Unstable Particles Research Articles

Mathematical Physics of Time Dilation through Curved Trajectories with Applications

In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas of time dilation for several trajectories of particle such as parabolic, elliptic, and circular and finds a relatively accurate trajectory. The obtained formulas are employed in order to analyze the time dilation of the muon particles decay. In this paper, it is found that the time dilation of the parabolic and the elliptical trajectories exceed the corresponding results utilizing the standard Lorentz-Einstein time dilation formula. Consequently, if we are able to control the trajectory of unstable particles by some external forces, then their life-times might be increased. Probably, the increase in lifetime via a curved trajectory occurs at lower relative velocity & acceleration energy if compared to the straight line trajectory. In addition, the circular trajectory leads to multiple values of time dilation at certain velocities of an observer in motion, which may give an interpretation of fluctuations of time dilation in quantum mechanics. The result arises from the present relatively accurate formula of time dilation that is very close to the experimental data of muon decay (CERN experiment) when it is compared to the result obtained by the Lorentz-Einstein formula. Finally, it may be concluded that the time dilation not only depends on relative velocity and acceleration energy of particles but also on curved trajectories. The present work may attract other researchers to study different trajectories.

Distinct signatures of spinning PBH domination and evaporation: doubly peaked gravitational waves, dark relics and CMB complementarity

Ultra-low mass primordial black holes (PBH), which may briefly dominate the energy density of the universe but completely evaporate before the big bang nucleosynthesis (BBN), can lead to interesting observable signatures. In our previous work, we studied the generation of a doubly peaked spectrum of induced stochastic gravitational wave background (ISGWB) for such a scenario and explored the possibility of probing a class of baryogenesis models wherein the emission of massive unstable particles from the PBH evaporation and their subsequent decay contributes to the matter-antimatter asymmetry. In this work, we extend the scope of our earlier work by including spinning PBHs and consider the emission of light relativistic dark sector particles, which contribute to the dark radiation (DR) and massive stable dark sector particles, thereby accounting for the dark matter (DM) component of the universe. The ISGWB can probe the non-thermal production of these heavy DM particles, which cannot be accessible in laboratory searches. For the case of DR, we find a novel complementarity between the measurements of ∆Neff from these emitted particles and the ISGWB from PBH domination. Our results indicate that the ISGWB has a weak dependence on the initial PBH spin. However, for gravitons as the DR particles, the initial PBH spin plays a significant role, and only above a critical value of the initial spin parameter a*, which depends only on initial PBH mass, the graviton emission can be probed in the CMB-HD experiment. Upcoming CMB experiments such as CMB-HD and CMB-Bharat, together with future GW detectors like LISA and ET, open up an exciting possibility of constraining the PBHs parameter space providing deeper insights into the expansion history of the universe between the end of inflation and BBN.

Polyvinyl alcohol nanoparticles loaded with propolis extract: Fabrication, characterization and antimicrobial activity.

Propolis has high potential beneficial bioactive properties such as anti-oxidative, antimicrobial, and anti-tumour activities. However, the bitter taste and the insolubility nature of propolis in water lead to some limitations in their usage in functional food applications. Herein, we evaluated the effects of nanoencapsulation of propolis at the different concentration levels (0, 0.4, 0.8, 1.0, and 1.2 %) into the polyvinyl alcohol (PVA) nanoparticles using the electrospraying method, on the structural, physical, antioxidant, antimicrobial and thermal properties. The results revealed that the fabricated nanocapsules (PVA-NPs) obtained under optimal conditions had uniform size distribution and unstable particles with small particle size between 104-258 nm, a polydispersity index <0.317, and a zeta potential between -5 and +5 mV. The maximum encapsulation efficiency of PVA-NPs was about 25.32 % for 1 % of the initial propolis loading level. DSC thermal experiments showed an increase in the thermal stability of the propolis loaded PVA nanoparticles as compared to the neat PVA nanoparticles. The percent inhibition of DPPH radical scavenging activity of the nanocapsules was between 80 and 89 %. SEM analysis revealed that PVA-NPs had a spherical shape with a rough surface and were composed of long and thin fibres at nanometric diameters. FT-IR analysis showed that no indications of any chemical reactions were found between the constituents of the core and wall material due to their physical mixing. Antibacterial efficacy was evaluated by the Broth dilution method and PVA-NPs exhibited good inhibitory activity against S. aureus at low concentration ratios, whereas it had no inhibitory activity against E. coli O157:H7. PVA-NPs fabricated using the electrospraying technique can be used for the development of a new promising natural and bioactive agent in the food and pharmaceutical industry.

