Nonzero Mass Research Articles

An Independent Analysis of the Six Recently Claimed Exomoon Candidates

Abstract It has been recently claimed that KOIs-268.01, 303.01, 1888.01, 1925.01, 2728.01, and 3320.01 are exomoon candidates, based on an analysis of their transit timing. Here, we perform an independent investigation, which is framed in terms of three questions: (1) Are there significant transit timing variations (TTVs)? (2) Is there a significant periodic TTV? (3) Is there evidence for a nonzero moon mass? We applied rigorous statistical methods to these questions alongside a reanalysis of the Kepler photometry and find that none of the Kepler objects of interest (KOIs) satisfy our three tests. Specifically, KOIs-268.01 and 3220.01 pass none of the tests and KOIs-303.01, 1888.01, and 1925.01 pass a single test each. Only KOI-2728.01 satisfies two, but fails the cross-validation test for predictions. Further, detailed photodynamical modeling reveals that KOI-2728.01 favors a negative-radius moon (as does KOI-268.01). We also note that we find a significant photoeccentric effect for KOI-1925.01 indicating an eccentric orbit of at least e > (0.62 ± 0.06). For comparison, we applied the same tests to Kepler-1625b, which reveals that (1) and (3) are passed, but (2) cannot be checked with the cross-validation method used here, due to the limited number of available epochs. In conclusion, we find no compelling evidence for exomoons among the six KOIs. Despite this, we were able to derive exomoon mass upper limits versus semimajor axis, with KOI-3220.01 leading to particularly impressive constraints of M S/M P < 0.4% [2σ] at a similar semimajor to that of the Earth–Moon.

Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

Semiclassical mathcal{S} -matrix and black hole entropy in dilaton gravity

We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass Mcr. We find that at energies below Mcr the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate black hole decaying into the final-state particle. Relating the suppression of the scattering probability to the number of the intermediate black hole states, we find an expression for the black hole entropy consistent with thermodynamics. In addition, we fix the constant part of the entropy which is left free by the thermodynamic arguments. We rederive this result by modifying the standard Euclidean entropy calculation.

Mass Prediction for the Last Discovered Member of the Axial-Vector Nonet with Quantum Numbers JPC = 1+−

In this paper, we have shown that the novel mass relation among the vector states, ϕ(1020) and ϕ(1680), with quantum numbers JPC = 1−− and axial-vector strangeonium state \({h_1}\left( {s\overline s } \right)\) with quantum numbers 1+− is also valid for nonzero current quark mass. This relation predicts the mass of recently discovered \({h_1}\left( {s\overline s } \right)\) state by the BESIII Collaboration within experimental accuracy.

Linking pseudo-Dirac dark matter to radiative neutrino masses in a singlet-doublet scenario

We examine a simple extension of the standard model with a pair of fermions, one singlet and a doublet, in a common thread linking the dark matter problem with the smallness of neutrino masses associated with several exciting features. In the presence of a small bare Majorana mass term, the singlet fermion brings in a pseudo-Dirac dark matter capable of evading the strong spin-independent direct detection bound by suppressing the dark matter annihilation processes mediated by the neutral current. In consequence, the allowed range of a mixing angle between the doublet and the singlet fermions gets enhanced substantially. The presence of the same mass term in an association with singlet scalars also elevates tiny but nonzero masses radiatively for light Majorana neutrino satisfying observed oscillation data.

Two-dimensional Dirac operators with singular interactions supported on closed curves

We study the two-dimensional Dirac operator with a class of interface conditions along a smooth closed curve, which model the so-called electrostatic and Lorentz scalar interactions of constant strengths, and we provide a rigorous description of their self-adjoint realizations and their qualitative spectral properties. We are able to cover in a uniform way all so-called critical combinations of coupling constants, for which there is a loss of regularity in the operator domain. For the case of a non-zero mass term, this results in an additional point in the essential spectrum, which reflects the creation of an infinite number of eigenvalues in the central gap, and the position of this point can be made arbitrary by a suitable choice of the parameters. The analysis is based on a combination of the extension theory of symmetric operators with a detailed study of boundary integral operators viewed as periodic pseudodifferential operators.

