Neutrino oscillations and Lorentz Invariance Violation in a Finslerian Geometrical model

Neutrino oscillations are one of the first evidences of physics beyond the Standard Model (SM). Since Lorentz Invariance is a fundamental symmetry of the SM, recently also neutrino physics has been explored to verify the eventual modification of this symmetry and its potential magnitude. In this work we study the consequences of the introduction of Lorentz Invariance Violation (LIV) in the high energy neutrinos propagation and evaluate the impact of this eventual violation on the oscillation predictions. An effective theory explaining these physical effects is introduced via Modified Dispersion Relations. This approach, originally introduced by Coleman and Glashow, corresponds in our model to a modification of the special relativity geometry. Moreover, the generalization of this perspective leads to the introduction of a maximum attainable velocity which is specific of the particle. This can be formalized in Finsler geometry, a more general theory of space-time. In the present paper the impact of this kind of LIV on neutrino phenomenology is studied, in particular by analyzing the corrections introduced in neutrino oscillation probabilities for different values of neutrino energies and baselines of experimental interest. The possibility of further improving the present constraints on CPT-even LIV coefficients by means of our analysis is also discussed.Comment: Accepted for publication with minor revisions, will appear on European Physics Journal

Solar Neutrinos

The study of solar neutrinos has given since ever a fundamental contribution both to astroparticle and to elementary particle physics, offering an ideal test of solar models and offering at the same time relevant indications on the fundamental interactions among particles. After reviewing the striking results of the last two decades, which were determinant to solve the long standing solar neutrino puzzle and refine the Standard Solar Model, we focus our attention on the more recent results in this field and on the experiments presently running or planned for the near future. The main focus at the moment is to improve the knowledge of the mass and mixing pattern and especially to study in detail the lowest energy part of the spectrum, which represents most of solar neutrino spectrum but is still a partially unexplored realm. We discuss this research project and the way in which present and future experiments could contribute to make the theoretical framemork more complete and stable, understanding the origin of some "anomalies" that seem to emerge from the data and contributing to answer some present questions, like the exact mechanism of the vacuum to matter transition and the solution of the so called solar metallicity problem.Comment: 51 pages, to be published in Special Issue on Neutrino Physics, Advances in High Energy Physics Hindawi Publishing Corporation 201

A New Basis for QED Bound State Computations

A simple method to compute QED bound state properties is presented, in which binding energy effects are treated non-perturbatively. It is shown that to take the effects of all ladder Coulomb photon exchanges into account, one can simply perform the derivative of standard QED amplitudes with respect to the external momentum. For example, the derivative of the light-by-light scattering amplitude gives an amplitude for orthopositronium decay to three photons where any number of Coulomb photon exchanges between the e-e+ is included. Various applications are presented. From them, it is shown that binding energy must be treated non-perturbatively in order to preserve the analyticity of positronium decay amplitudes. Interesting perspectives for quarkonium physics are briefly sketched.Comment: LaTeX, 23 pages, 16 figures. Minor corrections. Some comments adde

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Weak solutions to problems involving inviscid fluids

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy

Calibrated American option pricing by stochastic linear programming

Cataloged from PDF version of article.We propose an approach for computing the arbitrage-free interval for the price of an American option in discrete incomplete market models via linear programming. The main idea is built replicating strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European options. Here, we extend the analysis to American options showing that the arbitrage-free interval can be characterized in terms of martingale measures and that it gets significantly reduced with respect to the non-calibrated case

Sifting the Network: Performing Packet Triage with NFR

We describe a set of Network Flight Recorder scripts designed to detect network intrusions. After developing scripts that detect some known attacks, we focus on sifting scripts that attempt to remove "normal" traffic from a packet stream, leaving behind fewer packets requiring manual inspection. We conclude with a description of our experiences with the NFR product.http://deepblue.lib.umich.edu/bitstream/2027.42/107922/1/citi-tr-98-6.pd

Positronium Decay : Gauge Invariance and Analyticity

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those non-factorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of order alpha^3. Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.Comment: 34 pages, 13 figure