Massless Model Research Articles

Measurement of Milli-Charged particles with a moderately large cross section from the Earth’s core at IceCube

It is assumed that heavy dark matter ϕ with O(TeV) mass captured by the Earth may decay to relativistic light milli-charged particles (MCPs). These MCPs could be measured by the IceCube neutrino telescope. The massless hidden photon model was taken for MCPs to interact with nuclei, so that the numbers and fluxes of expected MCPs may be evaluated at IceCube. Meanwhile, the numbers of expected neutrino background events were also evaluated at IceCube. Based on the assumption that no events are observed at IceCube in 10 years, the corresponding upper limits on MCP fluxes were calculated at 90% C. L. These results indicated that the MCPs from the Earth’s core could be directly detected at O(1TeV) energies at IceCube when 2 × 10−5 ≲ ϵ2 ≲ 4.5 × 10−3. And a new region of 4 GeV < mMCP < 10 GeV and 4.47 × 10−3 ≲ ϵ ≲ 9.41 × 10−2 is ruled out in the mMCP-ϵ plane with 10 years of IceCube data.

A gyrokinetic simulation model for 2D equilibrium potential in the scrape-off layer of a field-reversed configuration

The equilibrium potential structure in the scrape-off layer (SOL) of the field-reversed configuration (FRC) can be affected by the penetration of edge biasing applied at the divertor ends. The primary focus of the paper is to establish a formulation that accurately captures both parallel and radial variations of the two-dimensional (2D) potential in SOL. The formulation mainly describes a quasi-neutral plasma with a logical sheath boundary. A full-f gyrokinetic ion model and a massless electron model are implemented in the GTC-X code to solve for the self-consistent equilibrium potential, given fixed radial potential profiles at the boundaries. The first essential point of this 2D model lies in its ability to couple radial and parallel dynamics stemming from resistive currents and drag force on ions. The model successfully recovers the fluid force balance and continuity equations. These collisional effects on 2D potential mainly appear through the density profile changes, modifying the potential through electron pressure gradient. This means an accurate prescription of electron density and temperature profiles is important in predicting the potential structure in the FRC SOL. The Debye sheath potential and the potential profiles applied at the boundaries can be additional factors contributing to the 2D variations in SOL. This comprehensive full-f scheme holds promise for future investigations into turbulent transport in the presence of the self-consistent 2D potential together with the non-Maxwellian distributions and open boundary conditions in the FRC SOL.

Massive Debris Disks May Hinder Secular Stirring by Planetary Companions: An Analytic Proof of Concept

Debris disks or exo-Kuiper belts, detected through their thermal or scattered emission from their dusty components, are ubiquitous around main-sequence stars. Since dust grains are short-lived, their sustained presence is thought to require dynamical excitation, i.e., “stirring,” of a massive reservoir of large planetesimals, such that mutual collisions are violent enough to continually supply fresh dust. Several mechanisms have been proposed to explain debris disk stirring, with the commonly accepted being long-term, secular planet–debris disk interactions. However, while effective, existing planet-stirring models are rudimentary; namely, they ignore the (self-)gravity of the disk, treating it as a massless reservoir of planetesimals. Here, using a simple analytical model, we investigate the secular interactions between eccentric planets and massive, external debris disks. We demonstrate that the disk gravity drives fast apsidal precession of both planetesimal and planetary orbits, which, depending on the system parameters, may well exceed the planet-induced precession rate of planetesimals. This results in strong suppression of planetesimal eccentricities and thus relative collisional velocities throughout the disk, often by more than an order of magnitude when compared to massless disk models. We thus show that massive debris disks may hinder secular stirring by eccentric planets orbiting near, e.g., the disk’s inner edge, provided the disk is more massive than the planet. We provide simple analytic formulae to describe these effects. Finally, we show that these findings have important implications for planet inferences in debris-bearing systems, as well as for constraining the total masses of debris disks (as done for β Pic).

Free vibration of cracked FGM Mindlin plate in fluid

The free vibration of cracked functionally graded material (FGM) plate in fluid is investigated in this paper. The material components are supposed following the power law and formulated by the Voigt model. The Mindlin plate theory (MPT) including the shear deformation effect is established and the physical neutral plane is adopted to simplify the derivation due to the in-plane displacements of this plane assumed as zero. A massless linear rotational spring model (LRSM) is established to simulate the through-width surface crack. The hydrodynamic pressure at the fluid-plate interface is derived by the potential flow theory, and is regarded as the added mass of cracked FGM plate during the analyses of fluid-plate coupled vibration. The derivation and discretization of vibrational equations for cracked FGM plates in fluid are respectively achieved though the Hamilton’s principle and differential quadrature (DQ) method. The frequencies and mode shapes are iteratively calculated with these values of the vacuum case. The influences of immersed depth, fluid density, gradient index, crack depth, crack location, length-to-width ratio, length-to-thickness ratio, and boundaries on vibration characteristics are conducted in the section of numerical results. The present vibration analyses of cracked structures can be applicable to avoid structural resonance and failure.

