Fine Structure Constant Research Articles

Relativistic Ritz approach to hydrogenlike atoms: Theoretical considerations

The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic foundation. Here I present a long-distance relativistic effective theory describing hydrogen-like systems with arbitrary mass ratios, thereby extending the canonical Ritz-like approach. Fitting the relativistic theory to the hydrogen energy levels predicted by bound-state QED indicates that it is superior to the canonical, nonrelativistic approach. An analytic analysis reveals nonlinear consistency relations within the bound-state QED level predictions that relate higher-order corrections to those at lower order, providing guideposts for future perturbative calculations as well as insights into the asymptotic behavior of Bethe logarithms. Applications of the approach include fitting to atomic spectroscopic data, allowing for the determination the fine-structure constant from large spectral data sets and also to check for internal consistency of the data independently from bound-state QED.

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks.

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20} eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28)Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

W-Boson Mass Anomaly as a Manifestation of Spontaneously Broken Additional SU(2) Global Symmetry on a New Fundamental Scale

Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW ≃ 3α8πMW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules.

Graphene multilayers for coherent perfect absorption: effects of interlayer separation.

We present a model study to estimate the sensitivity of the optical absorption of multilayered graphene structure to the subnanometer interlayer separation. Starting from a transfer-matrix formalism we derive semi-analytical expressions for the far-field observables. Neglecting the interlayer separation, results in upper bounds to the absorption of 50% for real-valued sheet conductivities, exactly the value needed for coherent perfect absorption (CPA), while for complex-valued conductivities we identify upper bounds that are always lower. For pristine graphene the number of layers required to attain this maximum is found to be fixed by the fine structure constant. For finite interlayer separations we find that this upper bound of absorption only exists until a particular value of interlayer separation (Dlim) which is less than the realistic interlayer separation in graphene multilayers. Beyond this value, we find a strong dependence of absorption with the interlayer separation. For an infinite number of graphene layers a closed-form analytical expression for the absorption is derived, based on a continued-fraction analysis that also leads to a simple expression for Dlim. Our comparison with experiments illustrates that multilayer Van der Waals crystals suitable for CPA can be more accurately modelled as electronically independent layers and more reliable predictions of their optical properties can be obtained if their subnanometer interlayer separations are carefully accounted for.

Sulfur doped FeSe: A first-principles study of its electronic and superconducting properties

The self-consistent first-principles calculations, based on density functional theory (DFT) approach and the Green’s-function-based Korringa-Kohn-Rostoker Atomic Sphere Approximation (KKR-ASA) method within coherent potential approximation (CPA), are performed to investigate the electronic and superconducting properties of FeSe1-xSx (x = 0.0, 0.05) alloys. The spin-unpolarized calculations show a significant effect on the electronic structure for the substitution of S in FeSe. The outcome for electronic and superconducting properties have been examined in terms of changes in the density of states, band structure, Fermi surface, bare Sommerfeld constant, Hopfield parameters, and the superconducting transition temperature (Tc) of FeSe and FeSe0.95S0.05 alloys, respectively. All calculated results in terms of Tc compare well with the available experimental data. It hopes that the studied properties of these alloys would give the possibility to understand the new physics of iron-based superconductors experimentally.

A limit on variations in the fine-structure constant from spectra of nearby Sun-like stars.

The fine structure constant α sets the strength of the electromagnetic force. The Standard Model of particle physics provides no explanation for its value, which could potentially vary. The wavelengths of stellar absorption lines depend on α but are subject to systematic effects owing to astrophysical processes in stellar atmospheres. We measured precise line wavelengths from observations of 17 stars, selected to have almost identical atmospheric properties to those of the Sun (solar twins), which reduces those systematic effects. We found that α varies by [Formula: see text] parts per billion within 50 parsecs from Earth. Combining the results from all 17 stars provides an empirical local reference for stellar measurements of α, with an ensemble precision of 12 parts per billion.