Biquaternionic Dirac Equation Predicts Zero Mass for Majorana Fermions

A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image under an outer automorphism of the Pauli algebra. The charge conjugation operator takes a particulary simple form in this formulation and switches the sign of the mass coefficient, so that for a solution invariant under charge conjugation the mass has to equal zero. The multiple of the charge conjugation operator by the imaginary unit turns out to be a complex Lorentz transformation. It commutes with the outer automorphism, while the charge conjugation operator itself anticommutes with it, providing a second more algebraic proof of the main theorem. Considering the Majorana equation, it is shown that non-zero mass of its solution is imaginary.

Dynamics of logarithmic negativity and mutual information in smooth quenches

Abstract We study the time evolution of mutual information (MI) and logarithmic negativity (LN) in two-dimensional free scalar theory with two kinds of time-dependent masses: one time evolves continuously from non-zero mass to zero; the other time evolves continuously from finite mass to finite mass, but becomes massless once during the time evolution. We call the former protocol ECP, and the latter protocol CCP. Through numerical computation, we find that the time evolution of MI and LN in ECP follows a quasi-particle picture except for their late-time evolution, whereas that in CCP oscillates. Moreover, we find a qualitative difference between MI and LN which has not been known so far: MI in ECP depends on the slowly moving modes, but LN does not.

Perturbative deflection angles of timelike rays

Geodesics of both lightrays and timelike particles with nonzero mass are deflected in a gravitational field. In this work we apply the perturbative method developed in reference [] to compute the deflection angle of both null and timelike rays in the weak field limit for four spacetimes. We obtained the deflection angles for the Bardeen spacetime to the eleventh order of m/b where m is the ADM mass and b is the impact parameter, and for the Hayward, Janis–Newman–Winicour and Einstein–Born–Infeld spacetimes to the thirteenth, seventh and eleventh order respectively. The effects of the impact parameter b, velocity v and spacetime parameters on the deflection angle are analyzed in each of the four spacetimes. It is found that in general, the perturbative deflection angle depends on and only on the asymptotic behavior of the metric functions, and in an order-correlated way. Moreover, it is shown that although these deflection angles are calculated in the large b/m limit, their minimal valid b can be as small as a few m’s as long as the order is high enough. At these impact parameters, the deflection angle itself is also found large. As velocity decreases, the deflection angle in all spacetime studied increases. For a given b, if the spacetime parameters allows a critical velocity vc, then the perturbative deflection angle will deviate from its true value as v decreases to vc. It is also found that if the variation of spacetime parameters can only change the spacetime qualitatively at small but not large radius, then these spacetime parameter will not cause a qualitative change of the deflection angle, although its value is still quantitatively affected. The application and possible extension of the work are discussed.

Sedeonic Equations in Field Theory

We consider the factorization of differential operator of Klein–Gordon equation on the base of space-time algebra of sixteen-component sedeons. It is shown that generalized sedeonic wave equations can be used both to describe quantum particles and the force fields responsible for the interaction of particles. In particular, we discuss the first-order and second-order wave equations for sedeonic potentials describing fields with zero and nonzero mass of quantum. We demonstrate the application of sedeonic space-time operators to describe quantum particles and in particular the calculation of energy spectrum of electron in an external magnetic field. The relations between the sedeons and the spinors are discussed.

Spontaneous scalarization of Gauss-Bonnet black holes surrounded by massive scalar fields

For massless scalar fields, a relation Δn=32π for n→∞ was observed in the scalar-Gauss-Bonnet theory. In the present paper, we extend the discussion by including a nonzero scalar field mass. For massive scalar fields, we show that the relation Δn=32π for n→∞ still holds. We demonstrate this relation with both analytical and numerical methods. The analytical analysis implies that this relation may be a very universal behavior.

Thermal degradation kinetics of a lignin particle-reinforced phenolic foam

In the present work, the thermal degradation kinetics of a phenolic (PF) and lignin particle-reinforced phenolic (LRPF) foam and the lignin used as the reinforcement (LR) were studied. The activation energies of the degradation processes were obtained using a discrete distributed activation energy model (discrete DAEM) and the Vyazovkin model-free kinetic (MFK) method. The discrete DAEM was validated by comparing the predicted values with the data obtained at 8 °C min−1. Heating ramps of 6 and 12 °C min−1were used to calculate the kinetic parameters through the model. The effect of the reinforcement on the kinetics of the LRPF was studied by comparison with the results obtained for the PF. For reactions with non-zero mass fractions, the activation energies of the PF were in the range between 79.9 and 177.6 kJ mol−1, and the activation energy for the LRPF ranged from 91 to 187 kJ mol−1. For the LR, the activation energy values were in a narrower range than for the foams: 150–187 kJ mol−1. The degradation process of the LRPF was modified due to the use of LR: the range of activation energy for LRPF was between the ranges for the PF and LR. The activation energy dependence on conversion was also calculated using the Vyazovkin method and compared with the DAEM results; no compensation effect for the kinetic parameters was found.

