Negative Mass Square Research Articles

Mass, Spacetime Symmetry, de Sitter Vacuum, and the Higgs Mechanism

We address the question of the intrinsic relation between mass, gravity, spacetime symmetry, and the Higgs mechanism implied by involvement of the de Sitter vacuum as its basic ingredient (a false vacuum). Incorporating the de Sitter vacuum, the Higgs mechanism implicitly incorporates the generic relation between mass, gravity, and spacetime symmetry revealed in the frame of General Relativity for all objects involving the de Sitter vacuum. We overview two observational cases which display and verify this relation, the case known as “negative mass square problem” for neutrino, and appearance of a minimal length scale in e + e − annihilation.

Spectrum from the warped compactifications with the de Sitter universe

We discuss the spectrum of the tensor metric perturbations and the stability of warped compactifications with the de Sitter spacetime in the higher-dimensional gravity. The spacetime structure is given in terms of the warped product of the non-compact direction, the spherical internal dimensions and the four-dimensional de Sitter spacetime. To realize a finite bulk volume, we construct the brane world model, using the cut-copy-paste method. Then, we compactify the spherical directions on the brane. In any case, we show the existence of the massless zero mode and the mass gap of it with massive Kaluza-Klein modes. Although the brane involves the spherical dimensions, no light massive mode is excited. We also investigate the scalar perturbations, and show that the model is unstable due to the existence of a tachyonic bound state, which seems to have the universal negative mass square, irrespective of the number of spacetime dimensions.

Linearized modes in extended and critical gravities

We construct explicit solutions for the linearized massive and massless spin-2, vector and scalar modes around the AdS spacetimes in diverse dimensions. These modes may arise in extended (super)gravities with higher curvature terms in general dimensions. Log modes in critical gravities can also be straightforwardly deduced. We analyze the properties of these modes and obtain the tachyon-free condition, which allows negative mass square for these modes. However, such modes may not satisfy the standard AdS boundary condition and can be truncated out from the spectrum.

Solutions of free higher spins in AdS

We consider free massive and massless higher integer spins in AdS backgrounds in general D dimensions. We obtain the solutions corresponding to the highest-weight state of the spin-ℓ representations of the SO(2,D−1) isometry groups. The solution for the spin-ℓ field is expressed recursively in terms of that for the spin-(ℓ−1). Thus starting from the explicit spin-0, all the higher-spin solutions can be obtained. These solutions allow us to derive the generalized Breitenlohner–Freedman bound, and analyze the asymptotic falloffs. In particular, solutions with negative mass square in general have falloffs slower than those of the Schwarzschild AdS black holes in the AdS boundaries.

Superluminal spectral densities of ultra-relativistic electrons in intense electromagnetic wave fields

Superluminal radiation from electrons accelerated in electromagnetic waves is investigated. The radiation field is a Proca field with negative mass-square, minimally coupled to the electron current. The spectrum is continuous in the ultra-relativistic regime, where steepest-descent asymptotics can be used to evaluate the power coefficients. The time averaging of Lissajous orbits in polarized wave fields is discussed, and the tachyonic spectral densities of electrons orbiting in intense laser beams are derived. In the ultra-relativistic limit, realized by high injection energy or high field intensity, the spectral functions are evaluated in closed form in terms of Airy integrals. In contrast to electromagnetic radiation, there is a longitudinal polarization component, and oscillations emerge at high beam intensity in the longitudinal and transversal spectral slopes, generated by the negative mass-square of the tachyonic quanta. The thermal ultra-relativistic electron plasma of two active galactic nuclei is analyzed in this regard, based on TeV spectral maps obtained with imaging air Cherenkov detectors. Specifically, tachyonic cascade fits are performed to γ-ray flares of the TeV blazars RGB J0152+017 and 3C 66A, and the transversal and longitudinal radiation components are disentangled in the spectral maps. The curvature of the spectral slopes is shown to be intrinsic, caused by the Boltzmann factor of the electronic source plasma radiating the tachyonic cascades.

