Testing the Principle of Equivalence by Solar Neutrinos

We discuss the possibility of testing the principle of equivalence with solar neutrinos. If there exists a violation of the equivalence principle quarks and leptons with different flavors may not universally couple with gravity. The method we discuss employs a quantum mechanical phenomenon of neutrino oscillation to probe into the non-universality of the gravitational couplings of neutrinos. We develop an appropriate formalism to deal with neutrino propagation under the weak gravitational fields of the sun in the presence of the flavor mixing. We point out that solar neutrino observation by the next generation water Cherenkov detectors can improve the existing bound on violation of the equivalence principle by 3-4 orders of magnitude if the nonadiabatic Mikheyev-Smirnov-Wolfenstein mechanism is the solution to the solar neutrino problem.Comment: Latex, 17 pages + 6 uuencoded postscript figures, KEK-TH-396, TMUP-HEL-9402 (unnecessary one reference was removed

A Two-Dimensional Model with Chiral Condensates and Cooper Pairs Having QCD-like Phase Structure

We describe how a generalization of the original Gross-Neveu model from U(N) to O(N) flavor symmetry leads to the appearance of a pairing condensate at high density, in agreement with the conjectured phenomenon of color superconductivity in $(3+1)$-dimensional QCD. Moreover, the model displays a rich phase structure which closely resembles the one expected in two-flavor QCD.Comment: 11 pages, 1 fugure, Presented at TMU-Yale Symposium on Dynamics of Gauge Fields: An External Activity of APCTP, Tokyo, Japan, 13-15 Dec 199

Dynamical Pion Production via Parametric Resonance from Disoriented Chiral Condensate

We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $\sigma$ oscillations, which may be appropriate for the late stage of nonequilibrium phase transition. It allows us to obtain an explicit quantum state of the produced pions and $\sigma$, the squeezed state of BCS type. Single particle distributions and two-pion correlation functions are computed within these approximations. The results obtained illuminate the characteristic features of multi-pion states produced through the parametric amplification mechanism. In particular, two-pion correlations of various charge combinations contain back-to-back correlations which cannot be masked by the identical particle interference effect.Comment: REVTEX 18 pages and 10 figure

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

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

Recoilless Resonant Absorption of Monochromatic Neutrino Beam for Measuring Delta m^2_{31} and theta_{13}

We discuss, in the context of precision measurement of Delta m^2_{31} and theta_{13}, physics capabilities enabled by the recoilless resonant absorption of monochromatic antineutrino beam enhanced by the M\"ossbauer effect recently proposed by Raghavan. Under the assumption of small relative systematic error of a few tenth of percent level between measurement at different detector locations, we give analytical and numerical estimates of the sensitivities to Delta m^2_{31} and sin^2 2theta_{13}. The accuracies of determination of them are enormous; The fractional uncertainty in Delta m^2_{31} achievable by 10 point measurement is 0.6% (2.4%) for sin^2 2theta_{13} = 0.05, and the uncertainty of sin^2 2theta_{13} is 0.002 (0.008) both at 1 sigma CL with the optimistic (pessimistic) assumption of systematic error of 0.2% (1%). The former opens a new possibility of determining the neutrino mass hierarchy by comparing the measured value of Delta m^2_{31} with the one by accelerator experiments, while the latter will help resolving the theta_{23} octant degeneracy.Comment: 23 pages, 3 figures, version to appear in New Journal of Physic

High Energy Cosmic Neutrinos and the Equivalence Principle

Observation of the ultra-high energy neutrinos, in particular, detection of $\nu_{\tau}$ from cosmologically distant sources like active galactic nuclei (AGN) opens new possibilities to search for neutrino flavor conversion. We consider effects of violation of the equivalence principle (VEP) on propagation of these cosmic neutrinos. Two effects are studied: (1) the oscillations of neutrinos due to the VEP in the gravitational field of our Galaxy and in the intergalactic space, (2) the resonance flavor conversion driven by the gravitational potential of the AGN. We show that the ultra-high energies of the neutrinos as well as cosmological distances to the AGN, or strong AGN gravitational potential will allow one to improve the accuracy of test of the equivalence principle by 21 orders of magnitude for massless or degenerate neutrinos ($\Delta f \sim 10^{-41}$) and at least by 12 orders of magnitude for massive neutrinos ($\Delta f \sim 10^{-28} \times (\Delta m^2/1 {\rm eV}^2)$). Experimental signatures of the transitions induced by the VEP are discussed.Comment: 24 pages, revtex, no figures, slightly revised with no change in conclusio

CP violation effects and high energy neutrinos

This work discusses critically the prospects of measuring CP and T violation effects in high energy neutrino factories. For this purpose we develop, in the standard framework with three neutrino flavors, simple expressions for the oscillation probabilities in matter that are valid for high E_nu. All CP violating effects vanish as E_nu^(-3) and are very difficult to detect with high energy neutrinos. A significantly easier task is the determination of the absolute value |delta| of the phase in the neutrino mixing matrix that controls the CP and T violation effects, performing precision measurements of the CP and T conserving part of the oscillation probabilities.Comment: Latex, 46 pages, 15 figure