By invoking the concept of twisted Poincaré symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations [x µ , x ν ] = iθ µν , where θ µν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré symmetry on QFT on such a space-time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincaré symmetry. PACS: 11.10.Nx Consequently, the commutators of operators are replaced by Moyal brackets and the equiv-

We propose the Hyper-Kamiokande (Hyper-K) detector as a next generation underground water Cherenkov detector. It will serve as a far detector of a long baseline neutrino oscillation experiment envisioned for the upgraded J-PARC, and as a detector capable of observing -far beyond the sensitivity of the Super-Kamiokande (Super-K) detector -proton decays, atmospheric neutrinos, and neutrinos from astronomical origins. The baseline design of Hyper-K is based on the highly successful Super-K, taking full advantage of a well-proven technology.Hyper-K consists of two cylindrical tanks lying side-by-side, the outer dimensions of each tank being 48 (W) × 54 (H) × 250 (L) m 3 . The total (fiducial) mass of the detector is 0.99 (0.56) million metric tons, which is about 20 (25) times larger than that of Super-K. A proposed location for Hyper-K is about 8 km south of Super-K (and 295 km away from J-PARC) at an underground depth of 1,750 meters water equivalent (m.w.e.). The inner detector region of the Hyper-K detector is viewed by 99,000 20-inch PMTs, corresponding to the PMT density of 20% photo-cathode coverage (one half of that of Super-K).Hyper-K presents unprecedented potential for precision measurements of neutrino oscillation parameters and discovery reach for CP violation in the lepton sector. With a total exposure of 5 years (one year being equal to 10 7 sec) to a 2.5-degree off-axis neutrino beam produced by the 1.66 MW J-PARC proton synchrotron, it is expected that the CP phase δ can be determined to better than 18 degrees for all possible values of δ and CP violation can be established with a statistical significance of 3σ for 74% of the δ parameter space if sin 2 2θ 13 > 0.03 and the mass hierarchy is known. If sin 2 2θ 13 is as large as 0.1 the mass hierarchy can be determined with more than 3σ statistical significance for 46% of the δ parameter space. In addition, a high statistics data sample of atmospheric neutrinos will allow us to extract the information on the mass hierarchy and the octant of θ 23 . With a full 10 year duration of data taking, the significance for the mass hierarchy determination is expected to reach 3σ or greater if sin 2 θ 23 > 0.4.Hyper-K can extend the sensitivity to nucleon decays beyond what was achieved by Super-K by an order of magnitude or more. The sensitivities to the partial lifetime of protons for the decay modes of p → e + π 0 and p → νK + are expected to exceed 1 × 10 35 years and 2 × 10 34 years, respectively. This is the only known, realistic detector option capable of reaching such a sensitivity for the p → e + π 0 mode.The scope of studies at Hyper-K also covers high precision measurements of solar neutrinos, observation of both supernova burst neutrinos and supernova relic neutrinos, dark matter searches, and possible detection of solar flare neutrinos. The prospects for neutrino geophysics using Hyper-K are also mentioned.

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Reference [15] should read as follows:[15] S. M. Bilenky and B.