Neutrinos with Lorentz-violating operators of arbitrary dimension

The behavior of fermions in the presence of Lorentz and CPT violation is studied. Allowing for operators of any mass dimension, we classify all Lorentz-violating terms in the quadratic Lagrange density for free fermions. The result is adapted to obtain the effective hamiltonian describing the propagation and mixing of three flavors of left-handed neutrinos in the presence of Lorentz violation involving operators of arbitrary mass dimension. A characterization of the neutrino coefficients for Lorentz violation is provided via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is discussed, including among others the renormalizable limit, the massless scenario, flavor-blind and oscillation-free models, the diagonalizable case, and several isotropic limits. The formalism is combined with existing data on neutrino oscillations and kinematics to extract a variety of measures of coefficients for Lorentz and CPT violation. For oscillations, we use results from the short-baseline experiments LSND and MiniBooNE to obtain explicit sensitivities to effects from flavor-mixing Lorentz-violating operators up to mass dimension 10, and we present methods to analyze data from long-baseline experiments. For propagation, we use time-of-flight measurements from the supernova SN1987A and from a variety of experiments including MINOS and OPERA to constrain oscillation-free Lorentz-violating operators up to mass dimension 10, and we discuss constraints from threshold effects in meson decays and Cherenkov emission.Comment: 35 pages two-column REVTe

Limits on isotropic Lorentz violation in QED from collider physics

We consider the possibility that Lorentz violation can generate differences between the limiting velocities of light and charged matter. Such effects would lead to efficient vacuum Cherenkov radiation or rapid photon decay. The absence of such effects for 104.5 GeV electrons at the Large Electron Positron collider and for 300 GeV photons at the Tevatron therefore constrains this type of Lorentz breakdown. Within the context of the standard-model extension, these ideas imply an experimental bound at the level of -5.8 x 10^{-12} <= \tilde{\kappa}_{tr}-(4/3)c_e^{00} <= 1.2 x 10^{-11} tightening existing laboratory measurements by 3-4 orders of magnitude. Prospects for further improvements with terrestrial and astrophysical methods are discussed.Comment: Replaced with final version published in PR

Matter-gravity couplings and Lorentz violation

The gravitational couplings of matter are studied in the presence of Lorentz and CPT violation. At leading order in the coefficients for Lorentz violation, the relativistic quantum hamiltonian is derived from the gravitationally coupled minimal Standard-Model Extension. For spin-independent effects, the nonrelativistic quantum hamiltonian and the classical dynamics for test and source bodies are obtained. A systematic perturbative method is developed to treat small metric and coefficient fluctuations about a Lorentz-violating and Minkowski background. The post-newtonian metric and the trajectory of a test body freely falling under gravity in the presence of Lorentz violation are established. An illustrative example is presented for a bumblebee model. The general methodology is used to identify observable signals of Lorentz and CPT violation in a variety of gravitational experiments and observations, including gravimeter measurements, laboratory and satellite tests of the weak equivalence principle, antimatter studies, solar-system observations, and investigations of the gravitational properties of light. Numerous sensitivities to coefficients for Lorentz violation can be achieved in existing or near-future experiments at the level of parts in 10^3 down to parts in 10^{15}. Certain coefficients are uniquely detectable in gravitational searches and remain unmeasured to date.Comment: 59 pages two-column REVTe

Could One Find Petroleum Using Neutrino Oscillations in Matter?

In neutrino physics, it is now widely believed that neutrino oscillations are influenced by the presence of matter, modifying the energy spectrum produced by a neutrino beam traversing the Earth. Here, we will discuss the reverse problem, i.e. what could be learned about the Earth's interior from a single neutrino baseline energy spectrum, especially about the Earth's mantle. We will use a statistical analysis with a low-energy neutrino beam under very optimistic assumptions. At the end, we will note that it is hard to find petroleum with such a method, though it is not too far away from technical feasibility.Comment: 6 pages, 4 figures, EPL LaTeX. Final version to be published in Europhys. Let

