578 research outputs found

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

We present a large-$N$ 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

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 $\nu_\mu$ wave packet
which, in turn, changes the group velocity and the distance $\nu_\mu$ travels.
We find that the change of the distance, $d_{osc}$, is proportional to the
length of the wave packet, $\sigma_x$, and the oscillation phase, $\phi_p$,
acquired by neutrinos in the $\pi-$ and $K-$ meson decay tunnel where neutrino
wave packet is formed: $d_{osc} \propto \sigma \phi_p$. Although the distance
$d_{osc}$ may effectively correspond to the superluminal motion, the effect is
too tiny ($\sim 10^{- 5}$ cm) to be reconciled with the OPERA result. We
analyze various possibilities to increase $d_{osc}$ and discuss experimental
setups in which $d_{osc}$ (corresponding to the superluminal motion) can reach
an observable value $\sim 1$ 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

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

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

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