Tachyon optics: Kirchhoff identities and superluminal Bragg diffraction

The diffraction of superluminal radiation fields in crystal lattices is studied. The negative mass-square of the tachyonic wave modes affects the modulation function of diffraction gratings and the scattering amplitude. The Bragg condition for tachyon diffraction as well as the longitudinal and transversal cross sections are derived. Scalar and vectorial Kirchhoff identities for superluminal Proca fields are obtained from Sommerfeld’s dipole functionals, in analogy to electromagnetic theory. These surface-integral representations of the tachyon potential and the tachyonic field strengths are used to calculate the asymptotic diffracted modes and the intensity ratios. The dependence of the primary and secondary intensity peaks on the tachyon mass is analyzed in the reciprocal lattice, and the conversion of transversal into longitudinal radiation by way of Bragg scattering is explained. Specifically, tachyonic spectral fits are performed to the TeV spectra of three active galactic nuclei, H2356−309, 1ES 1218+304, and 1ES 1101−232, obtained with the imaging atmospheric Cherenkov detectors HESS, MAGIC, and VERITAS. The curvature in the spectral maps of these blazars is shown to be intrinsic, generated by ultra-relativistic electron populations in the galactic nuclei rather than by intergalactic absorption, and is reproduced by a tachyonic cascade fit.

Refraction angles and transmission rates of polarized superluminal radiation

Abstract The propagation of superluminal waves in dispersive media is investigated, in particular the refraction at surfaces of discontinuity in layered dielectrics. The negative mass-square of the tachyonic modes is manifested in the transmission and reflection coefficients, and the polarization of the incident waves (TE, TM, or longitudinal) can be determined from the refraction angles. The conditions for total internal reflection in terms of polarization and tachyon mass are derived. Brewster angles can be used to discriminate longitudinal from transversal incidence. Superluminal transmission through dielectric boundary layers is studied, and the dependence of the intensity maxima on the transversal and longitudinal refractive indices of the layer is analyzed. Estimates of the tachyonic plasma frequency and permittivity of metals are given. The integral version of the tachyonic Maxwell equations is stated, boundary conditions at the surfaces of discontinuity are derived for transversal and longitudinal wave propagation, and singular surface fields and currents are pointed out. The spectral maps of three TeV γ-ray sources associated with supernova remnants, which have recently been obtained with imaging atmospheric Cherenkov detectors, are fitted with tachyonic cascade spectra. The transversal and longitudinal polarization components are disentangled in the spectral maps, and the thermodynamic parameters of the shock-heated ultra-relativistic electron plasma generating the tachyon flux are extracted from the cascade fits.

Dynamically solving the μ/Bμproblem in gauge-mediated supersymmetry breaking

We provide a simple solution to the {mu}/B{sub {mu}} problem in the gauge-mediated Next-to-Minimal Supersymmetric Standard Model. In this model the messenger sector contains one pair of 3+{bar 3} and one pair of 2+{bar 2} messengers. These two messenger pairs couple to different gauge singlets in the hidden sector in which supersymmetry (SUSY) is broken. Such a gauge-mediation structure can naturally arise in many backgrounds. Because of the two effective SUSY breaking scales / in the messenger sector, the renormalization group evolutions of the soft SUSY breaking parameters can be properly modified, leading to a negative enough singlet soft mass square m{sub N}{sup 2}({Lambda}{sub EW}) and hence reasonable {mu}/B{sub {mu}} values. In most of the perturbative (up to the GUT scale) parameter region, as a result, the electroweak scale is stabilized and phenomenologically interesting mass spectra of particles and superparticles are obtained. In addition, this model favors large values of tan {beta}: 5 {approx} 50 and a heavy scalar spectrum. With the relatively large tan {beta}, the light U(1){sub R} pseudoscalar (mainly appearing in the low-scale gauge-mediated SUSY breaking models) becomes extremely singlet-like, and is no longer a problem in this model. These features apply to all casesmore » of low-, intermediate- and high-scale gauge-mediated SUSY breaking.« less

Tachyonic spectral map of a binary pulsar

Abstract We study tachyonic synchrotron densities of ultra-relativistic electrons in helical motion. There is a longitudinally polarized spectral component due to the negative mass square of the superluminal quanta. The helical pitch-angle scaling of the transversal and longitudinal spectral densities is investigated, in particular the transition from circular to rectilinear motion. The magnetic field induces oscillations along the power-law slopes of the superluminal radiation densities, whose amplitude depends on the pitch angle. At moderate field strength and ultra-relativistic orbital speed, the modulations are tiny, but they become quite pronounced in the surface fields of γ -ray pulsars, resulting in cockscomb distributions. A tachyonic spectral fit to the γ -ray flux of the binary pulsar PSR B1259–63 is performed. The γ -ray wideband of this millisecond pulsar is reproduced by a tachyonic cascade spectrum, capable of generating the spectral curvature in double-logarithmic plots as well as the extended spectral plateau defined by ISGRI, OSSE, COMPTEL, and EGRET flux points.

