Large-Theta(13) Perturbation Theory of Neutrino Oscillation for Long-Baseline Experiments

The Cervera et al. formula, the best known approximate formula of neutrino oscillation probability for long-baseline experiments, can be regarded as a second-order perturbative formula with small expansion parameter epsilon \equiv Delta m^2_{21} / Delta m^2_{31} \simeq 0.03 under the assumption s_{13} \simeq epsilon. If theta_{13} is large, as suggested by a candidate nu_{e} event at T2K as well as the recent global analyses, higher order corrections of s_{13} to the formula would be needed for better accuracy. We compute the corrections systematically by formulating a perturbative framework by taking theta_{13} as s_{13} \sim \sqrt{epsilon} \simeq 0.18, which guarantees its validity in a wide range of theta_{13} below the Chooz limit. We show on general ground that the correction terms must be of order epsilon^2. Yet, they nicely fill the mismatch between the approximate and the exact formulas at low energies and relatively long baselines. General theorems are derived which serve for better understanding of delta-dependence of the oscillation probability. Some interesting implications of the large theta_{13} hypothesis are discussed.Comment: Fig.2 added, 23 pages. Matches to the published versio

Parameter Degeneracies in Neutrino Oscillation Measurement of Leptonic CP and T Violation

The measurement of the mixing angle \theta_{13}, sign of \Delta m^2_{13} and the CP or T violating phase \delta is fraught with ambiguities in neutrino oscillation. In this paper we give an analytic treatment of the paramater degeneracies associated with measuring the \nu_\mu -> \nu_e probability and its CP and/or T conjugates. For CP violation, we give explicit solutions to allow us to obtain the regions where there exist two-fold and four-fold degeneracies. We calculate the fractional differences, \Delta \theta / \bar{\theta}, between the allowed solutions which may be used to compare with the expected sensitivities of the experiments. For T violation we show that there is always a complete degeneracy between solutions with positive and negative \Delta m^2_{13} which arises due to a symmetry and cannot be removed by observing one neutrino oscillation probability and its T conjugate. Thus, there is always a four fold parameter degeneracy apart from exceptional points. Explicit solutions are also given and the fractional differences are computed. The bi-probability CP/T trajectory diagrams are extensively used to illuminate the nature of the degeneracies.Comment: 35 pages, Latex, 11 postscript figures, minor correction

The Complementarity of Eastern and Western Hemisphere Long-Baseline Neutrino Oscillation Experiments

We present a general formalism for extracting information on the fundamental parameters associated with neutrino masses and mixings from two or more long baseline neutrino oscillation experiments. This formalism is then applied to the current most likely experiments using neutrino beams from the Japan Hadron Facility (JHF) and Fermilab's NuMI beamline. Different combinations of muon neutrino or muon anti-neutrino running are considered. To extract the type of neutrino mass hierarchy we make use of the matter effect. Contrary to naive expectation, we find that both beams using neutrinos is more suitable for determining the hierarchy provided that the neutrino energy divided by baseline ($E/L$) for NuMI is smaller than or equal to that of JHF. Whereas to determine the small mixing angle, $\theta_{13}$, and the CP or T violating phase $\delta$, one neutrino and the other anti-neutrino is most suitable. We make extensive use of bi-probability diagrams for both understanding and extracting the physics involved in such comparisons.Comment: 21 pages, Latex, 3 postscript figure

Perturbation Theory of Neutrino Oscillation with Nonstandard Neutrino Interactions

We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking \Delta m^2_{21} / \Delta m^2_{31}, s_{13}, and the NSI elements \epsilon_{\alpha \beta} (\alpha, \beta = e, \mu, \tau) as small expansion parameters of the same order \epsilon. Within the \epsilon perturbation theory we obtain the S matrix elements and the neutrino oscillation probability formula to second order (third order in \nu_e related channels) in \epsilon. The formula allows us to estimate size of the contribution of any particular NSI element \epsilon_{\alpha beta} to the oscillation probability in arbitrary channels, and gives a global bird-eye view of the neutrino oscillation phenomena with NSI. Based on the second-order formula we discuss how all the conventional lepton mixing as well as NSI parameters can be determined. Our results shows that while \theta_{13}, \delta, and the NSI elements in \nu_e sector can in principle be determined, complete measurement of the NSI parameters in the \nu_\mu - \nu_\tau sector is not possible by the rate only analysis. The discussion for parameter determination and the analysis based on the matter perturbation theory indicate that the parameter degeneracy prevails with the NSI parameters. In addition, a new solar-atmospheric variable exchange degeneracy is found. Some general properties of neutrino oscillation with and without NSI are also illuminated.Comment: manuscript restructured, discussion of new type of parameter degeneracy added. 47 page

Unity of CP and T Violation in Neutrino Oscillations

In a previous work a simultaneous P- CP[P] and P- T[P] bi-probability plot was proposed as a useful tool for unified graphical description of CP and T violation in neutrino oscillation. The ``baseball diamond'' structure of the plot is understood as a consequence of the approximate CP-CP and the T-CP relations obeyed by the oscillation probabilities. In this paper, we make a step forward toward deeper understanding of the unified graphical representation by showing that these two relations are identical in its content, suggesting a truly unifying view of CP and T violation in neutrino oscillations. We suspect that the unity reflects the underlying CPT theorem. We also present calculation of corrections to the CP-CP and the T-CP relations to leading order in Delta m^2_{21} / Delta m^2_{31} and s^2_{13}.Comment: 20 references added, version to appear in "Focus Issue on Neutrino Physics" of New Journal of Physic

