578 research outputs found

    Large-N Collective Field Theory Applied to Anyons in Magnetic Fields

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    We present a large-NN collective field formalism for anyons in external magnetic fields interacting with arbitrary two-body potential. We discuss how the Landau level is reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of collective modes for arbitrary statistical parameters.Comment: 10 pages(Plain TeX) TMUP-HEL-930

    Neutrino Velocity and Neutrino Oscillations

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    We study distances of propagation and the group velocities of the muon neutrinos in the presence of mixing and oscillations assuming that Lorentz invariance holds. Oscillations lead to distortion of the νμ\nu_\mu wave packet which, in turn, changes the group velocity and the distance νμ\nu_\mu travels. We find that the change of the distance, doscd_{osc}, is proportional to the length of the wave packet, σx\sigma_x, and the oscillation phase, ϕp\phi_p, acquired by neutrinos in the π\pi- and KK- meson decay tunnel where neutrino wave packet is formed: doscσϕpd_{osc} \propto \sigma \phi_p. Although the distance doscd_{osc} may effectively correspond to the superluminal motion, the effect is too tiny (105\sim 10^{- 5} cm) to be reconciled with the OPERA result. We analyze various possibilities to increase doscd_{osc} and discuss experimental setups in which doscd_{osc} (corresponding to the superluminal motion) can reach an observable value 1\sim 1 m.Comment: LaTeX, 24 pages, 1 eps figure, matches to the published versio

    Large-Theta(13) Perturbation Theory of Neutrino Oscillation for Long-Baseline Experiments

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    The Cervera et al. formula, the best known approximate formula of neutrino oscillation probability for long-baseline experiments, can be regarded as a second-order perturbative formula with small expansion parameter epsilon \equiv Delta m^2_{21} / Delta m^2_{31} \simeq 0.03 under the assumption s_{13} \simeq epsilon. If theta_{13} is large, as suggested by a candidate nu_{e} event at T2K as well as the recent global analyses, higher order corrections of s_{13} to the formula would be needed for better accuracy. We compute the corrections systematically by formulating a perturbative framework by taking theta_{13} as s_{13} \sim \sqrt{epsilon} \simeq 0.18, which guarantees its validity in a wide range of theta_{13} below the Chooz limit. We show on general ground that the correction terms must be of order epsilon^2. Yet, they nicely fill the mismatch between the approximate and the exact formulas at low energies and relatively long baselines. General theorems are derived which serve for better understanding of delta-dependence of the oscillation probability. Some interesting implications of the large theta_{13} hypothesis are discussed.Comment: Fig.2 added, 23 pages. Matches to the published versio

    Parameter Degeneracies in Neutrino Oscillation Measurement of Leptonic CP and T Violation

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    The measurement of the mixing angle \theta_{13}, sign of \Delta m^2_{13} and the CP or T violating phase \delta is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the \nu_\mu -> \nu_e probability and its CP and/or T conjugates. For CP violation, we give explicit solutions to allow us to obtain the regions where there exist two-fold and four-fold degeneracies. We calculate the fractional differences, \Delta \theta / \bar{\theta}, between the allowed solutions which may be used to compare with the expected sensitivities of the experiments. For T violation we show that there is always a complete degeneracy between solutions with positive and negative \Delta m^2_{13} which arises due to a symmetry and cannot be removed by observing one neutrino oscillation probability and its T conjugate. Thus, there is always a four fold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The bi-probability CP/T trajectory diagrams are extensively used to illuminate the nature of the degeneracies.Comment: 35 pages, Latex, 11 postscript figures, minor correction