Non-Hermitian extension of the Nambu–Jona-Lasinio model in 3+1 and 1+1 dimensions

This paper presents a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics in 3+1 and 1+1 dimensions. In 3+1 dimensions, the SU(2)-symmetric NJL Hamiltonian $H_{\textrm{NJL}} = \bar\psi (-i \gamma^k \partial_k + m_0) \psi - G [ (\bar\psi \psi)^2 + (\bar\psi i \gamma_5 \vec{\tau} \psi)^2 ]$ is extended by the non-Hermitian, PT- and chiral-symmetric bilinear term $ig\bar\psi \gamma_5 B_{\mu} \gamma^{\mu} \psi$; in 1+1 dimensions, where $H_{\textrm{NJL}}$ is a form of the Gross-Neveu model, it is extended by the non-Hermitian PT-symmetric but chiral symmetry breaking term $g \bar\psi \gamma_5 \psi$. In each case, the gap equation is derived and the effects of the non-Hermitian terms on the generated mass are studied. We have several findings: in previous calculations for the free Dirac equation modified to include non-Hermitian bilinear terms, contrary to expectation, no real mass spectrum can be obtained in the chiral limit; in these cases a nonzero bare fermion mass is essential for the realization of PT symmetry in the unbroken regime. Here, in the NJL model, in which four-point interactions are present, we {\it do} find real values for the mass spectrum also in the limit of vanishing bare masses in both 3+1 and 1+1 dimensions, at least for certain specific values of the non-Hermitian couplings $g$. Thus, the four-point interaction overrides the effects leading to PT symmetry-breaking for these parameter values. Further, we find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass. In both models, this contribution can be tuned to be small; we thus fix the fermion mass to its value when $m_0=0$ in the absence of the non-Hermitian term, and then determine the value of the coupling required so as to generate a bare fermion mass.

Tests of general relativity with stellar-mass black hole binaries observed by LISA

We consider the observation of stellar-mass black holes binaries with the Laser Interferometer Space Antenna (LISA). Preliminary results based on Fisher information matrix analyses have suggested that gravitational waves from those sources could be very sensitive to possible deviations from the theory of general relativity and from the strong equivalence principle during the low-frequency binary inspiral. We perform a full Markov Chain Monte Carlo Bayesian analysis to quantify the sensitivity of these signals to two phenomenological modifications of general relativity, namely a putative gravitational dipole emission and a non-zero mass for the graviton, properly accounting for the detector's response. Moreover, we consider a scenario where those sources could be observed also with Earth-based detectors, which should measure the coalescence time with precision better than $1 \ {\rm ms}$. This constraint on the coalescence time further improves the bounds that we can set on those phenomenological deviations from general relativity. We show that tests of dipole radiation and the graviton's mass should improve respectively by seven and half an order(s) of magnitude over current bounds. Finally, we discuss under which conditions one may claim the detection of a modification to general relativity.

Complex poles and spectral functions of Landau gauge QCD and QCD-like theories

In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and various numbers of quark flavors $N_F$ within the asymptotic free region. Both the gluon and quark propagators at the best-fit parameters for $N_F=2$ QCD have one pair of complex conjugate poles, while the number of complex poles in the gluon propagator varies between zero and four depending on the number of quark flavors and quark mass. Moreover, as a general feature, we argue that the gluon spectral function of this model with nonzero quark mass is negative in the infrared limit. In sharp contrast to gluons, the quark and ghost propagators are insensitive to the number of quark flavors within the current approximations adopted in this paper. These results suggest that details of the confinement mechanism may depend on the number of quark flavors and quark mass.

Bridging the chiral symmetry and confinement with singularity

We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model. Both models correctly reproduce the linear Regge trajectory of hadrons for zero quark mass. For the case of non-zero quark mass, the model lead us to Heun's equation. The mass term is precisely the origin of the higher singularity, which changes the system behavior drastically. Our result can shed some light on why the chiral transition is so close to the confinement transition. In the massive case, the Schroedinger equation is exactly solvable, but only if a surprising new quantization condition, additional to the energy quantization, is applied.