Entanglement of stationary states in the presence of unstable quasiparticles

The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.

Electrically controlled silver salt oxide particle synthesis on a closed wireless nanopore electrode

Ag6O8·AgHSO4 is a strong oxidizer that can be easily synthesized, but its unstability causes the self-decomposition easily. To effectively control and monitor this unstable process for synthesis, we used a closed wireless nanopore electrode (CWNE) to realize the repeated electrosynthesis and decomposition of Ag6O8·AgHSO4 at the nano interface. The in situ dark field images traced the highly repeatable growth and dissolution of the Ag6O8·AgHSO4 particle. The real-time current recording revealed that the Ag6O8·AgHSO4 particle growth process is synchronized with the electrocatalytic process. The rapid catalytic process of water oxidation causes two-step bubble coverage to block the electrode surface area. The calculated effective electrode area ratio (Φ) of the two stages were 68.9–82.6% and 14.5–25.6%. These results indicated that with the growth of the Ag6O8·AgHSO4 particle, the crystal plane also grew proportionally, which allowed the bubbles to block similarly on this crystal plane during the electrodeposition. Therefore, our results demonstrate that the CWNE can not only electrically control the growth of an unstable single particle with high repeatability, but also directly and in situ characterize gas−liquid−solid catalytic reactions for unstable catalysts.

Unitarity and unstable-particle scattering amplitudes

Unitarity is the fundamental property of the S-matrix, while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of a higher-point amplitude at an appropriate complex pole, we find unitarity equations for the 2-to-2 unstable-particle amplitudes from unitarity and analyticity of stable-particle scattering amplitudes. The unstable-particle unitarity equations take a form analogous to those of the stable-particle amplitudes when the in and out states are chosen to be complex-conjugate positions. In particular, as in the optical theorem, we find a positivity constraint on a discontinuity of the amplitudes in a positive region of the momentum transfer variable.

Improving the prediction accuracy of small-strain shear modulus of granular soils through PSD: An investigation enabled by DEM and machine learning technique

This study presents a numerical investigation into the effect of particle size distribution (PSD) on the small-strain shear modulus (G0) of granular soils using the discrete element method (DEM). Drained triaxial tests were conducted on a set of spherical particle assemblies covering a wide variety of PSDs. The tests demonstrated that the G0 decreases with increasing the coefficient of uniformity (Cu), assuming the confining pressure (p’) and the void ratio (e) remain constant. A corrected void ratio (e4), which regards mechanically unstable particles with less than four contacts as void, was developed. Analyses performed afterward revealed that e4 is more strongly correlated with G0 than e. Consequently, a Hardin-based G0 model parameterized by e4 and p’ was established and it is more accurate than two commonly used models, which are parameterized by e, p’ and Cu. Furthermore, micromechanical and microstructural features were investigated to acquire a better understanding of why models based on e and Cu yield less accurate results than models based on e4. Finally, a hybrid model combining the high explanatory power of statistical models with the high predictive power of machine learning models were proposed. The hybrid model which only uses measurable macroscopic parameters performs on par with the microstructural model and is more accurate than conventional empirical models. The proposed model offers a simple and streamlined approach to predicting G0 with satisfactory accuracy, which is a feasible strategy for maximizing the utilization of copious experimental data.