Universal rotation gauge via quantum anomalous Hall effect

Integer quantum Hall effect allows to gauge the resistance standard up to more than one part in a billion. Combining it with the speed of light, one obtains the fine-structure constant α ≈ 1/137, a dimensionless reference number that can be extracted from a physical experiment. Most exact notion of this value and especially its possible variation on the cosmological time scales is of enormous relevance for fundamental science. In an optical experiment, the fine-structure constant can be directly obtained as purely geometrical angle by measuring the quantized rotation of light polarization in two-dimensional quantum wells. In realistic conditions, high external magnetic fields have to be applied, which strongly affects possible attainable accuracy. An elegant solution of this problem is provided by quantum anomalous Hall effect where a universal quantized value can be obtained in zero magnetic field. Here, we measure the fine-structure constant in a direct optical experiment that requires no material adjustments or technical calibrations. By investigating the Faraday rotation at the interference maxima of the dielectric substrate, the angle close to one α is obtained at liquid helium temperatures without using a dilution refrigerator. Such calibration and parameter-free experiment provides a system-of-unit-independent access to universal quantum of rotation.

Fundamental Units of Measurement and Extra Dimensions

The space available to our perception is three-dimensional with full evidence. The development of physics led to the hypothesis of extra dimensions. It is believed that an important role in the unification of physics should play by the Planck units of mass, length and time, built on the universal constants c (the speed of light in a vacuum), G (the gravitational constant), and ħ (the reduced Planck constant). In August 2021, published work in which it is shown that the fundamental role in the unification of physics, in fact, was played by the Stoney units, built on the universal constants c − G − e or c − G − ħ and α (where e is the elementary electric charge, and α is the fine-structure constant). Using this result, the presented work offers a possible solution to the riddle of extra dimensions; it is shown that any additional spatial dimension can be expressed in terms of the fundamental length or the product of the fundamental time and the speed of light in a vacuum.

Constraints on extended Bekenstein models from cosmological, astrophysical, and local data

Searching for variations of nature's fundamental constants is a crucial step in our quest to go beyond our current standard model of fundamental physics. If they exist, such variations will be very likely driven by the existence of a new fundamental field. The Bekenstein model and its extensions introduce such a scalar field in a purely phenomenological way, inducing a variation of the fine-structure constant on cosmological scales. This theoretical framework is as simple and general as possible while still preserving all the symmetries of standard quantum electrodynamics. When allowing for couplings to the other sectors of the Universe, such as baryons, dark matter, and the cosmological constant, the Bekenstein model is expected to reproduce the low energy limits of several grand unification, quantum gravity, and higher dimensional theories. In this work, we constrain different versions of the Bekenstein model by confronting the full cosmological evolution of the field with an extensive set of astrophysical, cosmological, and local measurements. We show that couplings of the order of parts per million are excluded for all the cases considered, imposing strong restrictions on theoretical frameworks aiming to deal with variations of the fine-structure constant.

Muon and electron g-2 anomalies in a flavor conserving 2HDM with an oblique view on the CDF M_W value

We consider a type I or type X two Higgs doublets model with a modified lepton sector. The generalized lepton sector is also flavor conserving but with the new Yukawa couplings completely decoupled from lepton mass proportionality. The model is one loop stable under renormalization group evolution and it allows to reproduce the g-2 muon anomaly together with the different scenarios one can consider for the electron g-2 anomaly, related to the Cesium and/or to the Rubidium recoil measurements of the fine structure constant. Thorough parameter space analyses are performed to constrain all the model parameters in the different scenarios, either including or not including the recent CDF measurement of the W boson mass. For light new scalars with masses in the 0.2–1.0 TeV range, the muon anomaly receives dominant one loop contributions; it is for heavy new scalars with masses above 1.2 TeV that two loop Barr–Zee diagrams are needed. The electron g-2 anomaly, if any, must always be obtained with the two loop contributions. The final allowed regions are quite sensitive to the assumptions about perturbativity of Yukawa couplings, which influence unexpected observables like the allowed scalar mass ranges. On that respect, intermediate scalar masses, highly constrained by direct LHC searches, are allowed provided that the new lepton Yukawa couplings are fully scrutinized, including values up to 250 GeV. In the framework of a complete model, fully numerically analysed, we show the implications of the recent M_{W} measurement.

Consistency test of the fine-structure constant from the whole ionization history

In cosmology, the fine-structure constant can affect the whole ionization history. However, the previous works confine themselves to the recombination epoch and give various strong constraints on the fine-structure constant. In this paper, we also take the reionization epoch into consideration and do a consistency test of the fine-structure constant from the whole ionization history.From the data combination of Planck 2018, BAO data, SNIa samples, SFR density from UV and IR measurements, and the Q HII constraints, we find the constraint on the fine-structure constant during the recombination epoch is α rec/α EM = 1.001494+0.002041 -0.002063 and its counterpart during the reionization epoch is α rei/α EM = 0.854034+0.031678 0.027209 at 68% C.L.. They are not consistent with each other by 4.64σ.A conservative explanation for such a discrepancy is that there are some issues in the data we used.We prefer a calibration of some important parameters involved in reconstructing the reionization history.

