Effects and influences on neutrino oscillations due to a thin density layer perturbation added to a matter density profile

In this paper, we show the effects on the transition probabilities for neutrino oscillations due to a thin constant density layer perturbation added to an arbitrary matter density profile. In the case of two neutrino flavors, we calculate the effects both analytically and numerically, whereas in the case of three neutrino flavors, we perform the studies purely numerically. As an realistic example we consider the effects of the Earth's atmosphere when added to the Earth's matter density profile on the neutrino oscillation transition probabilities for atmospheric neutrinos.Comment: 9 pages, 6 figures, LaTeX. Final version to be published in Phys. Lett.

Extrinsic CPT Violation in Neutrino Oscillations

In this talk, we investigate extrinsic CPT violation in neutrino oscillations in matter with three flavors. Note that extrinsic CPT violation is different from intrinsic CPT violation. Extrinsic CPT violation is one way of quantifying matter effects, whereas intrinsic CPT violation would mean that the CPT invariance theorem is not valid. We present analytical formulas for the extrinsic CPT probability differences and discuss their implications for long-baseline experiments and neutrino factory setups.Comment: 4 pages, 1 figure, aipproc LaTeX. Talk presented at the 5th International Workshop on Neutrino Factories & Superbeams (NuFact'03), Columbia University, New York, USA, June 5-11, 2003. To be published in the Proceedings of NuFact'03 (AIP Conference Proceedings

Running of Fermion Observables in Non-Supersymmetric SO(10) Models

We investigate the complete renormalization group running of fermion observables in two different realistic non-supersymmetric models based on the gauge group $\textrm{SO}(10)$ with intermediate symmetry breaking for both normal and inverted neutrino mass orderings. Contrary to results of previous works, we find that the model with the more minimal Yukawa sector of the Lagrangian fails to reproduce the measured values of observables at the electroweak scale, whereas the model with the more extended Yukawa sector can do so if the neutrino masses have normal ordering. The difficulty in finding acceptable fits to measured data is a result of the added complexity from the effect of an intermediate symmetry breaking as well as tension in the value of the leptonic mixing angle $\theta^\ell_{23}$.Comment: 15 pages, 3 figures, 4 tables. Final version published in JHE

Signatures of Compact Halos of Sterile-Neutrino Dark Matter

We investigate compact halos of sterile-neutrino dark matter and examine observable signatures with respect to neutrino and photon emission. Primarily, we consider two cases: primordial black-hole halos and ultra-compact mini-halos. In both cases, we find that there exists a broad range of possible parameter choices such that detection in the near future with X-ray and gamma-ray telescopes might be well possible. In fact, for energies above $10\,{\rm TeV}$, the neutrino telescope IceCube would be a splendid detection machine for such macroscopic dark-matter candidates.Comment: 6 pages, 2 figures, 2 tables; v2: minor modifications to match published versio

Analysis of A Nonsmooth Optimization Approach to Robust Estimation

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure

Effective Neutrino Mixing and Oscillations in Dense Matter

We investigate the effective case of two-flavor neutrino oscillations in infinitely dense matter by using a perturbative approach. We begin by briefly summarizing the conditions for the three-flavor neutrino oscillation probabilities to take on the same form as the corresponding two-flavor probabilities. Then, we proceed with the infinitely dense matter calculations. Finally, we study the validity of the approximation of infinitely dense matter when the effective matter potential is large, but not infinite, this is done by using both analytic and numeric methods.Comment: 12 pages, 4 figures, Elsevier LaTeX, Final version to be published in Phys. Lett.

Neutrino oscillations with three flavors in matter of varying density

In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the Earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the Sun's matter density profile are discussed. We show that for matter density profiles, which do not fluctuate too much, the total evolution operator consisting of $n$ operators can be replaced by one single evolution operator in the semi-classical approximation.Comment: 13 pages, 8 figures, RevTeX. Final version to be published in European Physical Journal

Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians

We investigate how to define in a consistent way the probabilities of the transitions between the "flavor" states of the two-level quantum system, which is described by a non-Hermitian but parity and time-reversal (PT) symmetric Hamiltonian. Explicit calculations are carried out to demonstrate the conservation of probability if a proper definition of the final state is adopted. Finally, this formalism is applied to two-flavor neutrino oscillations $\nu^{}_\mu \to \nu^{}_\mu$ and $\nu^{}_\mu \to \nu^{}_\tau$ in vacuum, where the exact PT symmetry requires the vacuum mixing angle to be maximal, which is compatible with current neutrino oscillation experiments. A possible generalization to the three-flavor case is briefly discussed.Comment: 23 pages, 1 figure. Final version published in J. Math. Phy

Exact series solution to the two flavor neutrino oscillation problem in matter

In this paper, we present a real non-linear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this non-linear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem.Comment: 18 pages, 5 figures, RevTeX4. Final version to be published in Journal of Mathematical Physic

A Probabilistic Perspective on Gaussian Filtering and Smoothing

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and smoothers can be derived straightforwardly by providing methods for computing these moments. Based on this insight, we derive the cubature Kalman smoother and propose a novel robust filtering and smoothing algorithm based on Gibbs sampling