Kurt Gottfried

Kurt Gottfried

Seepage failure prediction of breakwater using an unresolved ISPH-DEM coupling method enriched with Terzaghi’s critical hydraulic gradient

This study develops a new numerical simulation model for rubble mound failure prediction caused by piping destruction under seepage flows. The piping has been pointed out as a significant cause of breakwater failure during tsunamis. Once boiling and heaving occur on the mound surface, the piping suddenly propagates in the opposite direction of seepage flow. For the seepage failure prediction, a coupled fluid-soil-structure simulator is developed by combining the ISPH for fluid and the DEM for rubble mounds and caisson blocks. The ISPH, a Lagrangian particle method for incompressible fluids, can simulate seepage and violent flows such as tsunamis. The DEM has been applied for discrete particle and rigid body simulations that include discontinuous deformation, as in the rubble mounds failure and large displacement of the caisson block. ISPH-DEM coupling simulations have already been proposed as a technique for multi-phase flows. Still, the technique cannot reproduce the sudden onset of piping from a stable mound. Two simple assumptions are applied to reduce the numerical cost for the fluid-soil-structure simulators of a breakwater structure composed of a rubble mound and the caisson block. Firstly, each rubble is modeled as an idealized spherical DEM particle with the mean diameter of the rubble. The ISPH particle size is assumed to be the same size as the DEM particle. Under these assumptions, the unresolved coupling model between rubble mound particles and fluid, which obtains the interaction through empirical drag force, should be applied. At the same time, the interaction between the fluid and the caisson block is fully resolved with the spatial resolution with the ISPH and DEM particle size. Our new contribution in this paper is how to model the interaction as an unresolved coupling between seepage flow simulated by ISPH and rubble mound particle modeled with DEM. Our original seepage failure experiment is simulated using the proposed ISPH-DEM coupling simulator. We identified the conventional drag force models as the unresolved coupling model are insufficient to initiate the boiling and piping observed in the experiment. It may be due in one part to excessive averaging of flow velocities caused by unresolved coupling. Therefore, Terzaghi’s critical hydraulic gradient is introduced to initiate the boiling and heaving. Unstable DEM particles, judged by Terzaghi’s critical hydraulic gradient, gradually lose their mass to represent unresolved suspended fine rubble mound particles. Our models qualitatively reproduce the sand boiling and backward erosion in the opposite direction of the seepage flow, as shown in the experiment.

Mass spectrum of elementary particles

In this study, we discuss different methods for quantifying the mass of elementary particles. The Barut’s model approach gives us a more comprehensive understanding of elementary particles and their formation through magnetic interaction. Through this model, we can understand the mechanism of the formation of hundreds of unstable elementary particles whose components are interconnected through positive energy and thus quickly disintegrate into their basic components.

Generalized Unitarity Method for Unstable Particles

In theories with unstable particles, unitarity is satisfied by the inclusion of only stable states in unitarity sums. Therefore, unitarity cuts are not to be taken through unstable particles. This presents a challenge to the generalized unitarity method, whose aim is to reconstruct amplitudes by analyzing sets of unitarity cuts. Nevertheless, under some general physical conditions, and perhaps some methodological modifications, we prove that the method is still reliable for one-loop amplitudes containing resonances. We discuss some simple examples which illustrate these features.

On the Stability of Particle–Particle Interaction during Gravitational Settling

The elevated energy demand and high dependency on fossil fuels have directed researchers’ attention to promoting and advancing hydraulic fracturing (HF) operations for a sustainable energy future. Even though previous studies have demonstrated that the proppant suspension and positioning in slickwater play a vital role during the shut-in stage of the HF operations, minimal experimental work has been conducted on the fundamental proppant–proppant interaction mechanisms, especially a complete mapping of the interactions. This study utilizes high-speed imaging to provide a 2D space- and time-resolved investigation of two-particle (proppant models: 2 mm Ø, 2.6 g·cm−3) interactions during gravitational settling in different initial spatial configurations and rheological properties. The mapping facilitates the identification of various interaction regimes and newly observed particle trajectories. Pure water results at a settling particle Reynolds number (Rep) ~ 470 show an unstable particle–particle interaction regime characterized by randomness while altering pure water to a 25% (v/v) water–glycerin mixture (Rep ~ 200) transitions an unstable interaction to a stable prominent repulsion regime where particles’ final separation distance can extend up to four times the initial distance. This indicates the existence of Rep at which the stability of the interactions is achieved. The quantified trajectories indicate that when particles are within minimal proximity, a direct relation between repulsion and Rep exists with varying repulsion characteristics. This was determined by observing unique bottle-shaped trajectories in the prominent repulsion regimes and further highlighted by investigating the rate of lateral separation distance and velocity characteristics. Additionally, a threshold distance in which the particles do not interact (or negligibly interact) and settle independently seems to exist at the normalized 2D lateral separation distance.