Power spectrum of domain-wall network, and its implications for isotropic and anisotropic cosmic birefringence

Recently, based on a novel analysis of the Planck satellite data, a hint of a uniform rotation of the polarization of cosmic microwave background photons, called isotropic cosmic birefringence, has been reported. The suggested rotation angle of polarization of about 0.2–0.4 degrees is close to the fine-structure constant, α ≃ 1/137 rad ≃ 0.42 deg. Interestingly, this coincidence can be naturally explained over a very wide parameter range by the domain walls of axion-like particles. Furthermore, the axion-like particle domain walls predict not only isotropic cosmic birefringence but also anisotropic one that reflects the spatial distribution of the axion-like particle field on the last scattering surface. In this paper, we perform lattice simulations of the formation and evolution of domain walls in the expanding universe and obtain for the first time the two-point correlation function and power spectrum of the scalar field that constitutes the domain walls. We find that for initial fluctuations at subhorizon scales, the power spectrum is roughly consistent with analytical predictions based on random wall distributions. However, there is some excess at scales corresponding to the Hubble radius. Applying our results to the anisotropic cosmic birefringence, we predict the power spectrum of the rotation angles induced by the axion-like particle domain walls for the similar initial condition, and show that it is within reach of future observations of the cosmic microwave background.

Fundamental physics with ESPRESSO: Constraining a simple parametrisation for varying α

Context. The spectrograph ESPRESSO recently obtained a limit on the variation of the fine-structure constant, α, through measurements along the line of sight of a bright quasar with a precision of 1.36 ppm at 1σ level. This imposes new constraints on cosmological models with a varying α. We assume such a model where the electromagnetic sector is coupled to a scalar field dark energy responsible for the current acceleration of the Universe. We parametrise the variation of α with two extra parameters, one defining the cosmological evolution of the quintessence component and the other fixing the coupling with the electromagnetic field. Aims. The objective of this work is to constrain these parameters with both astrophysical and local probes. We also carried out a comparative analysis of how each data probe may constrain our parametrisation. Methods. We performed a Bayesian analysis by comparing the predictions of the model with observations. The astrophysical datasets are composed of quasar spectra measurements, including the latest ESPRESSO data point, as well as Planck observations of the cosmic microwave background. We combined these with local results from atomic clocks and the MICROSCOPE experiment. Results. The constraints placed on the quintessence parameter are consistent with a null variation of the field, and are therefore compatible with a ΛCDM cosmology. The constraints on the coupling to the electromagnetic sector are dominated by the Eötvös parameter local bound. Conclusions. More precise measurements with ESPRESSO will be extremely important to study the cosmological evolution of α as it probes an interval of redshift not accessible to other types of observations. However, for this particular model, current available data favour a null variation of α resulting mostly from the strong MICROSCOPE limits.

Review force general conjectural modeling transforms formalism physics

This review article discusses recent advance formalisms trying to resolve inconsistencies of algorithmic grand unified physics. Logical conjectures starting with considering universe as a matrix of existential points and developing knowhow mechanics to configure algorithms to quantify quantum physical discontinuum dissipative process mechanism is emphasized. This projects algorithmic generalized transforms to model fundamentally force out of first definitional principle that will consider infinitum multiverses that encompasses universes allowing information leaking. These aspects may explain why none of the universal constants, especially Planck’s constant, speed of light, universal gravitational constant, fine structure constant, as well as others may not be constant after all!! Hereafter, emphasis will be on observable that are theoretically and/or theoretically testable measurable observations. Realizing that a real astrophysical parameter may be only signal/noise matrix, step by via step algorithms are developed from first principles of physical mathematics especially matrices, properties, rules, mathematical conceptuality, and physical attributable entity simple common-sense approach. Types of symmetries, intensity matrix versus density matrix, hidden causality, functor, functional algebra function point absolute microblackhole gage gravity force PHYSICS transforms superluminous plenum vacuum quanta with quantum sub-quantum hod-PDP micromechanics have been analyzed extensively with grand unifiable algorithm equating formalisms.