Tachyonic cascade spectra of supernova remnants and TeV blazars

The superluminal spectral densities of relativistic electrons in uniform motion are derived, semiclassically and in second quantization. The effect of electron spin on the tachyonic radiation field, a Proca field with negative mass-square, is studied. There is a longitudinally polarized spectral component due to the negative mass-square of the tachyonic quanta. The radiation densities are averaged with electron distributions, and high- and low-temperature expansions are obtained. Spectral fits to the γ-ray spectra of the Crab Nebula, the supernova remnant RX J1713.7–3946, and the BL Lacertae objects H1426+428, 1ES 1959+650, Mkn 501, and Mkn 421 are performed. In contrast to TeV photons, the extragalactic tachyon flux is not attenuated by interaction with the background light; there is no absorption of tachyonic γ-rays, as tachyons do not interact with infrared photons. The curvature of the TeV spectra in double-logarithmic plots is caused by the Boltzmann factor of the electron densities generating the tachyon flux. The extended spectral plateau in the GeV band, visible in the spectral maps of the two Galactic supernova remnants as well as in the flare spectra of the BL Lacertae objects, is reproduced by the tachyonic radiation densities. Estimates of the electron populations in the supernova remnants and active galactic nuclei are inferred from the spectral fits, such as power-law indices, electron temperatures, and source counts. Upper bounds on the Lorentz factors in the source populations are derived and compared to the breaks in the high-energy cosmic-ray spectrum.

Braneworld inflation from an effective field theory after WMAP three-year data

In light of the results from the WMAP three-year sky survey, we study an inflationary model based on a single-field polynomial potential, with up to quartic terms in the inflaton field. Our analysis is performed in the context of the Randall-Sundrum II braneworld theory, and we consider both the high-energy and low-energy (i.e. the standard cosmology case) limits of the theory. We examine the parameter space of the model, which leads to both large-field and small-field inflationary type solutions. We conclude that small-field inflation, for a potential with a negative mass square term, is in general favored by current bounds on the tensor-to-scalar perturbation ratio ${r}_{s}$.

A THEORETICAL CASE FOR NEGATIVE MASS-SQUARE FOR SUB-eV PARTICLES

Electroweak gauge bosons have masses of the order of 102 GeV [/c2], while masses of additional bosons involved in gravito-electroweak unification are expected to be still higher. These are at least eleven orders of magnitude higher than sub-eV range indications for neutrino masses. Under these circumstances we suspect that the sub-eV particles are created in a spacetime where gravitational effects of massive gauge bosons may become important. The question that we thus ask is: What is the spacetime group around a gravito-electroweak vertex? Modeling it as de-Sitter we find that sub-eV particles may carry a negative mass square of the order of [Formula: see text]. Neutrino oscillation data then hints at 30–75 TeV scale for M unif. , where M unif. characterizes gravito-electroweak unification scale.

Quantum statistics of superluminal radiation

A statistical quantization of superluminal (tachyon) radiation is introduced. The tiny tachyonic fine structure constant suggests to depart from the usual quantum field theoretic expansions, and to use more elementary methods such as detailed equilibrium balancing of emission and absorption rates. Instead of commencing with an operator interpretation of the wave function, we quantize the time-averaged energy functional and the energy-balance equation. This allows to use different statistics for different types of modes. Transversal superluminal modes are quantized in Bose statistics, longitudinal ones are turned into fermions, resulting in a positive definite Hamiltonian for the radiation field. We discuss the absorptive space structure underlying superluminal quanta and the energy dissipation related to it. This dissipation leads to an adiabatic time variation of the temperature in the bosonic and fermionic spectral functions, gray-body quasi-equilibrium distributions with a dispersion relation adapted to the negative mass-square of the tachyonic modes. The superluminal radiation field couples by minimal substitution to subluminal matter. Adiabatically damped Einstein coefficients are obtained by detailed balancing, as well as emission and absorption rates for tachyon radiation in hydrogenic systems, in particular the possibility of spontaneous emission of superluminal fermionic quanta is pointed out, and time scales for the approach to equilibrium are derived.

Tachyonsand the Wheeler-Feynman absorber theory

The Proca equation with negative mass-square is studiedin a refractive and absorptive spacetime. The generationof superluminal radiation fields by subluminal currentsis discussed. The possibility of time-symmetric wavepropagation is analysed in the context of theWheeler-Feynman absorber theory; it is shown howadvanced modes of the Proca field can be turned intoretarded ones in a permeable spacetime capable ofproducing an absorber field. A microscopic oscillatormodel for the permeability is suggested. TachyonicLiénard-Wiechert potentials are studied and strictlycausal retarded wave solutions are obtained. Energytransfer by superluminal radiation is discussed, andexplicit formulae for the spectral energy density andintensity are derived. Superluminal radiation fieldsgenerated by classical damped oscillators carryingtachyonic charge are investigated, including thetachyonic analogue to Thomson and Rayleigh crosssections. The Maxwell equations for negative mass-squareare derived, their non-local generalization tofrequency-dependent permeabilities, as well as thePoynting theorem for superluminal radiation in anabsorptive spacetime.