Electrodynamics with Lorentz-violating operators of arbitrary dimension

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentz- and CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete characterization of the coefficients for Lorentz violation for all mass dimensions via a decomposition using spin-weighted spherical harmonics. The resulting nine independent sets of spherical coefficients control birefringence, dispersion, and anisotropy. We discuss the restriction of the general theory to various special models, including among others the minimal Standard-Model Extension, the isotropic limit, the case of vacuum propagation, the nonbirefringent limit, and the vacuum-orthogonal model. The transformation of the spherical coefficients for Lorentz violation between the laboratory frame and the standard Sun-centered frame is provided. We apply the results to various astrophysical observations and laboratory experiments. Astrophysical searches of relevance include studies of birefringence and of dispersion. We use polarimetric and dispersive data from gamma-ray bursts to set constraints on coefficients for Lorentz violation involving operators of dimensions four through nine, and we describe the mixing of polarizations induced by Lorentz and CPT violation in the cosmic-microwave background. Laboratory searches of interest include cavity experiments. We present the theory for searches with cavities, derive the experiment-dependent factors for coefficients in the vacuum-orthogonal model, and predict the corresponding frequency shift for a circular-cylindrical cavity.Comment: 58 pages two-column REVTeX, accepted in Physical Review

Bounds on Lorentz and CPT Violation from the Earth-Ionosphere Cavity

Electromagnetic resonant cavities form the basis of many tests of Lorentz invariance involving photons. The effects of some forms of Lorentz violation scale with cavity size. We investigate possible signals of violations in the naturally occurring resonances formed in the Earth-ionosphere cavity. Comparison with observed resonances places the first terrestrial constraints on coefficients associated with dimension-three Lorentz-violating operators at the level of 10^{-20} GeV.Comment: 8 pages REVTe

Modelling silvicultural alternatives for conifer regeneration in boreal mixedwood stands (aspen/white spruce/balsam fir)

We model and compare the biological and financial constraints of four prescriptions that serve as alternatives to conventional clearcutting followed by planting in eastern and western boreal mixedwood stands. These alternative prescriptions for full or partial conifer stocking are (1) reliance on advance regeneration with or without augmentation by fill-planting; (2) understory scarification during a mast year; (3) direct seeding either aerially or with a scarifier-seeder; and (4) underplanting. Our main conclusions concerning the biological constraints are that (1) advance regeneration, mainly of balsam fir in the east and white spruce in the west, requires >26 000 and > 4000 trees/ha (because of different distributions), respectively, to achieve full conifer stocking; (2) reliance on a mast year requires at least 6 m2/ha of mature conifer basal area, but much less if some advance regeneration is present or only moderate stocking is desired; (3) aerial seeding with 35% scarification requires about a half-million seeds/ha to achieve full conifer stocking, while a scarifier-seeder would require only a third of this application rate; and (4) underplanting is constrained to aspen stands with >25% incident light at planting height. In all cases, alternative prescriptions become more feasible if only moderate or minimal stocking is the silvicultural objective. A costing exercise for the four prescriptions in comparison with a clearcut followed by planting shows that reliance on advance regeneration or understory planting are the cheapest alternatives to achieve full or partial conifer stocking. With the exception of full conifer stocking in situations where there is little advance regeneration (and where herbicides can be used), conventional plantations are never the cheapest approach. In such cases, fill planting and use of a scarifier-seeder become viable options. Aerial seeding and reliance on a mast year are the most expensive of the alternatives. We conclude, tentatively, that there is enough conifer basal area in most of the eastern boreal mixedwood of Canada to allow for the use of either or both a mast year and advance regeneration to achieve full or partial conifer stocking. By contrast, in the west conifer basal area will seldom be sufficient for natural seeding, and the density of advance regeneration is likewise often too low. Finally, because of light constraints, understory planting appears to have a much wider applicability in the west than in the east

Signals for Lorentz Violation in Post-Newtonian Gravity

The pure-gravity sector of the minimal Standard-Model Extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation. The linearized effective equations are solved to obtain the post-newtonian metric. The corresponding post-newtonian behavior of a perfect fluid is studied and applied to the gravitating many-body system. Illustrative examples of the methodology are provided using bumblebee models. The implications of the general theoretical results are studied for a variety of existing and proposed gravitational experiments, including lunar and satellite laser ranging, laboratory experiments with gravimeters and torsion pendula, measurements of the spin precession of orbiting gyroscopes, timing studies of signals from binary pulsars, and the classic tests involving the perihelion precession and the time delay of light. For each type of experiment considered, estimates of the attainable sensitivities are provided. Numerous effects of local Lorentz violation can be studied in existing or near-future experiments at sensitivities ranging from parts in 10^4 down to parts in 10^{15}.Comment: 46 pages two-column REVTeX, accepted in Physical Review

Light and tree size influence belowground development in yellow birch and sugar maple

The effects of light and tree size on the root architecture and mycorrhiza of yellow birch (Betula alleghaniensis Britton) and sugar maple (Acer saccharum Marsh) growing in the understory of deciduous forests in southern Qu