We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the set of all stable perturbations of the system, known as the ‘versal unfolding’. This construction yields a comprehensive classification of qualitatively distinct solutions and their metamorphoses into new topological forms, parametrized by the codimension of the bifurcation in each case. We illustrate these ideas through bifurcations in the simplest Friedmann models, the Oppenheimer-Snyder black hole, the evolution of causal geodesic congruences in cosmology and black hole spacetimes, crease flow on event horizons, and the Friedmann–Lemaître equations. Finally, we list open problems and briefly discuss emerging aspects such as partial differential equation stability of versal families, the general relativity landscape, and potential connections between gravitational versal unfoldings and those of the Maxwell, Dirac, and Schrödinger equations.
Samuel Victor Bernardo da Silva, Luiz Augusto Stuani Pereira, Rita de Cássia Dos Anjos
In this work, we present updated models of the spectral energy distributions (SEDs) for two high-frequency-peaked BL Lac objects (HBLs), that is, 1ES 0414+009 and 1ES 1959+650. The hard gamma-ray spectra observed during their flaring states suggest the presence of an additional emission component beyond the standard synchrotron self-Compton (SSC) scenario. We explore the possibility that this hard gamma-ray emission arises from inverse Compton (IC) scattering by Bethe–Heitler pairs produced along the line of sight, pointing to a more complex high-energy emission mechanism in these sources.
In this paper, we investigate the stability and feasibility of an anisotropic stellar model under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity that embraces the Karmarkar condition. In order to develop the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity model, the functional form of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> is taken into consideration as the linear function of the trace of the energy-momentum tensor <i>T</i> and the Ricci scalar <i>R</i>, respectively. This study proposes a well-known form of the radial metric function and finds another metric function by employing the Karmakar condition, which provides the exact solution to the field equation. The expression of the model parameters is derived by matching the obtained interior solutions with the Schwarzschild exterior metric over the bounding surface of a celestial object, along with the requirement that the radial pressure vanish at the boundary. The current estimated data of the star, pulsar 4U1608-52, is used to graphically explore the model. The physical attributes of the celestial object are thoroughly examined within the framework of the present model. Adjusting the model parameter, a detailed analysis of the stability criterion is presented that involves the adiabatic index, the Herrera cracking technique, and the causality condition. Furthermore, the Tolman–Oppenheimer–Volkhoff equation is used to analyze the stellar model’s equilibrium state. In order to maintain the stability condition of the anisotropic stellar structure, a suitable range for the model parameter is determined by the graphical analysis of the present model in this study. In addition, the numerical values of the physical parameters related to the compact stars Her X-1, LMC X-4, Cen X-3 and KS1731-207 are used to examine the model solution within the desired range of the model parameter.
CMS Collaboration, A. Hayrapetyan, A. Tumasyan
et al.
Abstract Using proton–proton collision data corresponding to an integrated luminosity of $$140\hbox { fb}^{-1}$$ 140 fb - 1 collected by the CMS experiment at $$\sqrt{s}= 13\,\text {Te}\hspace{-.08em}\text {V} $$ s = 13 Te V , the $${{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{\text {J}/\uppsi }} {{{\Xi }} ^{{-}}} {{\text {K}} ^{{+}}} $$ Λ b 0 → J / ψ Ξ - K + decay is observed for the first time, with a statistical significance exceeding 5 standard deviations. The relative branching fraction, with respect to the $${{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{{\uppsi }} ({2\textrm{S}})} {{\Lambda }} $$ Λ b 0 → ψ ( 2 S ) Λ decay, is measured to be $$\mathcal {B}({{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{\text {J}/\uppsi }} {{{\Xi }} ^{{-}}} {{\text {K}} ^{{+}}} )/\mathcal {B}({{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{{\uppsi }} ({2\textrm{S}})} {{\Lambda }} ) = [3.38\pm 1.02\pm 0.61\pm 0.03]\%$$ B ( Λ b 0 → J / ψ Ξ - K + ) / B ( Λ b 0 → ψ ( 2 S ) Λ ) = [ 3.38 ± 1.02 ± 0.61 ± 0.03 ] % , where the first uncertainty is statistical, the second is systematic, and the third is related to the uncertainties in $$\mathcal {B}({{{\uppsi }} ({2\textrm{S}})} \rightarrow {{\text {J}/\uppsi }} {{{\uppi }} ^{{+}}} {{{\uppi }} ^{{-}}} )$$ B ( ψ ( 2 S ) → J / ψ π + π - ) and $$\mathcal {B}({{{\Xi }} ^{{-}}} \rightarrow {{\Lambda }} {{{\uppi }} ^{{-}}} )$$ B ( Ξ - → Λ π - ) .