Resolving Octant Degeneracy at LBL experiment by combining Daya Bay Reactor Setup

Long baseline Experiment (LBL) have promised to be a very powerful experimental set up to study various issues related to Neutrinos. Some ongoing and planned LBL and medium baseline experiments are - T2K, MINOS, NOvA, LBNE, LBNO etc. But the long baseline experiments are crippled due to presence of some parameter degeneracies, like the Octant degeneracy. In this work, we first show the presence of Octant degeneracy in LBL experiments, and then combine it with Daya Bay Reactor experiment, at different values of CP violation phase. We show that the Octant degeneracy in LBNE can be resolved completely with this proposal.Comment: 4 pages, 8 figure

Physics Potential of a 2540 Km Baseline Superbeam Experiment

We study the physics potential of a neutrino superbeam experiment with a 2540 km baseline. We assume a neutrino beam similar to the NuMI beam in medium energy configuration. We consider a 100 kton totally active scintillator detector at a 7 mr off-axis location. We find that such a configuration has outstanding hierarchy discriminating capability. In conjunction with the data from the present reactor neutrino experiments, it can determine the neutrino mass hierarchy at 3 sigma level in less than 5 years, if sin^2(2*theta13) > 0.01, running in the neutrino mode alone. As a stand alone experiment, with a 5 year neutrino run and a 5 year anti-neutrino run, it can determine non-zero theta13 at 3 sigma level if sin^2(2*theta13) > 7*10^{-3} and hierarchy at 3 sigma level if sin^2(2*theta13) > 8*10^{-3}. This data can also distinguish deltaCP = pi/2 from the CP conserving values of 0 and pi, for sin^2(2*theta13) > 0.02.Comment: 16 pages, 7 figures and 1 table: Published versio

Reactor Measurement of θ13\theta_{13} and Its Complementarity to Long-Baseline Experiments

A possibility to measure $\sin^22\theta_{13}$ using reactor neutrinos is examined in detail. It is shown that the sensitivity $\sin^22\theta_{13}>0.02$ can be reached with 20 ton-year data by placing identical CHOOZ-like detectors at near and far distances from a giant nuclear power plant whose total thermal energy is 24.3 ${\text{GW}_{\text{th}}}$. It is emphasized that this measurement is free from the parameter degeneracies which occur in accelerator appearance experiments, and therefore the reactor measurement plays a role complementary to accelerator experiments. It is also shown that the reactor measurement may be able to resolve the degeneracy in $\theta_{23}$ if $\sin^22\theta_{13}$ and $\cos^22\theta_{23}$ are relatively large.Comment: 25 pages, 8 figures, uses revtex4 and graphicx. Several modifications added to make the text easier to understand. Two more figures added. To be published in Phys. Rev.

Probing Non-Standard Neutrino Interactions with Neutrino Factories

We discuss the sensitivity reach of a neutrino factory measurement to non-standard neutrino interactions (NSI), which may exist as a low-energy manifestation of physics beyond the Standard Model. We use the muon appearance mode \nu_e --> \nu_\mu and consider two detectors, one at 3000 km and the other at 7000 km. Assuming the effects of NSI at the production and the detection are negligible, we discuss the sensitivities to NSI and the simultaneous determination of \theta_{13} and \delta by examining the effects in the neutrino propagation of various systems in which two NSI parameters \epsilon_{\alpha \beta} are switched on. The sensitivities to off-diagonal \epsilon's are found to be excellent up to small values of \theta_{13}. We demonstrate that the two-detector setting is powerful enough to resolve the \theta_{13}-NSI confusion problem. We believe that the results obtained in this paper open the door to the possibility of using neutrino factory as a discovery machine for NSI while keeping its primary function of performing precision measurements of the lepton mixing parameters.Comment: 47 pages, 22 figures. Color version of Figs. 18, 19 and 22 can be found in the article published in JHE

Prospects of accelerator and reactor neutrino oscillation experiments for the coming ten years

We analyze the physics potential of long baseline neutrino oscillation experiments planned for the coming ten years, where the main focus is the sensitivity limit to the small mixing angle $\theta_{13}$. The discussed experiments include the conventional beam experiments MINOS, ICARUS, and OPERA, which are under construction, the planned superbeam experiments J-PARC to Super-Kamiokande and NuMI off-axis, as well as new reactor experiments with near and far detectors, represented by the Double-Chooz project. We perform a complete numerical simulation including systematics, correlations, and degeneracies on an equal footing for all experiments using the GLoBES software. After discussing the improvement of our knowledge on the atmospheric parameters $\theta_{23}$ and $\Delta m^2_{31}$ by these experiments, we investigate the potential to determine $\theta_{13}$ within the next ten years in detail. Furthermore, we show that under optimistic assumptions and for $\theta_{13}$ close to the current bound, even the next generation of experiments might provide some information on the Dirac CP phase and the type of the neutrino mass hierarchy.Comment: 38 pages, 13 figures, Eqs. (1) and (5) corrected, small corrections in Figs. 8, 9, and Tab. 4, discussion improved, ref. added, version to appear in PRD, high resolution figures are available at http://www.sns.ias.edu/~winter/figs0403068.htm