Atomic clocks highly sensitive to the variation of the fine-structure constant based on Hf ii, Hf iv, and W vi ions

We demonstrate that several metastable excited states in Hf ii, Hf iv, and W vi ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. The cooling electric dipole ($E1$) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using ${\mathrm{Ca}}^{+}$ or ${\mathrm{Sr}}^{+}$ ions. Energy levels; Land\'e $g$ factors; transition amplitudes for electric dipole ($E1$), electric quadrupole ($E2$), and magnetic dipole ($M1$) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory ($\mathrm{CI}+\mathrm{SD}$), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches $K=8.3$. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.

Constraining Einstein-dilaton models using joint gravitational-wave and electromagnetic observations

With the advent of gravitational-wave astronomy it has now been possible to constrain modified theories of gravity that were invoked to explain the dark energy. In a class of dilaton models, distances to cosmic sources inferred from electromagnetic and gravitational wave observations would differ due to the presence of a friction term. In such theories, the ratio of the Newton's constant to the fine structure constant varies with time. In this paper we explore the degree to which it will be possible to test such models. If collocated sources (e.g. supernovae and binary neutron star mergers), but not necessarily multimessengers, can be identified by electromagnetic telescopes and gravitational-wave detectors one can probe if light and gravitational radiation are subject to the same laws of propagation over cosmological distances. This helps in constraining the variation of Newton's constant relative to fine-structure constant. The next generation of gravitational wave detectors, such as the Cosmic Explorer and Einstein Telescope, in tandem with the Vera Rubin Observatory and gamma ray observatories such as the Fermi Space Observatory will be able to detect or constrain such variations at the level of a few parts in 100. We apply this method to GW170817 with distances inferred by the LIGO and Virgo detectors and the observed Kilonova.

Variational vs perturbative relativistic energies for small and light atomic and molecular systems.

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α4Eh) non-radiative QED correction is 5% of the leading-order (α3Eh) non-radiative QED correction for Z = 2 (He), but it is 40% already for Z = 4 (Be2+), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

Constraining a possible time-variation of the speed of light along with the fine-structure constant using strong gravitational lensing and Type Ia supernovae observations

The possible time variation of the fundamental constants of nature has been an active subject of research since the large-number hypothesis was proposed by Dirac. In this paper, we propose a new method to investigate a possible time variation of the speed of light (c) along with the fine-structure constant (α) using Strong Gravitational Lensing (SGL) and Type Ia Supernovae (SNe Ia) observations. We assume a general approach to describe the mass distribution of lens-type galaxies, the one in favor of the power-law index model (PLAW). We also consider the runaway dilaton model to describe a possible time-variation of α. In order to explore the results deeply, we split the SGL sample into five sub-samples according to the lens stellar velocity dispersion and three sub-samples according to lens redshift. The results suggest that it is reasonable to treat the systems separately, but no strong indication of varying c was found.

Wigner crystallization at large fine structure constant

We consider the fate of the Wigner crystal state in a two-dimensional system of massive Dirac electrons as the effective fine structure constant $\ensuremath{\alpha}$ is increased. In a Dirac system, larger $\ensuremath{\alpha}$ naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with quantum and thermal melting of the Wigner crystal state using two independent approaches. We show that at $\ensuremath{\alpha}\ensuremath{\gg}1$, the Wigner crystal state is best understood in terms of logarithmically interacting electrons, and that both the critical density and the melting temperature approach a universal, $\ensuremath{\alpha}$-independent value. We discuss our results in the context of recent experiments in twisted bilayer graphene near the magic angle.

The generation of mass in a non-linear field theory

Abstract The mass spectrum of elementary particles is calculated in a new approach, based on B. Heim’s quantum field theory, which manifests in a non-linear eigenvalue equation and merges into the Einstein field equation in the macroscopic limit. The poly-metric of the theory allows spacetime and matter to be described in a unified formalism, representing a radical geometrisation of physics. The calculated mass energies are in very good agreement with the empirical data (error < 1 % ${< }1\%$ on average) if the mass scale is gauged to the electron as lowest mass and the second main parameter, determining the strength of obtained mass hierarchy levels, is close to the half inverse of the fine structure constant, describing the difference in strength between the electromagnetic and the strong interaction. The obtained hierarchy levels are not identical to the particle generations of the Standard Model; however, show a self-similarity typical for non-linear theories. For higher values of the main quantum number N, the calculated mass formula becomes identical to the phenomenological formulae of Nambu, respectively, Mac Gregor.