Precise Formulation of Neutrino Oscillation in the Earth

We give a perturbation theory of neutrino oscillation in the Earth. The perturbation theory is valid for neutrinos with energy E \gsim 0.5 GeV. It is formulated using trajectory dependent average potential. Non-adiabatic contributions are included as the first order effects in the perturbation theory. We analyze neutrino oscillation with standard matter effect and with non-standard matter effect. In a three flavor analysis we show that the perturbation theory gives a precise description of neutrino conversion in the Earth. Effect of the Earth matter is substantially simplified in this formulation.Comment: References added, 21 pages, 10 figures, version to appear in PR

Solar neutrinos and 1-3 leptonic mixing

Effects of the 1-3 leptonic mixing on the solar neutrino observables are studied and the signatures of non-zero $\theta_{13}$ are identified. For this we have re-derived the formula for $3\nu$-survival probability including all relevant corrections and constructed the iso-contours of observables in the $\sin^2 \theta_{12} - \sin^2 \theta_{13}$ plane. Analysis of the solar neutrino data gives $\sin^2\theta_{13} = 0.007^{+ 0.080}_{-0.007}$ (90% C.L.) for $\Delta m^2 = 8 \cdot 10^{-5}$ eV$^2$. The combination of the ratio CC/NC at SNO and gallium production rate selects $\sin^2\theta_{13} = 0.017 \pm 0.026$ ($1\sigma$). The global fit of all oscillation data leads to zero best value of $\sin^2 \theta_{13}$. The sensitivity ($1\sigma$ error) of future solar neutrino studies to $\sin^2 \theta_{13}$ can be improved down to 0.01 - 0.02 by precise measurements of the pp-neutrino flux and the CC/NC ratio as well as spectrum distortion at high ($E > 4$ MeV) energies. Combination of experimental results sensitive to the low and high energy parts of the solar neutrino spectrum resolves the degeneracy of angles $\theta_{13}$ and $\theta_{12}$. Comparison of $\sin^2 \theta_{13}$ as well as $\sin^2 \theta_{12}$ measured in the solar neutrinos and in the reactor/accelerator experiments may reveal new effects which can not be seen otherwise.Comment: 36 pages, latex, 10 figures. Analysis and figures are updated with new (salt phase II) SNO results, several clarifications added, typos correcte

Density profiles of supernova matter and determination of neutrino parameters

The flavor conversion of supernova neutrinos can lead to observable signatures related to the unknown neutrino parameters. As one of the determinants in dictating the efficiency of resonant flavor conversion, the local density profile near the MSW resonance in a supernova environment is, however, not so well understood. In this analysis, variable power-law functions are adopted to represent the independent local density profiles near the locations of resonance. It is shown that the uncertain matter density profile in a supernova, the possible neutrino mass hierarchies, and the undetermined 1-3 mixing angle would result in six distinct scenarios in terms of the survival probabilities of $\nu_{e}$ and $\bar{\nu_{e}}$. The feasibility of probing the undetermined neutrino mass hierarchy and the 1-3 mixing angle with the supernova neutrinos is then examined using several proposed experimental observables. Given the incomplete knowledge of the supernova matter profile, the analysis is further expanded to incorporate the Earth matter effect. The possible impact due to the choice of models, which differ in the average energy and in the luminosity of neutrinos, is also addressed in the analysis.Comment: 27 pages, 10 figures. text and figures revised, references added, to appear in Phys. Rev.

Random magnetic fields inducing solar neutrino spin-flavor precession in a three generation context

We study the effect of random magnetic fields in the spin-flavor precession of solar neutrinos in a three generation context, when a non-vanishing transition magnetic moment is assumed. While this kind of precession is strongly constrained when the magnetic moment involves the first family, such constraints do not apply if we suppose a transition magnetic moment between the second and third families. In this scenario we can have a large non-electron anti-neutrino flux arriving on Earth, which can lead to some interesting phenomenological consequences, as, for instance, the suppression of day-night asymmetry. We have analyzed the high energy solar neutrino data and the KamLAND experiment to constrain the solar mixing angle, and solar mass difference, and we have found a larger shift of allowed values.Comment: 10 pages, 3 figure

Bilarge neutrino mixing from supersymmetry with high-scale nonrenormalizable interactions

We suggest a supersymmetric (SUSY) explanation of neutrino masses and mixing, where nonrenormalizable interactions in the hidden sector generate lepton number violating Majorana mass terms for both right-chiral sneutrinos and neutrinos. It is found necessary to start with a superpotential including an array of gauge singlet chiral superfields. This leads to nondiagonal $\Delta L = 2$ mass terms and almost diagonal SUSY breaking $A$-terms. As a result, the observed pattern of bilarge mixing can be naturally explained by the simultaneous existence of the seesaw mechanism and radiatively induced masses. Allowed ranges of parameters in the gauge singlet sector are delineated, corresponding to each of the cases of normal hierarchy, inverted hierarchy and degenerate neutrinos.Comment: 19 pages, 5 figures. Minor modifications are made in the title and the text, some new references are added. To appear in this form in Physical Review

Solar neutrino spectrum, sterile neutrinos and additional radiation in the Universe