Boosting unstable particles

In relativity, there is no absolute notion of simultaneity, because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable particles. We show that, when a wavefunction is boosted, its tails travel one to the past and the other to the future. As a consequence, in the new frame of reference, the particle is in a quantum superposition "decayed + non decayed", where the property "decayed-ness" is entangled with the position. Since a particle cannot be localised in a region smaller than the Compton wavelength, there is a non-zero lower bound on this effect, which is fundamental in nature. The surprising implication is that, in a quantum world, decay probabilities can never be Lorentz-invariant. We show that this insight was the missing ingredient to reconcile the seemingly conflicting views about time dilation in relativistic quantum mechanics and quantum field theory.

Resonance form factors from finite-volume correlation functions with the external field method

A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of the Lüscher method in the presence of such a field. It is shown that the resonance form factor is given by the derivative of the resonance pole position in the complex plane with respect to the coupling constant to the external field. Unlike the standard approach, this proposal does not suffer from problems caused by the presence of the triangle diagram.

Reservoir Characteristics and Controlling Factors of Sedimentary Pyroclastic Rocks in Deep-Buried Basins: A Case Study of Yingtai Fault Depression, Southern Songliao Basin

In this article, based on core description, thin section, scanning electron microscope (SEM), well logging and reservoir physical properties, the reservoir controlling factors of sedimentary pyroclastic rocks in deep-buried basins are assessed via the relation between reservoirs and defining factors, including lithological characteristics, sedimentary microfacies and diagenesis. In addition, the contributing factors of anomalously high-porosity and high-permeability zone are analyzed. The lithological characteristics and diagenesis of the sedimentary pyroclastic rocks are closely related to reservoirs. The reservoir porosity–permeability of sedimentary pyroclastic rocks with large volcanic clastic particles is better than in those with small volcanic clastic particles. Sedimentary pyroclastic rocks with high content of unstable clastic particles, such as feldspar and rock debris, are easier to form the high-quality reservoirs than those with high content of quartz. The dissolution is the most important and direct reason to form the anomalously high-porosity and high-permeability zones of the sedimentary pyroclastic rocks in deep-buried basins. It is concluded that the size and composition of the clastic particles in the sedimentary pyroclastic rocks are the internal-controlling factors of the effective reservoirs, while the diagenetic fluid and the burial process are the external-controlling factors which form the effective reservoirs.

Micromagnetic Modeling of a Magnetically Unstable Zone and Its Geological Significances

AbstractRecent micromagnetic simulations have found that particles in the transitional zone between the single domain (SD) and single vortex (SV) zone are prone to thermal and external magnetic field instabilities that could adversely affect the accuracy of interpretations of paleomagnetic recordings. In this study, we attempt to evaluate the internal magnetization characteristics of these magnetically unstable (MU) particles and the influence on paleomagnetic observations by simulating the magnetic behavior of 68–104 nm truncated octahedral magnetite particles using the MERRILL modeling software. We found that: (a) The size region of the “MU zone” for grains of truncated octahedron shape is different from cubic octahedrons and spheres, indicating that the zone may be controlled by the geometry and shape of particles; (b) The MU zone has a range of 79–97 nm region, which is dominated by a hard‐axis aligned single vortex (HSV); and (c) MU particles are unstable as a function of temperature and have low coercive fields. Finally, the numerical fitting of hysteresis parameters for experimental data suggests that the influence of such MU particles in samples should not be ignored, especially for samples with fine‐grained magnetic minerals as the primary magnetic recording carriers. This research has extended our understanding of the behavior of the “MU zone” and its significance on paleomagnetic records.

