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

Measuring the mass of a sterile neutrino with a very short baseline reactor experiment

An analysis of the world's neutrino oscillation data, including sterile neutrinos, (M. Sorel, C. M. Conrad, and M. H. Shaevitz, Phys. Rev. D 70, 073004) found a peak in the allowed region at a mass-squared difference $\Delta m^2 \cong 0.9$ eV$^2$. We trace its origin to harmonic oscillations in the electron survival probability $P_{ee}$ as a function of L/E, the ratio of baseline to neutrino energy, as measured in the near detector of the Bugey experiment. We find a second occurrence for $\Delta m^2 \cong 1.9$ eV$^2$. We point out that the phenomenon of harmonic oscillations of $P_{ee}$ as a function of L/E, as seen in the Bugey experiment, can be used to measure the mass-squared difference associated with a sterile neutrino in the range from a fraction of an eV$^2$ to several eV$^2$ (compatible with that indicated by the LSND experiment), as well as measure the amount of electron-sterile neutrino mixing. We observe that the experiment is independent, to lowest order, of the size of the reactor and suggest the possibility of a small reactor with a detector sitting at a very short baseline.Comment: 4 pages, 2 figure

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

Neutrino Oscillations: Hierarchy Question

The only experimentally observed phenomenon that lies outside the standard model of the electroweak interaction is neutrino oscillations. A way to try to unify the extensive neutrino oscillation data is to add a phenomenological mass term to the Lagrangian that is not diagonal in the flavor basis. The goal is then to understand the world's data in terms of the parameters of the mixing matrix and the differences between the squares of the masses of the neutrinos. An outstanding question is what is the correct ordering of the masses, the hierarchy question. We point out a broken symmetry relevant to this question, the symmetry of the simultaneous interchange of hierarchy and the sign of $\theta_{13}$. We first present the results of an analysis of data that well determine the phenomenological parameters but are not sensitive to the hierarchy. We find $\theta_{13} = 0.152\pm 0.014$, $\theta_{23} = 0.25^{+0.03}_{-0.05} \pi$ and $\Delta_{32} = 2.45\pm 0.14 \times 10^{-3}$ eV$^2$, results consistent with others. We then include data that are sensitive to the hierarchy and the sign of $\theta_{13}$. We find, unlike others, four isolated minimum in the $\chi^2$-space as predicted by the symmetry. Now that Daya Bay and RENO have determined $\theta_{13}$ to be surprisingly large, the Super-K atmospheric data produce meaningful symmetry breaking such that the inverse hierarchy is preferred at the 97.2 % level.Comment: to appear in Proceedings of the 5th International Conference on Fission and Neutron Rich Nuclei (ICFN5), (Sanibel Island, Florina, Nov. 4-10, 2012).10 pages, 8 figure

Three-flavour neutrino oscillation update

We review the present status of three-flavour neutrino oscillations, taking into account the latest available neutrino oscillation data presented at the Neutrino 2008 Conference. This includes the data released this summer by the MINOS collaboration, the data of the neutral current counter phase of the SNO solar neutrino experiment, as well as the latest KamLAND and Borexino data. We give the updated determinations of the leading 'solar' and 'atmospheric' oscillation parameters. We find from global data that the mixing angle $\theta_{13}$ is consistent with zero within $0.9\sigma$ and we derive an upper bound of $\sin^2\theta_{13} < 0.035 (0.056)$ at 90% CL (3$\sigma$).Comment: 17 pages, 7 figures. An appendix is added providing three-neutrino parameter determinations as of February 2010. We include all oscillation data, such as the first MINOS electron neutrino appearance data, the low energy threshold analysis given by the SNO Collaboration, as well as recently updated Standard Solar Model