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 $\theta_{13}$. This is done with a mass ordering that permits the map $\Delta_{31} \mapsto -\Delta_{31}$. 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 $L/E$ of the peak oscillation in the $\nu_e$--$\nu_\mu$ 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 $\theta_{13}$ 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