Angular momentum non-conserving decays in isotropic media

Various processes that are forbidden in the vacuum due to angular momentum conservation can occur in a medium that is isotropic and does not carry any angular momentum. We illustrate this by considering explicitly two examples. The first one is the decay of a spin-0 particle into a photon and another spin-0 particle, using a model involving the Yukawa interactions of the scalar particles with a charged fermion field. The second one involves the decay of a neutrino into another neutrino and a graviton, in the standard model of particle interactions augmented with the linearized gravitational couplings.Comment: 22 pages, Latex, uses axodraw.sty. 3 figures embedded in the tex file. This paper contains the same material as that presented in two earlier papers, arXiv:0901.2981 and arXiv:0901.2982, written by us. This version supersedes those two paper

Gravitational couplings of charged leptons in a medium

We calculate the leading order matter-induced corrections to the gravitational interactions of charged leptons and their antiparticles in a medium that contains electrons but not the other charged leptons, such as normal matter. The gravitational coupling, which is universal at the tree level, is found to be flavor-dependent, and also different for the corresponding antiparticles, when the corrections of $O(\alpha)$ are taken into account. General expressions are obtained for the matter-induced corrections to the gravitational mass in a generic matter background, and explicit formulas for those corrections are given in terms of the macroscopic parameters of the medium for particular conditions of the background gases.Comment: Latex, axodraw, 39 pages. Added a few stylistic corrections and clarifying statements in the treatment of the photon tadpole diagra

The electromagnetic vertex of neutrinos in an electron background and a magnetic field

We study the electromagnetic vertex function of a neutrino that propagates in an electron background in the presence of a static magnetic field. The structure of the vertex function under the stated conditions is determined and it is written down in terms of a minimal and complete set of tensors. The one-loop expressions for all the form factors is given, up to terms that are linear in the magnetic field, and the approximate integral formulas that hold in the long wavelength limit are obtained. We discuss the physical interpretation of some of the form factors and their relation with the concept of the neutrino induced charge. The neutrino acquires a longitudinal and a transverse charge, due to the fact that the form factors depend on the transverse and longitudinal components of the photon momentum independently. We compute those form factors explicitly in various limiting cases and find that the longitudinal and transverse charge are the same for the case of a non-relativistic electron gas, but not otherwise.Comment: 18 pages. Revtex4, axodra

CP-violating Majorana phases, lepton-conserving processes and final state interactions

The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as \mu -> eee+, \mu + e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates depends on such phases. Our calculations illustrate in detail the mechanics that operate behind the scene, and set the stage for carrying out the analogous, more complicated (as we explain), calculations for other processes such as \mu -> eee+ and its conjugate.Comment: Latex, axodraw, 24 page

Light propagation in generally covariant electrodynamics and the Fresnel equation

Within the framework of generally covariant (pre-metric) electrodynamics, we specify a local vacuum spacetime relation between the excitation $H=({\cal D},{\cal H})$ and the field strength $F=(E,B)$. We study the propagation of electromagnetic waves in such a spacetime by Hadamard's method and arrive, with the constitutive tensor density $\kappa\sim\partial H/\partial F$, at a Fresnel equation which is algebraic of 4th order in the wave covector. We determine how the different pieces of $\kappa$, in particular the axion and the skewon pieces, affect the propagation of light.Comment: 6 pages, uses ws-ijmpa.cls. Invited talk given at Journees Relativistes, University College Dublin, Sept. 2001. Will appear in Int.J.Mod.Phys.

Photons, neutrinos and optical activity

We compute the one-loop helicity amplitudes for low-energy $\nu\gamma\to\nu\gamma$ scattering and its crossed channels in the standard model with massless neutrinos. In the center of mass, with $\sqrt{s} = 2\omega\ll 2m_e$, the cross sections for these $2\to 2$ channels grow roughly as $\omega^6$. The scattered photons in the elastic channel are circularly polarized and the net value of the polarization is non-zero. We also present a discussion of the optical activity of a sea of neutrinos and estimate the values of its index of refraction and rotary power.Comment: 9 pages, ReVTeX4, 6 figures include

Faraday effect : a field theoretical point of view

We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. We use various discrete symmetries and crossing symmetry to constrain the form factors obtained for the most general case. From these symmetry arguments, we show why the vacuum polarization tensor has to be even in the background field when there is no background medium. Taking then the background field to be purely magnetic, we evaluate the vacuum polarization to linear order in it. The result shows the phenomenon of Faraday rotation, i.e., the rotation of the plane of polarization of a plane polarized light passing through this background. We find that the usual expression for Faraday rotation, which is derived for a non-degenerate plasma in the non-relativistic approximation, undergoes substantial modification if the background is degenerate and/or relativistic. We give explicit expressions for Faraday rotation in completely degenerate and ultra-relativistic media.Comment: 20 pages, Latex, uses axodraw.st

Neutrinoless Double Beta Decay and CP Violation

We study the relation between the Majorana neutrino mass matrices and the neutrinoless double beta decay when CP is not conserved. We give an explicit form of the decay rate in terms of a rephasing invariant quantity and demonstrate that in the presence of CP violation it is impossible to have vanishing neutrinoless double beta decay in the case of two neutrino generations (or when the third generation leptons do not mix with other leptons and hence decouple).Comment: 9 pages, UTPT-93-1

Optical activity of neutrinos and antineutrinos

Using the one-loop helicity amplitudes for low-energy $\nu\gamma\to\nu\gamma$ and $\bar\nu\gamma\to\bar\nu\gamma$ scattering in the standard model with massless neutrinos, we study the optical activity of a sea of neutrinos and antineutrinos. In particular, we estimate the values of the index of refraction and rotary power of this medium in the absence of dispersion.Comment: Additional reference

Plasma wave instabilities induced by neutrinos

Quantum field theory is applied to study the interaction of an electron plasma with an intense neutrino flux. A connection is established between the field theory results and classical kinetic theory. The dispersion relation and damping rate of the plasma longitudinal waves are derived in the presence of neutrinos. It is shown that Supernova neutrinos are never collimated enough to cause non-linear effects associated with a neutrino resonance. They only induce neutrino Landau damping, linearly proportional to the neutrino flux and $G_{\mathrm{F}}^{2}$.Comment: 18 pages, 3 figures, title and references correcte