Astrophysics, Nuclear and particle physics. Atomic energy. Radioactivity
Femtoscopy has the capacity to probe the space-time geometry of the particle-emitting source in heavy-ion collisions. In particular, femtoscopy of like-sign kaon pairs may shed light on the origin of non-Gaussianity of the spatial emission probability density. The momentum correlations between like-sign kaon pairs are measured in data recorded by the STAR experiment, from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><msub><mi>s</mi><msub><mrow></mrow><mi>NN</mi></msub></msub></msqrt><mo>=</mo><mn>200</mn></mrow></semantics></math></inline-formula> GeV <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></semantics></math></inline-formula> collisions at RHIC, BNL. Preliminary results hint at the possible existence of non-Gaussian, Lévy-stable sources, with the likely presence of an anomalous diffusion process in the signal for the identically charged kaon pairs so produced. More statistically significant studies at lower centre-of-mass energies may contribute to the search for the critical end point of QCD.
A search for new phenomena giving rise to pairs of opposite electrically charged muons with impact parameters in the millimeter range is presented, using 139 fb−1 of s=13 TeV pp collision data from the ATLAS detector at the LHC. The search targets the gap in coverage between existing searches targeting final states with leptons with large displacement and prompt leptons. No significant excess over the background expectation is observed and exclusion limits are set on the mass of long-lived scalar supersymmetric muon-partners (smuons) with much lower lifetimes than previously targeted by displaced muon searches. Smuon lifetimes down to 1 ps are excluded for a smuon mass of 100 GeV, and smuon masses up to 520 GeV are excluded for a proper lifetime of 10 ps, at 95% confidence level. Finally, model-independent limits are set on the contribution from new phenomena to the signal-region yields.
It is known that, in quantum field theory, localized operations, e.g., given by unitary operators in local observable algebras, may lead to non-causal, or superluminal, state changes within their localization region. In this article, it is shown that, both in quantum field theory as well as in classical relativistic field theory, there are localized operations which correspond to “instantaneous” spatial rotations (leaving the localization region invariant) leading to superluminal effects within the localization region. This shows that “impossible measurement scenarios” which have been investigated in the literature, and which rely on the presence of localized operations that feature superluminal effects within their localization region, do not only occur in quantum field theory, but also in classical field theory.
In Schwarzschild acoustic black hole (SABH) spacetime, we investigate the wave dynamics for the fermions. To this end, we first take into account the Dirac equation in the SABH by employing a null tetrad in the Newman–Penrose (NP) formalism. Then, we consider the Dirac and Rarita–Schwinger equations, respectively. The field equations are reduced to sets of radial and angular equations. By using the analytical solution of the angular equation set, we decouple the radial wave equations and obtain the one-dimensional Schrödinger-like wave equations with their effective potentials. The obtained effective potentials are graphically depicted and analyzed. Finally, we investigate the fermionic greybody factors (GFs) radiated by the SABH spacetime. A thorough investigation is conducted into how the acoustic tuning parameter affects the GFs of the SABH spacetime. Both the semi-analytic WKB method and bounds for the GFs are used to produce the results, which are shown graphically and discussed.
Sushil Kumar, Manpreet Kaur, Sukhjeet Singh
et al.