Polar planets around highly eccentric binaries are the most stable

ABSTRACT We study the orbital stability of a non-zero mass, close-in circular orbit planet around an eccentric orbit binary for various initial values of the binary eccentricity, binary mass fraction, planet mass, planet semimajor axis, and planet inclination by means of numerical simulations that cover 5 × 104 binary orbits. For small binary eccentricity, the stable orbits that extend closest to the binary (most stable orbits) are nearly retrograde and circulating. For high binary eccentricity, the most stable orbits are highly inclined and librate near the so-called generalized polar orbit which is a stationary orbit that is fixed in the frame of the binary orbit. For more extreme mass ratio binaries, there is a greater variation in the size of the stability region (defined by initial orbital radius and inclination) with planet mass and initial inclination, especially for low binary eccentricity. For low binary eccentricity, inclined planet orbits may be unstable even at large orbital radii (separation ${\gt}5 \, a_{\rm b}$). The escape time for an unstable planet is generally shorter around an equal mass binary compared with an unequal mass binary. Our results have implications for circumbinary planet formation and evolution and will be helpful for understanding future circumbinary planet observations.

One-boson scattering processes in the massive Spin-Boson model

The Spin-Boson model describes a two-level quantum system that interacts with a second-quantized boson scalar field. Recently the relation between the integral kernel of the scattering matrix and the resonance in this model has been established in [18] for the case of massless bosons. In the present work, we treat the massive case. On the one hand, one might rightfully expect that the massive case is easier to handle since, in contrast to the massless case, the corresponding Hamiltonian features a spectral gap. On the other hand, it turns out that the non-zero boson mass introduces a new complication as the spectrum of the complex dilated, free Hamiltonian exhibits lines of spectrum attached to every multiple of the boson rest mass energy starting from the ground and excited state energies. This leads to an absence of decay of the corresponding complex dilated resolvent close to the real line, which, in [18], was a crucial ingredient to control the time evolution in the scattering regime. With the new strategy presented here, we provide a proof of an analogous formula for the scattering kernel as compared to the massless case and use the opportunity to provide the required spectral information by a Mourre theory argument combined with a suitable application of the Feshbach-Schur map instead of complex dilation.

Time diffraction and Zitterbewegung of two-dimensional massless Dirac excitations

We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cut-off plane wave. We show that the probability density is governed by an interplay between {\it diffraction in time} and {\it Zitterbewegung} phenomena, typical of relativistic quantum shutter systems with nonzero mass. The {\it time-diffraction} appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. \textbf{88}, 625] for Schr\"odinger free matter-waves. The {\it Zitterbewegung} manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, $k_y$, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the {\it Zitterbewegung} appears as a series of {\it quantum beats} in the probability density, with a beating frequency $2k_yv_F$, where $v_F$ is the Fermi velocity.

Wavefunctions and energy eigenvalues of charge carriers in zigzag carbon nanotubes and in armchair nanoribbons in the vicinity of Dirac point under the influence of longitudinal electric field

Abstract Finite length graphene nanoribbon with armchair edges impacted by the external electrical field longitudinal to the edges was investigated, and approximate solutions for the electrons energy and wavefunctions in the neighborhood of the Dirac point were obtained. Matrix elements for the position operators are also calculated. Based on the four-point unit cell for elongated zigzag carbon nanotubes and staggered armchair-edge graphene nanoribbons under the influence of longitudinal electric field, the eigenvalues and eigenfunctions are obtained in vicinity of the Dirac point. It is shown that for the not-perturbed Hamilton operator H 0 the eigenvalues of armchair nanoribbon and zigzag nanotube coincide if their lengths are the same, while their spectrum is equidistant. Similarly to carbyne and zigzag edge nanotubes, for armchair edge nanoribbons based on the four-point unit phase cell in the vicinity of Dirac points, the wavefunction is expressed in the form of two-component Dirac function. It is shown that in the case of semiconducting N armchair-edge nanoribbons, where N + 1 = 3 p + δ , δ = ± 1 , N > > 1 , electronic properties can be described using the two uncoupled Majorana equations of 1 + 1 dimension for the particle with non-zero mass. Solutions of these equations are charge-neutral Majorana fields φ ± ( δ ) . These results are of practical interest in designing the supercomputers and experiments in this area. The possibility of generation of terahertz radiation by the Cherenkov mechanism and by analogy with cascade lasers is also discussed.