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The SNO Collaboration, Phys. Lett. B 194, 321 (1987), and references therein. 2. Q. , Phys. Rev. Lett. 87, 071301 (2001). 3. N. Tatara, Y. Kohyama and K. Kubodera, Phys. Rev. C 42, 1694 (1990); S. Ying, W. C. Haxton and E. M. Henley, Phys. Rev. C 45, 1982 (1992); for a review, see K. Kubodera and S. Nozawa, Int. J. Mod. Phys. E 3, 101 (1994). 29 4. S. Nakamura, T. Sato, V. Gudkov and K. Kubodera, Phys. Rev. C 63, 034617 (2001). 5. For a review, see U. van Kolck, Prog. Part. Nucl. R. Beane et al, in "At the Frontiers of Particle Physics - Handbook of QCD", ed.

Acknowledgments This analysis relies crucially on Super-Kamiokande data. The author acknowledges the extensive help and cooperation of the Super-Kamiokande collaboration as well as the Kamioka Mining and Smelting Company. S. S. National Science Foundation. Appendix: Fitting Method To estimate and limit oscillation parameters, a \2 describing the shape of the SK zenith spectrum is extended to take into account the measured neutrino interaction rates by various experiments. " (due to hep neutrinos) in energy bin i and zenith-angle bin z are calculated.

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