC, ES, and NC events above threshold using pdfs in Teff , 011301-4 assuming the standard 8 B shape. Combining the statistical and systematic uncertainties in quadrature, fmt 10.66 is 3.4120.64 , which is 5.3s above zero, providing strong evidence for flavor transformation consistent with neutrino oscillations [10,11]. Adding the SuperKamiokande ES measurement of the 8B flux [12] SK fES 苷 2.32 6 0.03共stat兲10.08 20.07 共syst兲 as an additional 10.65 constraint, we find fmt 苷 3.4520.62 , which is 5.5s above zero. Figure 3 shows the flux of nonelectron flavor active neutrinos vs the flux of electron neutrinos deduced from the SNO data. The three bands represent the one standard deviation measurements of the CC, ES, and NC rates. The error ellipses represent the 68%, 95%, and 99% joint probability contours for fe and fmt . Removing the constraint that the solar neutrino energy spectrum is undistorted, the signal decomposition is repeated using only the cosuØ and 共R兾RAV 兲3 information. The total flux of active 8 B neutrinos measured with the NC reaction is SNO 11.57 fNC 苷 6.4221.57 共stat兲10.55 20.58 共syst兲 , which is in agreement with the shape constrained value above and with the standard solar model (SSM) prediction 11.01 [13] for 8 B, fSSM 苷 5.0520.81 . 011301-4 VOLUME 89, NUMBER 1 TABLE II. PHYSICAL REVIEW LETTERS 1 JULY 2002 Systematic uncertainties on fluxes. The experimental uncertainty for ES (not shown) is 24.8, 15.0 percent. Source CC uncertainty (percent) NC uncertainty (percent) fmt uncertainty (percent) Energy scalea Energy resolutiona Energy nonlinearitya Vertex resolutiona Vertex accuracy Angular resolution Internal source pda External source pd DO2 Cherenkova HO2 Cherenkov AV Cherenkov PMT Cherenkova Neutron capture Cut acceptance Experimental uncertainty Cross section [8] 24.2, 14.3 20.9, 10.0 60.1 60.0 22.8, 12.9 20.2, 10.2 60.0 60.1 20.1, 10.2 60.0 60.0 60.1 60.0 20.2, 10.4 25.2, 15.2 61.8 26.2, 16.1 20.0, 14.4 60.4 60.1 61.8 20.3, 10.3 21.5, 11.6 21.0, 11.0 22.6, 11.2 20.2, 10.4 20.2, 10.2 22.1, 11.6 24.0, 13.6 20.2, 10.4 28.5, 19.1 61.3 210.4, 110.3 20.0, 16.8 60.6 60.2 61.4 20.3, 10.3 22.0, 12.2 61.4 23.7, 11.7 20.2, 10.6 20.3, 10.3 23.0, 12.2 25.8, 15.2 20.2, 10.4 213.2, 114.1 61.4 a Denotes CC vs NC anticorrelation. In summary, the results presented here are the first direct measurement of the total flux of active 8 B neutrinos arriving from the Sun and provide strong evidence for neutrino flavor transformation. The CC and ES reaction rates are consistent with the earlier results [2] and with the NC reaction rate under the hypothesis of flavor transformation. The total flux of 8 B neutrinos measured with the NC reaction is in agreement with the SSM prediction. FIG. 3 (color). Flux of 8 B solar neutrinos which are m or t flavor vs flux of electron neutrinos deduced from the three neutrino reactions in SNO. The diagonal bands show the total 8 B flux as predicted by the SSM [13] (dashed lines) and that measured with the NC reaction in SNO (solid band). The intercepts of these bands with the axes represent the 61s errors. The bands intersect at the fit values for fe and fmt , indicating that the combined flux results are consistent with neutrino flavor transformation assuming no distortion in the 8 B neutrino energy spectrum. 011301-5 This research was supported by Canada: NSERC, Industry Canada, NRC, Northern Ontario Heritage Fund Corporation, Inco, AECL, Ontario Power Generation; U.S.: Department of Energy; U.K.: PPARC. We thank the SNO technical staff for their strong contributions. *Permanent address: Birkbeck College, University of London, Malet Road, London WC1E 7HX, UK. † Deceased. [1] H. H. Chen, Phys. Rev. Lett. 55, 1534 (1985). [2] Q. R. Ahmad et al., Phys. Rev. Lett. 87, 071301 (2001). [3] SNO Collaboration, J. Boger et al., Nucl. Instrum. Methods Phys. Res., Sect. A 449, 172 (2000). [4] M. R. Dragowsky et al., Nucl. Instrum. Methods Phys. Res., Sect. A 481, 284 (2002). [5] M.-Q. Liu, H. W. Lee, and A. B. McDonald, Nucl. Instrum. Methods Phys. Res., Sect. A 329, 291 (1993). [6] C. E. Ortiz et al., Phys. Rev. Lett. 85, 2909 (2000). [7] We note that this rate of neutron events also leads to a lower bound on the proton lifetime for “invisible” modes {based on the free neutron that would be left in deuterium [V. I. Tretyak and Yu. G. Zdesenko, Phys. Lett. B 505, 59 (2001)] in excess of 1028 years, approximately 3 orders of magnitude more restrictive than previous limits [J. Evans and R. Steinberg, Science 197, 989 (1977)]}. The possible contribution of this mechanism to the solar neutrino NC background is ignored. [8] Cross section uncertainty includes gA uncertainty 共0.6%兲, difference between NSGK [S. Nakamura, T. Sato, V. Gudkov, and K. Kubodera, Phys. Rev. C 63, 034617 (2001)] and BCK [M. Butler, J.-W. Chen, and X. Kong, Phys. Rev. C 63, 035501 (2001)] in SNO’s calculations 共0.6%兲, radiative correction uncertainties [0.3% for CC, 0.1% for NC; A. Kurylov, M. J. Ramsey-Musolf, and P. Vogel, Phys. Rev. C 65, 055501 (2002)], uncertainty associated with neglect of real photons in SNO (0.7% for CC), and 011301-5 VOLUME 89, NUMBER 1 PHYSICAL REVIEW LETTERS theoretical cross section uncertainty [1%, S. Nakamura et al., arXiv:nucl-th/0201062 (to be published)]. [9] This change of variables allows a direct test of the null hypothesis of no flavor transformation 共fmt 苷 0兲 without requiring calculation of the CC, ES, and NC signal correlations. 011301-6 1 JULY 2002 [10] Z. Maki, N. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28, 870 (1962). [11] V. Gribov and B. Pontecorvo, Phys. Lett. 28B, 493 (1969). [12] S. Fukuda et al., Phys. Rev. Lett. 86, 5651 (2001). [13] John N. Bahcall, M. H. Pinsonneault, and Sarbani Basu, Astrophys. J. 555, 990 (2001). 011301-6