Massive ambitwistor-strings; twistorial models

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends the framework to massive particles in 4d, obtained via a symmetry reduction of higher dimensional massless models based on twistors. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and the worldsheet theory agrees with the two-twistor string previously introduced by the authors. The paper has been written so as to be largely self-contained. We discuss two interesting classes of massive theories in detail. For gauge theories, the reduction procedure is explicitly adapted to supersymmetric gauge theories on the Coulomb branch. For supergravity theories, the reduction is adapted to give theories obtained via Cremmer, Scherk & Schwartz (CSS) reduction, with broken supersymmetry and massive multiplets. The reduction procedure gives explicit and systematic rules to obtain amplitudes for all these theories and their amplitudes from two compact master formulae that have their origins in 6d based on the polarized scattering equations; in the CSS case the formulae are new, and in both cases their derivation is systematic. The freedom to include mass allows the definition of a loop insertion operator, thereby extending the formulae to 1-loop. Unlike the massless 4d twistorial models, these all display a perfect double copy structure, here incorporating massive particles in the relationship between gauge theory and CSS supergravity amplitudes.

Ultrasonic evaluation of ply and interleaf layer properties of interleaved composite laminates

An ultrasonic nondestructive evaluation procedure is presented for the ply and interleaf layer properties of carbon/epoxy composite laminates having interleaf resin layers at their interlaminar interfaces. It is shown that the material properties of plies (density, thickness, and transversely isotropic complex elastic moduli) and elastic interleaf layers (density, thickness, Young’s modulus, and Poisson’s ratio) can be identified by best fitting the theoretical energy transmission spectra of longitudinal waves through the laminate immersed in water to those obtained in ultrasonic measurement. It is also demonstrated that compared to the mass-less and null-thickness spring-type interlaminar interface model employed in the previous works, the present finite-thickness interleaf layer model can better reproduce the experimental transmission spectra of a unidirectional interleaved composite laminate containing ultrasonic bandgaps. Furthermore, the property characterization in the case where the plies and interleaf layers are assumed to be elastic and viscoelastic, respectively, is also examined. It is also shown that the ply and interleaf layer properties determined for the unidirectional laminate can be used to reproduce the transmission spectra measured for a quasi-isotropic laminate consisting of the same plies and interleaf layers.

Dynamic response of nanobeams with randomly distributed multiple vertical cracks

This paper aims to systematically study the steady-state forced vibrations of nanobeams weakened by multiple vertical cracks, which may conform to random or determined distributions. The variable separation and the Laplace transform methods are employed to obtain the Green’s function of beams with one crack for three typical kinds of beams, namely Hinged–Hinged, Clamped–Clamped, and Clamped–Free. Green’s functions for the nanobeams with an arbitrary number of cracks are figured out from the counterparts of beams with one crack by virtue of the massless elastic spring model and the transfer matrix method. The validity of the present solutions is discussed in comparison to those in literature in degenerated situations. The influence of statistical parameters of the random cracks on the dynamic responses of the weakened beams is studied in a systematic fashion. The present work may be beneficial to future structural designs on the nano-scales.

The Coleman correspondence at the free fermion point

We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on \mathbb{R}^2 with \beta=4\pi exist for all coupling constants and are equal to those of the chiral densities and vector current of free massive Dirac fermions. This is an instance of Coleman's prediction that the massless sine-Gordon model and the massive Thirring model are equivalent (in the above sense of correlation functions). Our main novelty is that we prove this correspondence starting from the Euclidean path integral in the nonperturbative regime of the infinite volume models. We use this correspondence to show that the correlation functions of the massless sine-Gordon model with \beta=4\pi decay exponentially and that the corresponding probabilistic field is localized.

Field-induced chiral transitions in the Weyl semimetal TaP

The chiral anomaly effect has been regarded as a hallmark of Weyl semimetals. While most research focuses on the change of electrical conductivity due to the chiral charge-pumping effect, these transport measurements are accompanied by other effects such as weak antilocalization which are difficult to exclude. Also, the magnetic field intensity at which the energy dispersion of the Landau level starts to display the chiral anomaly effect is hard to identify. Here, we report the evolutionary process of the energy dispersion of the zeroth Landau level under increasing magnetic fields, and we elucidate the relationship between the chiral Landau level and the Fermi level via magneto-optical measurements in Weyl semimetal TaP. Two series of Landau-level transitions have been extracted and fitted well to a massless Weyl fermion model and a classical semiconductor model, respectively. The field-induced chiral Landau-level transition is obtained from a comparison between the spectra under Voigt geometry and Faraday geometry in an increasing magnetic field. The chiral nature of the zeroth Landau level is found to enhance with the increase of magnetic field and clearly manifests in the magneto-optical spectrum above 13 T. The state transition of the zeroth Landau level can be explained by the strength of the field-induced chiral anomaly effect and the position of the Fermi level. These magneto-optical results unveil the chiral Landau-level transitions in TaP, which serves as an ideal material platform to analyze the chiral anomaly effect.

