1,203 research outputs found
On the degeneracies of the mass-squared differences for three-neutrino oscillations
Using an algebraic formulation, we explore two well-known degeneracies
involving the mass-squared differences for three-neutrino oscillations assuming
CP symmetry is conserved. For vacuum oscillation, we derive the expression for
the mixing angles that permit invariance under the interchange of two
mass-squared differences. This symmetry is most easily expressed in terms of an
ascending mass order. This can be used to reduce the parameter space by one
half in the absence of the MSW effect. For oscillations in matter, we derive
within our formalism the known approximate degeneracy between the standard and
inverted mass hierarchies in the limit of vanishing . This is done
with a mass ordering that permits the map .
Our techniques allow us to translate mixing angles in this mass order
convention into their values for the ascending order convention. Using this
dictionary, we demonstrate that the vacuum symmetry and the approximate
symmetry invoked for oscillations in matter are distinctly different.Comment: 5 pages, revised manuscrip
Contributions of LANDSAT to natural resource protection and future recreational development in the state of West Virginia
There are no author-identified significant results in this report
On detecting CP violation in a single neutrino oscillation channel at very long baselines
We propose a way of detecting CP violation in a single neutrino oscillation
channel at very long baselines (on the order of several thousands of
kilometers), given precise knowledge of the smallest mass-squared difference.
It is shown that CP violation can be characterized by a shift in of the
peak oscillation in the -- appearance channel, both in vacuum
and in matter. In fact, matter effects enhance the shift at a fixed energy. We
consider the case in which sub-GeV neutrinos are measured with varying baseline
and also the case of a fixed baseline. For the varied baseline, accurate
knowledge of the absolute neutrino flux would not be necessary; however,
neutrinos must be distinguishable from antineutrinos. For the fixed baseline,
it is shown that CP violation can be distinguished if the mixing angle
were known.Comment: 8 pages, 9 figures; minor typos correcte
Calculating error bars for neutrino mixing parameters
One goal of contemporary particle physics is to determine the mixing angles
and mass-squared differences that constitute the phenomenological constants
that describe neutrino oscillations. Of great interest are not only the best
fit values of these constants but also their errors. Some of the neutrino
oscillation data is statistically poor and cannot be treated by normal
(Gaussian) statistics. To extract confidence intervals when the statistics are
not normal, one should not utilize the value for chisquare versus confidence
level taken from normal statistics. Instead, we propose that one should use the
normalized likelihood function as a probability distribution; the relationship
between the correct chisquare and a given confidence level can be computed by
integrating over the likelihood function. This allows for a definition of
confidence level independent of the functional form of the !2 function; it is
particularly useful for cases in which the minimum of the !2 function is near a
boundary. We present two pedagogic examples and find that the proposed method
yields confidence intervals that can differ significantly from those obtained
by using the value of chisquare from normal statistics. For example, we find
that for the first data release of the T2K experiment the probability that
chisquare is not zero, as defined by the maximum confidence level at which the
value of zero is not allowed, is 92%. Using the value of chisquare at zero and
assigning a confidence level from normal statistics, a common practice, gives
the over estimation of 99.5%.Comment: 9 pages, 6 figure
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