Einstein coefficients and equilibrium formalism for tachyon radiation

The spectral energy density of an ideal Bose gas of superluminal particles (tachyons) is derived. To this end, we consider atoms in equilibrium with tachyon radiation, study spontaneous and induced transitions effected by tachyons, calculate the Einstein coefficients, all semiclassically, and obtain, by detailed balancing, the equilibrium distribution of the tachyon gas. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Atomic transitions induced by tachyons are compared to photonic ones, and the tachyonic analog to the photoelectric effect is discussed. The cosmic tachyon background is scrutinized in detail; high- and low-temperature expansions of the internal energy, the entropy, the heat capacities, and the number density are compared with the corresponding quantities of the photon background. The negative mass square in the wave equation changes the frequency scaling in the Rayleigh–Jeans law, and there are also significant changes in the low-temperature regime, in particular in the caloric and thermal equations of state. Quantitative estimates on the tachyon background and on Rydberg transitions induced by tachyon radiation are derived.

Tachyons, Lamb shifts and superluminal chaos

An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 keV/c2 and estimate the tachyonic coupling strength to subluminal matter. The impact of the tachyon field on ground state hyperfine transitions in hydrogen and muonium is investigated. Bounds on atomic transition rates effected by tachyon radiation as well as estimates on the spectral energy density of a possible cosmic tachyon background radiation are derived.

INTERACTION OF TACHYONS WITH MATTER

A new interaction mechanism of superluminal particles with matter is suggested. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. The potential of a static point source in this field theory is a damped periodic function with 1/r-decay. We treat this potential as a perturbation of the Coulomb potential, and study its effects on cross-sections and energy levels. In the limit of large impact parameter, the periodicity of the potential has a pronounced effect on the classical cross-section, which gets singular at the accumulating extrema of the scattering angle. In this limit we define the cross-section wave mechanically, by semiclassical rainbow scattering. The impact of the tachyon potential on the energy levels of hydrogen and hydrogenic ions is calculated by means of Bohr–Sommerfeld quantization. Estimates for the tachyon mass (3 keV) and the coupling constant of the tachyon potential are derived on the basis of high-precision Lamb shift measurements.

COSMIC TACHYON BACKGROUND RADIATION

The equilibrium statistical mechanics of a background radiation of superluminal particles is investigated, based on a vectorial wave equation for tachyons of the Proca type. The partition function, the spectral energy density, and the various thermodynamic variables of an ideal Bose gas of tachyons in an open Robertson–Walker cosmology are derived. The negative mass square in the wave equation changes the frequency scaling in the Rayleigh–Jeans law, and there are also significant changes in the low temperature regime as compared to the microwave background, in particular in the caloric and thermal equations of state.

POSSIBLE EXPLANATION FOR THE SUPERFICIALLY NEGATIVE ELECTRON-NEUTRINO-MASS-SQUARE OBSERVED IN NUCLEAR β-DECAYS

The superficially negative mass square of the electron neutrino recently reported in several tritium β-decay experiments can be explained by a possible effect of the weak neutral current interaction of the produced neutrino with quarks in the nucleus, which has previously been predicted. The effect may present a serious obstacle to precise measurements of the neutrino mass within the accuracy of a few eV but, once established experimentally, it may be very useful to measure the weak mixing angle and the quark density in various nuclei.

Can the negative mass square of the electron neutrino be an indication of degenerated relic neutrinos?

The unphysical result of the negative mass square of the electron neutrinos recently reported in several tritium β-decay experiments, is one of the most attractive subjects among remaining physical problems. As a possible scenario to explain the anomaly, we have assumed a reaction with relic neutrinos which are predicted by the standard big bang cosmology. If such neutrinos could exist, the interaction of the relic neutrinos with the target tritium, ν e + 3 H→ 3 He+ e − could be laid under the large amount of the β-decay process, 3H→ 3He+e −+ ν e ̄ , which would cause a peak-like structure beyond the end-point in the Kurie plot. Based on the assumption, we evaluated the cross section from the event rate found in the peak by re-fitting to the 1991 data published by the Mainz Group. In this letter we will provide a scenario that can account for the evaluated cross section by introducing a spatially inhomogeneous neutrino degeneration, which would result much lower temperature than the prediction from the standard big bang cosmology.