Renormalisation group equations for BRST-restored chiral theory in dimensional renormalisation: application to two-loop chiral-QED

We discuss how renormalisation group equations can be consistently formulated using the algebraic renormalisation framework, in the context of a dimensionally-renormalised chiral field theory in the BMHV scheme, where the BRST symmetry, originally broken at the quantum level, is restored via finite counterterms. We compare it with the more standard multiplicative renormalisation approach, which application would be more cumbersome in this setting. Both procedures are applied and compared on the example of a massless chiral right-handed QED model, and beta-function and anomalous dimensions are evaluated up to two-loop orders.

Partition functions on squashed seven-spheres and holography

Our paper presents two main results. First, we study the renormalized free energies of Euclidean Einstein gravity in asymptotically AdS8 and various field theories on a squashed seven sphere. In the gravity theory, we demonstrate the absence of the Hawking-Page transition, while in the field theory, we focus on the O(N) vector model and the massless free fermion model. The conformal symmetry governs the universal behaviors of the free energies for small and large squashings, which we confirm numerically and analytically. Second, we evaluate the second-order derivative of CFT free energy with respect to the squashing parameter, finding universal results that hold for generic conformal field theories. We examine two different squashings, one with an SU(2) bundle, which is the primary focus of our paper, and another with a U(1) bundle, where our results align with the conjectured formula from the gravity side in the literature.

Stability Analyses of Cracked Functionally Graded Graphene-Platelets Reinforced Composite Beam Covered with Piezoelectric Layers

As cracks are unavoidable and always reduce structural local stiffness and strength, this paper pays attention to the effect of cracks on the stability of the cracked functionally graded (FG) graphene-nanoplates reinforced composite (GRC) beam covered with piezoelectric layers. Both the critical buckling loads and postbuckling paths of the novel structures with cracks are considered. The massless rotational spring model is employed to calculate the bending stiffness of the cracked section. Three different graphene platelets (GPLs) distribution patterns along the thickness direction of the FG-GRC core beam are studied. The effective material properties of the FG-GRC core beam are calculated by Halpin–Tsai model and the rule of mixture. The governing equations of stability of the cracked FG-GRC piezoelectric beam are established within the framework of the first-order shear deformation beam theory, von Kármán geometric nonlinearity and Ritz method. The direct iteration method is used to examine the effects of boundary conditions, crack parameters, piezoelectric layers and GPL parameters on the critical buckling loads and postbuckling responses of the cracked FG-GRC piezoelectric beams. Results clearly illustrate that GPLs can significantly improve the stability of the cracked FG-GRC piezoelectric beams, while the increasing crack depth has the opposite effect.

Noninvertible Chiral Symmetry and Exponential Hierarchies

We elucidate the fate of classical symmetries which suffer from Abelian Adler-Bell-Jackiw anomalies. Instead of being completely destroyed, these symmetries survive as noninvertible topological global symmetry defects with world volume anyon degrees of freedom that couple to the bulk through a magnetic 1-form global symmetry as in the fractional Hall effect. These noninvertible chiral symmetries imply selection rules on correlation functions and arise in familiar models of massless quantum electrodynamics and models of axions (as well as their non-Abelian generalizations). When the associated bulk magnetic 1-form symmetry is broken by the propagation of dynamical magnetic monopoles, the selection rules of the noninvertible chiral symmetry defects are violated nonperturbatively. This leads to technically natural exponential hierarchies in axion potentials and fermion masses.Received 3 August 2022Accepted 2 February 2023DOI:https://doi.org/10.1103/PhysRevX.13.011034Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnomaliesPhysical SystemsAxionsPropertiesChiral symmetryTechniquesMonopolesParticles & Fields

Four-fermion deformations of the massless Schwinger model and confinement

We consider the massless charge-N Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a ℤ2 subgroup of chiral symmetry for even N, hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on ℝ2 using bosonization, and also analyze the mechanism of confinement on ℝ × S1, where we find that confinement is driven by fractional instantons.

