Arbitrary Mass Research Articles

Gravitational Condensate Stars: An Alternative to Black Holes

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein’s equations is obtained, characterized by an interior de Sitter region of p=−ρ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order kBℓMc/ℏ, instead of the Bekenstein–Hawking entropy, SBH=4πkBGM2/ℏc. Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox.

Self-binding energies in AdS

The Positive Binding Conjecture is a proposed formulation of the Weak Gravity Conjecture appropriate to Anti de-Sitter (AdS) space. It proposes that in a consistent gravitational theory, with a U(1) gauge symmetry, there must exist a charged particle with non-negative self-binding energy. In order to formulate this as a constraint on a given effective theory, we calculate the self-binding energy for a charged particle in AdS4 and AdS5. In particular, we allow it to couple to an additional scalar field of arbitrary mass. Unlike the flat-space case, even when the scalar field is massive it contributes significantly to the binding energy, and therefore is an essential component of the conjecture. In AdS5, we give analytic expressions for the self-binding energy for the cases when the scalar field is massless and when it saturates the Breitenlohner-Freedman (BF) bound, and in AdS4 when it is massless. We show that the massless case reproduces the flat-space expressions in the large AdS radius limit, and that both analytic cases lead to vanishing total self-binding energy for BPS particles in example supersymmetric models. For other masses of the scalar we give numerical expressions for its contribution to the self-binding energy.

Parity violation in the scalar trispectrum: no-go theorems and yes-go examples

We derive a set of no-go theorems and yes-go examples for the parity-odd primordial trispectrum of curvature perturbations. We work at tree-level in the decoupling limit of the Effective Field Theory of Inflation and assume scale invariance and a Bunch-Davies vacuum. We show that the parity-odd scalar trispectrum vanishes in the presence of any number of scalar fields with arbitrary mass and any parity-odd scalar correlator vanishes in the presence of any number of spinning fields with massless de Sitter mode functions, in agreement with the findings of Liu, Tong, Wang and Xianyu [1]. The same is true for correlators with an odd number of conformally-coupled external fields. We derive these results using both the (boostless) cosmological bootstrap, in particular the Cosmological Optical Theorem, and explicit perturbative calculations. We then discuss a series of yes-go examples by relaxing the above assumptions one at the time. In particular, we provide explicit results for the parity-odd trispectrum for (i) violations of scale invariance in single-clock inflation, (ii) the modified dispersion relation of the ghost condensate (non-Bunch-Davies vacuum), and (iii) interactions with massive spinning fields. Our results establish the parity-odd trispectrum as an exceptionally sensitive probe of new physics beyond vanilla inflation.

D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled F(4) gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS2× Σ1 solutions giving rise to four-dimensional orbifold solutions, AdS2× Σ1 ⋉ Σ2. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U(1)2-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS6 black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp(2N) theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein-Hawking entropy holographically.

Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism

This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters $\beta$ and $\gamma$. It is shown that there can still exist a collinear equilibrium configuration and a triangular one, each of which is a generalization of the post-Newtonian equilibrium configuration in general relativity. The collinear configuration can exist for arbitrary mass ratio, $\beta$, and $\gamma$. On the other hand, the PPN triangular configuration depends on the nonlinearity parameter $\beta$ but not on $\gamma$. For any value of $\beta$, the equilateral configuration is possible, if and only if three finite masses are equal or two test masses orbit around one finite mass. For general mass cases, the PPN triangle is not equilateral as in the post-Newtonian case. It is shown also that the PPN displacements from the Lagrange points in the Newtonian gravity $L_1$, $L_2$ and $L_3$ depend on $\beta$ and $\gamma$, whereas those to $L_4$ and $L_5$ rely only on $\beta$.

The [formula omitted] symmetry of string scatterings from D-branes

By using the solvability of Lauricella function FD(K)(α;β1,...,βK;γ;x1,...,xK) with nonpositive integer βJ, we show that each scattering or decay process of string and D-brane states at arbitrary mass levels can be expressed in terms of a single Lauricella function. This result extends the previous exact SL(K+3,C) symmetry of tree-level open bosonic string theory to include the D-brane.

Recoil Corrections to the Energy Levels of Hydrogenic Atoms.

We have completed the calculation of pure-recoil corrections of order (Zα)^{6} to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, as well as hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order (Zα)^{7} corrections.

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.

On electric fields in hot QCD: perturbation theory

We investigate the response of a hot gas of quarks to external electric fields via leading-order perturbation theory. In particular, we discuss how equilibrium is maintained in the presence of the electric field and calculate the electric susceptibility, providing its high-temperature expansion for arbitrary quark mass. Furthermore, we point out that there is a mismatch between this, direct determination of the susceptibility at zero field and the weak-field expansion of the effective action at nonzero electric fields, as obtained using Schwinger’s exact propagator. We discuss the origin of this mismatch and elaborate on the generalization of our results to full QCD in electric fields.

ABJM at finite N via 4d supergravity

We apply the conjecture of [1] for gravitational building blocks to the effective supergravity description of M-theory on S7/ℤk. Utilizing known localization results for the holographically dual ABJM theory, we determine a complete tower of higher derivative corrections to the AdS4 supergravity and a further set of quantum corrections. This uniquely fixes the gravitational block, leading to holographic predictions for a number of exact ABJM observables, excluding only constant and non-perturbative corrections in the gauge group rank N. The predicted S3 partition function is an Airy function that reproduces previous results and generalizes them to include arbitrary squashing and mass deformations/R-charge assignments. The topologically twisted and superconformal indices are instead products of two different Airy functions, in agreement with direct numeric calculations in the unrefined limit of the former object. The general fixed-point formula for an arbitrary supersymmetric background is similarly given as a product of Airy functions.

