708 research outputs found
Oscillations of high energy neutrinos in matter: Precise formalism and parametric resonance
We present a formalism for precise description of oscillation phenomena in
matter at high energies or high densities, V > \Delta m^2/2E, where V is the
matter-induced potential of neutrinos. The accuracy of the approximation is
determined by the quantity \sin^2 2\theta_m \Delta V/2\pi V, where \theta_m is
the mixing angle in matter and \Delta V is a typical change of the potential
over the oscillation length (l \sim 2\pi/V). We derive simple and physically
transparent formulas for the oscillation probabilities, which are valid for
arbitrary matter density profiles. They can be applied to oscillations of high
energy (E > 10 GeV) accelerator, atmospheric and cosmic neutrinos in the matter
of the Earth, substantially simplifying numerical calculations and providing an
insight into the physics of neutrino oscillations in matter. The effect of
parametric enhancement of the oscillations of high energy neutrinos is
considered. Future high statistics experiments can provide an unambiguous
evidence for this effect.Comment: LaTeX, 5 pages, 1 figure. Linestyles in the figure corrected to match
their description in the caption; improved discussion of the accuracy of the
results; references added. Results and conclusions unchange
A reparametrization invariant surface ordering
We introduce a notion of a non-Abelian loop gauge field defined on points in
loop space. For this purpose we first find an infinite-dimensional tensor
product representation of the Lie algebra which is particularly suited for
fields on loop space. We define the non-Abelian Wilson surface as a `time'
ordered exponential in terms of this loop gauge field and show that it is
reparametrization invariant.Comment: 11 pages, clarifications and added ref
Quantum field theoretic approach to neutrino oscillations in matter
We consider neutrino oscillations in non-uniform matter in a quantum field
theoretic (QFT) approach, in which neutrino production, propagation and
detection are considered as a single process. We find the conditions under
which the oscillation probability can be sensibly defined and demonstrate how
the properly normalized oscillation probability can be obtained in the QFT
framework. We derive the evolution equation for the oscillation amplitude and
discuss the conditions under which it reduces to the standard
Schr\"odinger-like evolution equation. It is shown that, contrary to the common
usage, the Schr\"odinger-like evolution equation is not applicable in certain
cases, such as oscillations of neutrinos produced in decays of free pions
provided that sterile neutrinos with eV exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos
correcte
Floquet theory of neutrino oscillations in the earth
We review the Floquet theory of linear differential equations with periodic
coefficients and discuss its applications to neutrino oscillations in matter of
periodically varying density. In particular, we consider parametric resonance
in neutrino oscillations which can occur in such media, and discuss
implications for oscillations of neutrinos traversing the earth and passing
through the earth's core.Comment: LaTeX, 28 pages, 8 eps figures. Contribution to the special issue of
Yad. Fiz. dedicated to the memory of A.B. Migda
Stimulated Neutrino Transformation with Sinusoidal Density Profiles
Large amplitude oscillations between the states of a quantum system can be
stimulated by sinusoidal external potentials with frequencies that are similar
to the energy level splitting of the states or a fraction thereof. Situations
when the applied frequency is equal to an integer fraction of the energy level
splittings are known as parametric resonances. We investigate this effect for
neutrinos both analytically and numerically for the case of arbitrary numbers
of neutrino flavors. We look for environments where the effect may be observed
and find that supernova are the one realistic possibility due to the necessity
of both large densities and large amplitude fluctuations. The comparison of
numerical and analytic results of neutrino propagation through a model
supernova reveals it is possible to predict the locations and strengths of the
stimulated transitions that occur.Comment: 14 pages, 6 figure
Supernova prompt neutronization neutrinos and neutrino magnetic moments
It is shown that the combined action of spin-flavor conversions of supernova
neutrinos due to the interactions of their Majorana-type transition magnetic
moments with the supernova magnetic fields and flavor conversions due to the
mass mixing can lead to the transformation of \nu_e born in the neutronization
process into their antiparticles \bar{\nu}_e. Such an effect would have a clear
experimental signature and its observation would be a smoking gun evidence for
the neutrino transition magnetic moments. It would also signify the leptonic
mixing parameter |U_{e3}| in excess of 10^{-2}.Comment: LaTex, 25 pages, 3 figures. v4: Discussion section expanded,
references added. Matches the published versio
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