18 Acknowledgments lifetime ratio α = 0 . 00 +0 . 90 − 0 0 × 10 − $^{3}$GeV/km and mixing angle θ = 45 . 0 ◦ +10 . 83 − 8 . 96 . From these results, we extract a 90% confidence level limit on the neutrino decay lifetime, τ$_{3}$/m$_{3}$ > 2 . 1 × 10 − $^{12}$s/eV. The pure decay scenario (Δ m 2 32 → 0) is disfavored by 5.4 standard deviations in our data as an alternative explanation to neutrino oscil- lations. Energy, the U.S. National Science Foundation, the U.K. Science and Technology Facilities Council, the State and University of Minnesota, the Office of Special Accounts for Research Grants of the University of Athens, Greece, FAPESP (Funda¸c˜ ao de Amparo a Pesquisa do Estado de S˜ ao Paulo) and CNPq (Conselho Nacional de Desenvolvi- mento Cient´ıfico e Tecnol´ ogico) in Brazil. We gratefully acknowledge the Minnesota Department of Natural Re- sources for their assistance and for allowing access to the facilities of the Soudan Underground Mine State Park. We thank the crew of the Soudan Underground Physics laboratory for their tireless work in building and operat- ing the MINOS far-detector. We thank S. Parke and P. Huber for useful discussions concerning oscillations between active and sterile neutri- nos. This work was supported by the U.S. Department of [1] R. Becker-Szendy et al. (IMB-3), Phys. Rev. D 46 , 3720 (1992); K. S. Hirata et al. (Kamiokande), Phys. Lett. B 280 , 146 (1992); W.W.M. Allison et al. (Soudan-2), Phys. Rev. D 72 , 052005 (2005); M. Ambrosio et al. (MACRO), Eur. Phys. J. C. 36 , 323 (2004). [17] P. Adamson et al. (MINOS), Phys. Rev. Lett. 101 , 221804 (2008). [18] V. Barger, J. G. Learned, S. Pakvasa, and T. J. Weiler, Phys. Rev. Lett. 82 , 2640 (1999). [19] Y. Ashie et al. (Super-Kamiokande), Phys. Rev. Lett. 93 , 101801 (2004). [20] D. G. Michael et al. (MINOS), Nucl. Instrum. Meth. A 596 , 190 (2008). [21] N. Tagg et al., Nucl. Instrum. Meth. A 539 , 668 (2005). [2] Y. Fukuda et al. (Super-Kamiokande), Phys. Rev. Lett. 81 , 1562 (1998); Y. Ashie et al. (Super-Kamiokande), Phys. Rev. Lett. 93 , 101801 (2004); Y. Ashie et al. (Super-Kamiokande), Phys. Rev. D 71 , 112005 (2005). [3] M. H. Ahn et al. (K2K), Phys. Rev. D 74 , 072003 (2006). [4] P. Adamson et al., Phys. Rev. D 77 072002 (2008); D. G. Michael et al., Phys. Rev. Lett. 97 , 191801 (2006). [5] R. Davis et al. (Homestake), Phys. Rev. Lett. 20 , 1205 (1968); P. Anselmann et al. (GALLEX), Phys. Lett. B 285 , 376 (1992); J. N. Abdurashitov et al. (SAGE), Phys. Lett. B 328 , 234 (1994); Y. Fukuda et al. (Super-Kamiokande), Phys. Rev. Lett. 86 , 5651 (2001); J. Hosaka et al. (Super-Kamiokande), Phys. Rev. D 73 , 112001 (2006); C. Arpesella et al. (Borexino) Phys. Rev. Lett. 101 , 091302 (2008). [22] K. Lang et al., Nucl. Instrum. Meth. A 545 , 852 (2005). [23] A. Ferrari, P. R. Sala, A. Fasso, and J. Ranft (2005), CERN-2005-010. [24] R. Brun et al. (1994), CERN Program Library Long Writeup W5013. [25] H. Gallagher, Nucl. Phys. Proc. Suppl. 112 , 188 (2002). [26] T. M. Raufer, Ph.D. Thesis, Oxford University (2007). [27] S. Avvakumov et al., Nucl. Instrum. Meth. A 545 , 145 (2005). [28] R. P. Litchfield, Ph.D. Thesis, University of Oxford (2008). [29] T. H. Osiecki, Ph.D. Thesis, University of Texas at Austin (2007). [6] Q. R. Ahmad et al. (SNO), Phys. Rev. Lett. 89 , 011301 (2002). [7] S. Abe et al. (KamLAND), Phys. Rev. Lett. 100 , 221803 (2008); T. Araki et al. (KamLAND), Phys. Rev. Lett. 94 , 081801 (2005). [30] D. J. Koskinen, Ph.D. Thesis, University College London (2009). [31] M. Apollonio et al. (CHOOZ), Eur. Phys. J. C 27 , 331 (2003). [32] Z. Maki, M. Nakagawa, and S. Sakata, Prog Theor. Phys. 28 , 870 (1962); B. Pontecorvo, Sov. Phys. JETP 34 , 172 (1958); V. N. Gribov and B. Pontecorvo, Phys. Lett. B 28 , 493 (1969). [33] J. Schechter and J. W. F. Valle, Phys. Rev. D 22 , 2227 (1980). [8] Y. Fukuda et al. (Super-Kamiokande), Phys. Rev. Lett. 85 , 3999 (2000). [9] K. Abe et al. (Super-Kamiokande), Phys. Rev. Lett. 97 , 171801 (2006). [10] P. Adamson et al. (MINOS), Phys. Rev. Lett. 101 , 131802 (2008). [34] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667 , 1 (2008); B. Kayser (2008), arXiv:hep- ph/0804.1121. [35] L. Wolfenstein, Phys. Rev. D 17 , 2369 (1978); S. P. Mikheev and A. Y. Smirnov, Sov. J. Nucl. Phys. 42 , 913 (1985); see, for example, P. Lipari and M. Lusig- noli, Phys. Rev. D 58 , 073005 (1998). [36] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Lett. B 663 , 405 (2008). [11] G. L. Fogli et al., Phys. Rev. D 64 , 093005 (2001). [12] A. Donini, M. Maltoni, D. Meloni, P. Migliozzi and F. Terranova, J. High En. Phys 12 , 013 (2007). [13] A. Dighe and S. Ray, Phys. Rev. D 76 , 113001 (2007). [14] A. de Gouvea, J. Jenkins, and N. Vasudevan, Phys. Rev. D 75 , 013003 (2007). [15] G. C. McLaughlin et al., Phys. Rev. C 59 , 2873 (1999); D. O. Caldwell et al., Phys. Rev. D 61 , 123005 (2000); J. Fetter et al., Astropart. Phys. 18 , 433 (2003). [16] A. A. Aguilar-Arevalo et al. (MiniBooNE), Phys. Rev. Lett. 98 , 231801 (2007).