Recent results from the SNO, Super-Kamiokande and Borexino experiments do not show the expected upturn of the energy spectrum of events (the ratio $R \equiv N_{obs}/N_{SSM}$) at low energies. At the same time, cosmological observations testify for possible existence of additional relativistic degrees of freedom in the early Universe: $\Delta N_{eff} = 1 - 2$. These facts strengthen the case of very light sterile neutrino, $\nu_s$, with $\Delta m^2_{01} \sim (0.7 - 2) \cdot 10^{-5}$ eV$^2$, which mixes weakly with the active neutrinos. The $\nu_s$ mixing in the mass eigenstate $\nu_1$ characterized by $\sin^2 2\alpha \sim 10^{-3}$ can explain an absence of the upturn. The mixing of $\nu_s$ in the eigenstate $\nu_3$ with $\sin^2 \beta \sim 0.1$ leads to production of $\nu_s$ via oscillations in the Universe and to additional contribution $\Delta N_{eff} \approx 0.7 - 1$ before the big bang nucleosynthesis and later. Such a mixing can be tested in forthcoming experiments with the atmospheric neutrinos as well as in future accelerator long baseline experiments. It has substantial impact on conversion of the supernova neutrinos.Comment: 27 pages, LaTeX, 14 eps figures, 3 figures and additional considerations adde

On in situ Determination of Earth Matter Density in Neutrino Factory

We point out that an accurate in situ determination of the earth matter density \rho is possible in neutrino factory by placing a detector at the magic baseline, L = \sqrt{2} \pi / G_{F} N_{e} where N_{e} denotes electron number density. The accuracy of matter density determination is excellent in a region of relatively large theta_{13} with fractional uncertainty \delta \rho / \rho of about 0.43%, 1.3%, and \lsim 3% at 1 sigma CL at sin^2 2theta_{13}=0.1, 10^{-2}, and 3 x 10^{-3}, respectively. At smaller theta_{13} the uncertainty depends upon the CP phase delta, but it remains small, 3%-7% in more than 3/4 of the entire region of delta at sin^2 2theta_{13} = 10^{-4}. The results would allow us to solve the problem of obscured CP violation due to the uncertainty of earth matter density in a wide range of theta_{13} and delta. It may provide a test for the geophysical model of the earth, or it may serve as a method for stringent test of the MSW theory of neutrino propagation in matter once an accurate geophysical estimation of the matter density is available.Comment: 21 pages, 4 figures, version to appear in PR

Testing CPT Symmetry with Supernova Neutrinos

Diagnosing core of supernova requires favor-dependent reconstruction of three species of neutrino spectra, \nu_e, \bar{\nu}_{e} and \nu_x (a collective notation for \nu_{\mu}, \bar{\nu}_{\mu}, \nu_{\tau}, and \bar{\nu}_{\tau}). We point out that, assuming the information available, CPT symmetry can be tested with supernova neutrinos. We classify all possible level crossing patterns of neutrinos and antineutrinos into six cases and show that half of them contains only the CPT violating mass and mixing patterns. We discuss how additional informations from terrestrial experiments help identifying CPT violation by narrowing down the possible flux patterns. Although the method may not be good at precision test, it is particularly suited to uncover gross violation of CPT such as different mass patterns of neutrinos and antineutrinos. The power of the method is due to the nature of level crossing in supernova which results in the sensitivity to neutrino mass hierarchy and to the unique characteristics of in situ preparation of both \nu and \bar{\nu} beams. Implications of our discussion to the conventional analyses with CPT conservation are also briefly mentioned.Comment: 24 pages, 4 figures, discussion added on narrowing down flux patterns by terrestrial measuremen

Supernova bound on keV-mass sterile neutrinos reexamined

Active-sterile neutrino mixing is strongly constrained for m_s > 100 keV to avoid excessive energy losses from supernova cores. For smaller m_s, matter effects suppress the effective mixing angle except for a resonant range of energies where it is enhanced. We study the case of \nu_tau-\nu_s-mixing where a \nu_tau-\bar\nu_tau asymmetry builds up due to the strong excess of \nu_s over \bar\nu_s emission or vice versa, reducing the overall emission rate. In the warm dark matter range m_s < 10 keV the mixing angle is essentially unconstrained.Comment: 6 pages, 4 figures; minor changes, references updated, matches the published versio

Construction and analysis of a simplified many-body neutrino model

In dense neutrino systems, such as found in the early Universe, or near a supernova core, neutrino flavor evolution is affected by coherent neutrino-neutrino scattering. It has been recently suggested that many-particle quantum entanglement effects may play an essential role in these systems, potentially invalidating the traditional description in terms of a set of single-particle evolution equations. We model the neutrino system by a system of interacting spins, following an earlier work which showed that such a spin system can in some cases be solved exactly. We extend this work by constructing an exact analytical solution to a more general spin system, including initial states with asymmetric spin distribution and, moreover, not necessarily aligned along the same axis. Our solution exhibits a rich set of behaviors, including coherent oscillations and dephasing and a transition from the classical to quantum regimes. We argue that the classical evolution of the spin system captures the entire coherent behavior of the neutrino system, while the quantum effects in the spin system capture some, but not all, of the neutrino incoherent evolution. By comparing the spin and neutrino systems, we find no evidence for the violation of the accepted one-body description, though the argument involves some subtleties not appreciated before. The analysis in this paper may apply to other two-state systems beyond the neutrino field.Comment: 22 pages, 7 figure