2 A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neu- trino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3 . 18 × 10 20 protons on target in which neutrinos of energies between ∼ 500 MeV and 120 GeV are produced predominantly as ν$_{µ}$ , the visible energy spectrum of candidate neutral-current reactions in the MINOS far-detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ν$_{µ}$ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles θ 24 and θ 34 are constrained to be less than 11 ◦ and 56 ◦ at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscilla- tions is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime τ 3 /m 3 > 2 . 1 × 10 − 12 s/eV at 90% C.L. PACS numbers: 14.60.St, 12.15.Mm, 14.60.Pq, 14.60.Lm, 29.27.-a, 29.30.-h alternatives. I. INTRODUCTION Compelling evidence has been presented demonstrat- ing the disappearance of muon and electron neutrinos as they propagate from their production point. Dis- appearance of muon neutrinos has been observed from neutrino fluxes originating in the atmosphere [1, 2] and accelerator beams [3, 4]; disappearance of electron neu- trinos has been observed with neutrino fluxes from the Sun [5, 6] and terrestrial reactors [7]. Super-Kamiokande and other atmospheric neutrino experiments were the first to report significant deficits of ν$_{µ}$ charged-current interactions from neutrinos propagating over baselines larger than several hundred kilometers. The K2K and MINOS experiments have observed the disappearance using accelerator-beam neutrinos propagating over fixed baselines of 250 km and 735 km, respectively. All experi- ments reporting muon-neutrino disappearance favor pure ν$_{µ}$ → ν$_{τ}$ oscillations as the explanation for the observed disappearance of ν$_{µ}$ [3, 8–10]. However, more exotic sce- narios in which one or more sterile neutrinos, ν$_{s}$ , mix with the three active neutrino species remain as viable Long-baseline experiments such as MINOS provide an opportunity to test alternative scenarios by com- paring the observed neutral-current interaction rates in near and far-detectors. Since all active neutrinos, ν$_{e}$, ν$_{µ}$ , and ν$_{τ}$ , participate in the neutral-current inter- action, this comparison provides a sensitive probe to the existence of processes that deplete the flux of active neu- trinos between the two detectors. If neutrinos only oscil- late among the active flavors, the rate of neutral-current interactions at the far site of a long-baseline experiment remains unchanged from the null-oscillation prediction. However, if another process occurs concurrently with ac- tive neutrino oscillations, the rate of neutral-current in- teractions at the far site may be different. Two such pos- sibilities have attracted considerable attention and are the focus of the analysis reported here, (i) active neutri- nos oscillating to ν$_{s}$ , and (ii) neutrino decay in conjunc- tion with oscillations. The possible existence of one or more sterile neutrinos that do not couple to the electroweak current but do mix with the active flavors has been discussed extensively in the literature [11–13]. The existence of sterile neutrinos would provide new degrees of freedom that could help clarify certain outstanding problems with the neutrino- mass spectrum [14] and with heavy element nucleosyn- thesis in supernovae [15]. A recent search for neutrino oscillations in a short baseline experiment provides no evidence for transitions that would imply existence of sterile neutrinos [16]. The coupling between sterile neutrinos and the ac- tive neutrinos would likely involve the third mass eigen- state. Observations by the SNO experiment show the total flux of active neutrinos from the Sun to agree with expectations from solar models [6], thereby limiting the potential coupling of the first or second neutrino-mass eigenstates to a sterile neutrino. Additionally, the Super- Kamiokande experiment strongly disfavors pure ν$_{µ}$ → ν$_{s}$ $^{∗}$Now at Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India. $^{†}$Now at Center for Cosmology and Astro Particle Physics, Ohio State University, Columbus, Ohio 43210 USA. $^{‡}$Now at Department of Physics, Pennsylvania State University, State College, Pennsylvania 16802, USA. $^{§}$Now at Physics Department, St. John Fisher College, Rochester, New York 14618 USA. $^{¶}$Deceased. $^{∗∗}$Now at Lawrence Berkeley National Laboratory, Berkeley, Cali- fornia 94720, USA. $^{††}$Now at Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA. $^{‡‡}$Now at Los Alamos National Laboratory, Los Alamos, New Mex- ico 87545, USA.