Seismic response of a nuclear island building with base isolation considering the soil–structure interaction effect

AbstractThis study aims to investigate the influence of soil–structure interaction (SSI) on the seismic response of a nuclear island (NI) building with base isolation. Hence, modal and dynamic time‐history analyses of the NI building with base isolation based on different soil dynamic numerical models that are applicable for homogeneous and layered sites to consider the SSI effect were conducted. After a comparison analysis of natural frequencies, floor response spectra (FRS), and acceleration response of superstructure, the following results are obtained. (i) For homogeneous sites, the degrees of freedom of the horizontal translation and torsion of the NI building with base isolation calculated using different site dynamic numerical models have equivalent natural frequencies. For layered sites, the natural frequencies increase slightly with the improvement of the shear wave velocity of the upper layered soil. (ii) For homogeneous sites, FRS calculated by the massless foundation model is generally larger than those of the dynamic model proposed by the ASCE code and the viscoelastic artificial boundary site model. Both the spectral and peak values of horizontal FRS at a low frequency band calculated by considering the SSI effect are larger than those without the SSI effect. (iii) For layered sites, both the spectral and peak values of horizontal FRS at a low frequency band have an amplification effect compared with that of a homogeneous site. (iv) For layered sites, the calculated horizontal acceleration response does not have evident law that changes with the degree of hardness and softness of the upper soil. Therefore, the SSI effect for particular homogeneous and layered sites should be considered when calculating the seismic response of the NI building with base isolation.

Mass perturbation theory in the 2-flavor Schwinger model with opposite masses with a review of the background

I discuss the 2-flavor Schwinger model with θ = 0 and small equal and opposite fermion masses (or θ = π with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special mass term modifies the conformal sector without breaking the conformal symmetry. I show in detail how mass-perturbation-theory works for correlators of flavor-diagonal fermion scalar bilinears. The result provides quantitative evidence that the theory has no mass gap for small non-zero fermion masses. The massive fermions are bound into conformally invariant unparticle stuff. I show how the long-distance conformal symmetry is maintained when small fermion masses are turned on and calculate the relevant scaling dimensions for small mass. I calculate the corrections to the 2- and 4-point functions of the fermion-bilinear scalars to leading order in perturbation theory in the fermion mass and describe a straightforward procedure to extend the calculation to all higher scalar correlators. I hope that this model is a useful and non-trivial example of unparticle physics, a sector with unbroken conformal symmetry coupled to interacting massive particles, in which we can analyze the particle physics in a consistent approximation.

Interacting Massless Infraparticles in 1+1 Dimensions

The Buchholz' scattering theory of waves in two dimensional massless models suggests a natural definition of a scattering amplitude. We compute such a scattering amplitude for charged infraparticles that live in the GNS representation of the 2$d$ massless scalar free field and obtain a non-trivial result. It turns out that these excitations exchange phases, depending on their charges, when they collide.

Search for Milli-Charged particles from the Sun at IceCube

It is assumed that heavy dark matter particles ϕ with O(TeV) mass captured by the Sun may decay to relativistic light milli-charged particles (MCPs). These MCPs could be measured by the IceCube detector. The massless hidden photon model was taken for MCPs to interact with nuclei, so that the numbers and fluxes of expected MCPs and neutrinos may be evaluated at IceCube. Based on the assumption that no events are observed at IceCube in 6 years, the corresponding upper limits on MCP fluxes were calculated at 90% C. L. These results indicated that MCPs could be directly detected in the secondaries’ energy range O(100GeV)-O(10TeV) at IceCube, when ϵ2 ≳ 10−10. And a new region of 0.6 MeV < mMCP < 10 MeV and 6 × 10−6 < ϵ ≲ 10−4 is ruled out in the mMCP-ϵ plane with 6 years of IceCube data.

Absence of ground states in the renormalized massless translation-invariant Nelson model

We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of the operator and form domains and prove that the fiber operators do not have a ground state. Our results hold for any non-zero coupling constant and arbitrary total momentum. Our proof for the absence of ground states is a new generalization of methods recently applied to related models. A major enhancement we provide is that the method can be applied to models with degenerate ground state eigenspaces.

Cosmological relaxation through the dark axion portal

The dark axion portal is a coupling of an axion-like particle to a dark photon kinetically mixed with the visible photon. We show how this portal, when applied to the relaxion, can lead to cosmological relaxation of the weak scale using dark photon production. The key backreaction mechanism involves the Schwinger effect: as long as electroweak symmetry is unbroken, Schwinger production of massless Standard Model fermions, which carry dark millicharges, suppresses the dark photon production. Once the electroweak symmetry is broken, the fermions acquire mass and the suppression is lifted. An enhanced dark photon dissipation then traps the relaxion at a naturally small weak scale. Our model thus provides a novel link between the phenomenological dark axion portal, dark photons, and the hierarchy problem of the Higgs mass.