Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev.

Neutrino flavor conversion in a neutrino background: single- versus multi-particle description

In the early Universe, or near a supernova core, neutrino flavor evolution may be affected by coherent neutrino-neutrino scattering. We develop a microscopic picture of this phenomenon. We show that coherent scattering does not lead to the formation of entangled states in the neutrino ensemble and therefore the evolution of the system can always be described by a set of one-particle equations. We also show that the previously accepted formalism overcounts the neutrino interaction energy; the correct one-particle evolution equations for both active-active and active-sterile oscillations contain additional terms. These additional terms modify the index of refraction of the neutrino medium, but have no effect on oscillation physics.Comment: 12 pages, 3 figures, minor typos correcte

Solar Neutrinos with Three Flavor Mixings

The recent 71Ga solar neutrino observation is combined with the 37Cl and Kamiokande-II observations in an analysis for neutrino masses and mixings. The allowed parameter region is found for matter enhanced mixings among all three neutrino flavors. Distortions of the solar neutrino spectrum unique to three flavors are possible and may be observed in continuing and next generation experiments.Comment: August 1992 (Revised) PURD-TH-92-

Matter effects in long baseline experiments, the flavor content of the heaviest (or lightest) neutrino and the sign of Delta m^2

The neutrinos of long baseline beams travel inside the Earth's crust where the density is approximately rho = 2.8 g cm^-3. If electron neutrinos participate in the oscillations, matter effects will modify the oscillation probabilities with respect to the vacuum case. Depending on the sign of Delta m^2 an MSW resonance will exist for neutrinos or anti-neutrinos with energy approximately E_nu(res) = 4.7 |\Delta m^2|/(10^-3 eV^2) GeV. For Delta m^2 in the interval indicated by the Super-Kamiokande experiment this energy range is important for the proposed long baseline experiments. For positive Delta m^2 the most important effects of matter are a 9% (25%) enhancement of the transition probability P(nu_mu -> nu_e) for the KEK to Kamioka (Fermilab to Minos and CERN to Gran Sasso) beam(s) in the energy region where the probability has its first maximum, and an approximately equal suppression of P(antinu_mu -> antinu_e). For negative Delta m^2 the effects for neutrinos and anti-neutrinos are interchanged. Producing beams of neutrinos and antineutrinos and measuring the oscillation probabilities for both (nu_mu -> nu_e) and (antinu_mu -> antinu_e) transitions can solve the sign ambiguity in the determination of Delta m^2.Comment: Latex, 28 pages, 12 postscript figure

Constraints on Exotic Mixing of Three Neutrinos

Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, reactor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow large electron-neutrino mixing of atmospheric neutrinos. Next generation long baseline experiments will constrain these possibilities.Comment: 27 pages, 4 figure

Neutrino Oscillations in the Early Universe with Nonequilibrium Neutrino Distributions

Around one second after the big bang, neutrino decoupling and $e^+$-$e^-$ annihilation distort the Fermi-Dirac spectrum of neutrino energies. Assuming neutrinos have masses and can mix, we compute the distortions using nonequilibrium thermodynamics and the Boltzmann equation. The flavor behavior of neutrinos is studied during and following the generation of the distortion.Comment: accepted for publication in Physical Review

Momentum-dependent contributions to the gravitational coupling of neutrinos in a medium

When neutrinos travel through a normal matter medium, the electron neutrinos couple differently to gravity compared to the other neutrinos, due to the presence of electrons in the medium and the absence of the other charged leptons. We calculate the momentum-dependent part of the matter-induced gravitational couplings of the neutrinos under such conditions, which arise at order $g^2/M^4_W$, and determine their contribution to the neutrino dispersion relation in the presence of a gravitational potential $\phi^{\mathrm{ext}}$. These new contributions vanish for the muon and tau neutrinos. For electron neutrinos with momentum $K$, they are of the order of the usual Wolfenstein term times the factor $(K^2/M^2_W)\phi^{\mathrm{ext}}$, for high energy neutrinos. In environments where the gravitational potential is substantial, such as those in the vicinity of Active Galactic Nuclei, they could be the dominant term in the neutrino dispersion relation. They must also be taken into account in the analysis of possible violations of the Equivalence Principle in the neutrino sector, in experimental settings involving high energy neutrinos traveling through a matter background.Comment: Minor corrections in the references; one reference adde

General relations of heavy quark-antiquark potentials induced by reparameterization invariance

A set of general relations between the spin-independent and spin-dependent potentials of heavy quark and anti-quark interactions are derived from reparameterization invariance in the Heavy Quark Effective Theory. It covers the Gromes relation and includes some new interesting relations which are useful in understanding the spin-independent and spin-dependent relativistic corrections to the leading order nonrelativistic potential.Comment: 11 pages, TUIMP-TH-93/54, CCAST-93-3

Quantum field theoretic approach to neutrino oscillations in matter

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos correcte