Semi-empirical frameworks are widely used in calculating the bandhead energies of three-quasiparticle (3qp) configurations observed in well-deformed odd-A nuclei. In the present study, our aim is to improve the previous version of the semi-empirical model [Physical Review C. 1992, 45(6), 3013]. This is achieved by incorporating the ignored vital contributions owing to the irrotational motion of valance protons/neutrons, diagonal components of particle–particle coupling (ppc), and rotor–particle coupling (rpc) terms. We tested the validity of the improved version of the model by calculating the bandhead energies of twelve 3qp npp/pnn quadruplets observed in <sup>163</sup>Er, <sup>171,175,177</sup>Lu, <sup>177</sup>Ta, and <sup>183</sup>Re nuclides. Our new results show better agreement with the experimental data indicating the importance of newly added terms. We strongly expect that the present version of the model will provide support to future experimental campaigns for making configuration assignments to the newly observed 3qp bands and also in the identification of exact Nilsson’s configurations of 3qp quadruplets where experimental data that differentiate among the competing configuration are scarce.
The United States has a rich history in high energy particle accelerators and colliders -- both lepton and hadron machines, which have enabled several major discoveries in elementary particle physics. To ensure continued progress in the field, U.S. leadership as a key partner in building next generation collider facilities abroad is essential; also critically important is the exploring of options to host a future collider in the U.S. The"Snowmass"study and the subsequent Particle Physics Project Prioritization Panel (P5) process provide the timely opportunity to develop strategies for both. What we do now will shape the future of our field and whether the U.S. will remain a world leader in these areas. In this white paper, we briefly discuss the US engagement in proposed collider projects abroad and describe future collider options for the U.S. We also call for initiating an integrated R\&D program for future colliders.
Quantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Eur Phys J C 80:275, 2020), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better agreement with experimental results, in particular for the case of MINOS experiment.
Nallaly Berenice Mata Carrizal, Enrique Valbuena Ordóñez, Adrián Jacob Garza Aguirre
et al.
Working in the SU(2) flavor version of the NJL model, we study the effect of taking a finite system volume on a strongly interacting system of quarks, and, in particular, the location of the chiral phase transition and the CEP. We consider two shapes for the volume, spherical and cubic regions with different sizes and different boundary conditions. To analyze the QCD phase diagram, we use a novel criterion to study the crossover zone. A comparison between the results obtained from the two different shapes and several boundary conditions is carried out. We use the method of Multiple Reflection Expansion to determine the density of states and three kinds of boundary conditions over the cubic shape. These boundary conditions are: periodic, anti-periodic and stationary boundary conditions on the quark fields.
Shahram Jalalzadeh, Seyed Meraj M. Rasouli, Paulo Moniz
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger–Wheeler–DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>2</mn></msub></semantics></math></inline-formula>. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schrödinger–Wheeler–DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mn>2</mn></msub></semantics></math></inline-formula>, are explicitly presented within a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> supersymmetric quantum mechanics framework.
Within the framework of the light-cone QCD sum rules method (LCSR’s), the radiative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mo>(</mo><mn>1600</mn><mo>)</mo><mo>→</mo><mi>γ</mi><mi>N</mi></mrow></semantics></math></inline-formula> decay is studied. In particular, the magnetic dipole moment <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>G</mi><mi>M</mi><mn>1</mn></msubsup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the electric quadrupole moment <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>G</mi><mi>E</mi><mn>1</mn></msubsup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are estimated. We also calculate the ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>E</mi><mi>M</mi></mrow></msub><mo>=</mo><mo>−</mo><mfrac><mrow><msubsup><mi>G</mi><mi>E</mi><mn>1</mn></msubsup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow><mrow><msubsup><mi>G</mi><mi>M</mi><mn>1</mn></msubsup><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></mfrac></mrow></semantics></math></inline-formula> and the decay rate. The predicted multipole moments and the decay rate strongly agree with the existing experimental results as well as with the other available phenomenological approaches.
In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in <i>f</i>(<i>R</i>) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.
The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.
Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the ‘BCS–BEC crossover’ connecting the physics of Bardeen–Cooper–Schrieffer (BCS) superconductivity with that of Bose–Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of 40K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS–BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.