Purely virtual particles versus Lee-Wick ghosts: Physical Pauli-Villars fields, finite QED, and quantum gravity

We reconsider the Lee-Wick (LW) models and compare their properties to the properties of the models that contain purely virtual particles. We argue against the LW premise that unstable particles can be removed from the sets of incoming and outgoing states in scattering processes. The removal leads to a non-Hermitian classical limit, besides clashing with the observation of the muon. If, on the other hand, all the states are included, the LW models have a Hamiltonian unbounded from below or negative norms. Purely virtual particles, on the contrary, lead to a Hermitian classical limit and are absent from the sets of incoming and outgoing states without implications on the observation of long-lived unstable particles. We give a vademecum to summarize the properties of most options to treat abnormal particles. We study a method to remove the LW ghosts only partially, by saving the physical particles they contain. Specifically, we replace a LW ghost with a certain superposition of a purely virtual particle and an ordinary particle, and drop only the former from the sets of the external states. The trick can be used to make the Pauli-Villars fields consistent and observable, without sending their masses to infinity, or to build a finite QED, by tweaking the original Lee-Wick construction. However, it has issues with general covariance, so it cannot be applied as is to quantum gravity, where a manifestly covariant decomposition requires the introduction of a massive spin-2 multiplet.

Dynamical behavior of the C -metric: Charged scalar fields, quasinormal modes, and superradiance

The $C$-metric is a boost-symmetric spacetime solution to the vacuum Einstein field equations which describes black holes that are uniformly accelerated under the tension of a cosmic string. Only recently the thermodynamics of accelerating black holes and their modal stability against neutral scalar perturbations were concisely established. The generalization of accelerating black holes to incorporate an electric charge, namely the charged $C$-metric, possess three distinct families of quasinormal mode frequencies; the complex photon surface quasinormal modes associated with unstable null particles at the equatorial plane of the photon surface, the purely imaginary acceleration modes whose existence solely depends on the acceleration of spacetime and the purely imaginary near-extremal modes which dominate the dynamics of the ringdown at late times when the event and Cauchy horizon approach each other. We extend the quasinormal mode analysis to charged scalar fluctuations and find that the photon surface modes are continuously deformed with respect to their neutral counterpart as the scalar charge is increased. We further find that the acceleration and near-extremal families acquire an oscillation frequency when the scalar charge is introduced. Finally, we study the superradiant amplification of charged scalar monochromatic waves impinging charged accelerating black holes. We find that even though the frequency range of superradiant amplification is lessened due to the acceleration, the amplification factors are considerably elevated with respect to those transpiring in Reissner-Nordstr\"om black holes and are maximized when the scalar charge is significantly large.

Leading Singularities in Higher-Derivative Yang–Mills Theory and Quadratic Gravity

In this work, we explore general leading singularities of one-loop amplitudes in higher-derivative Yang–Mills and quadratic gravity. These theories are known to possess propagators which contain quadratic and quartic momentum dependence, which leads to the presence of an unstable ghostlike resonance. However, unitarity cuts are not to be taken through unstable particles and therefore unitarity is still satisfied. On the other hand, this could engender issues when calculating leading singularities which are generalizations of unitarity cuts. Nevertheless, we will show with explicit examples how leading singularities are still well defined and accordingly they are able to capture relevant information on the analytic structure of amplitudes in such higher-derivative theories. We discuss some simple one-loop amplitudes which clarify these features.

Dressed propagators, fakeon self-energy and peak uncertainty

We study the resummation of self-energy diagrams into dressed propagators in the case of purely virtual particles and compare the results with those obtained for physical particles and ghosts. The three geometric series differ by infinitely many contact terms, which do not admit well-defined sums. The peak region, which is outside the convergence domain, can only be reached in the case of physical particles, thanks to analyticity. In the other cases, nonperturbative effects become important. To clarify the matter, we introduce the energy resolution ∆E around the peak and argue that a “peak uncertainty” ∆E ≳ ∆Emin ≃ Γf/2 around energies E ≃ mf expresses the impossibility to approach the fakeon too closely, mf being the fakeon mass and Γf being the fakeon width. The introduction of ∆E is also crucial to explain the observation of unstable long-lived particles, like the muon. Indeed, by the common energy-time uncertainty relation, such particles are also affected by ill-defined sums at ∆E = 0, whenever we separate their observation from the observation of their decay products. We study the regime of large Γf, which applies to collider physics (and situations like the one of the Z boson), and the regime of small Γf, which applies to quantum gravity (and situations like the one of the muon).