Semiclassical Quantization Condition of the Energy Levels for the Relativistic System of Two Fermions with Arbitrary Masses

New semiclassical quantization conditions of the energy levels are obtained for the relativistic systems of two fermions of arbitrary masses interacting by means of the singular con.ning Coulomb-like potential. Quantization conditions of the energy levels were found for the pseudoscalar, vector, and pseudovector mesons. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic con.guration representation for the case of two relativistic spin particles with arbitrary masses.

Quantum electrodynamics of two-body systems with arbitrary masses up to α6 order

We perform a calculation of quantum electrodynamics effects in excited states with $l>1$ of arbitrary two-body systems up to $\alpha^6\,\mu$ order. The obtained results are valid for hadronic atoms, as long as the strong interaction effects are negligible. We demonstrate that for circular states with $l\sim n$, the effective expansion parameter is $Z\,\alpha/n$, which extends the applicability of the derived formulas to heavy ions. Moreover, inclusion of higher-order terms is feasible, which indicates that accurate measurements of excited states of, for example, muonic or antiprotonic hydrogenic ions can be used to determine the fundamental constants and to search for the existence of yet unknown long-range interactions.

Semi-analytical frameworks for subhaloes from the smallest to the largest scale

ABSTRACT Substructures of dark matter halo, called subhaloes, provide important clues to understand the nature of dark matter. We construct a useful model to describe the properties of subhalo mass functions based on the well-known analytical prescriptions, the extended Press–Schechter theory. The unevolved subhalo mass functions at arbitrary mass scales become describable without introducing free parameters. The different host halo evolution histories are directly recast to their subhalo mass functions. As applications, we quantify the effects from (i) the Poisson fluctuation, (ii) the host-mass scatter, and the (iii) different tidal evolution models on observables in the current Universe with this scheme. The Poisson fluctuation dominates in the number count of the mass ratio to the host of $\sim {\cal O}(10^{-2})$, where the intrinsic scatter is smaller by a factor of a few. The host-mass scatter around its mean does not affect the subhalo mass function. Different models of the tidal evolution predict a factor of ∼2 difference in numbers of subhaloes with $\lesssim {\cal O}(10^{-5})$, while the dependence of the Poisson fluctuation on the tidal evolution models is subtle. The scheme provides a new tool for investigating the smallest scale structures of our Universe which are to be observed in near future experiments.

Monolepton production in SMEFT to mathcal{O} (1/Λ4) and beyond

We calculate pp → ℓ+ν, ℓ− overline{nu} to mathcal{O} (1/Λ4) within the Standard Model Effective Field Theory (SMEFT) framework. In particular, we calculate the four-fermion contribution from dimension six and eight operators, which dominates at large center of mass energy. We explore the relative size of the mathcal{O} (1/Λ4) and mathcal{O} (1/Λ2) results for various kinematic regimes and assumptions about the Wilson coefficients. Results for Drell-Yan production pp → ℓ+ℓ− at mathcal{O} (1/Λ4) are also provided. Additionally, we develop the form for four fermion contact term contributions to pp → ℓ+ν, ℓ− overline{nu} , pp → ℓ+ℓ− of arbitrary mass dimension. This allows us to estimate the effects from even higher dimensional (dimension > 8) terms in the SMEFT framework.

Evaluation of Feynman integrals with arbitrary complex masses via series expansions

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the Mathematica package SeaSyde. The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals. At variance with respect to other existing codes, the analytical continuation of the solution is performed in the complex plane associated to each kinematical invariant. We present the results of the evaluation of the Master Integrals relevant for the NNLO QCD-EW corrections to the neutral-current Drell-Yan processes. Program summaryProgram Title:SeaSydeCPC Library link to program files:https://doi.org/10.17632/4hk9rbw4y8.1Developer's repository link:https://github.com/TommasoArmadillo/SeaSydeLicensing provisions: GPLv3Programming language:MathematicaNature of problem: Solution of multi-loop Feynman integrals with an arbitrary number of internal complex-valued massive lines.Solution method:: Solution via series expansions of the systems of differential equations satisfied by the loop integrals. Analytic continuation of the solution to any point of the kinematic variables. The solution is transported from the initial to the final point, by moving in the complex plane associated to each kinematic variable. In multi-variable problems, the transport is computed one variable at the time.

Space-time resolved inference-based neurophysiological process imaging: Application to resting-state alpha rhythm

Neural processes are complex and difficult to image. This paper presents a new space-time resolved brain imaging framework, called Neurophysiological Process Imaging (NPI), that identifies neurophysiological processes within cerebral cortex at the macroscopic scale. By fitting uncoupled neural mass models to each electromagnetic source time-series using a novel nonlinear inference method, population averaged membrane potentials and synaptic connection strengths are efficiently and accurately inferred and imaged across the whole cerebral cortex at a resolution afforded by source imaging. The efficiency of the framework enables return of the augmented source imaging results overnight using high performance computing. This suggests it can be used as a practical and novel imaging tool. To demonstrate the framework, it has been applied to resting-state magnetoencephalographic source estimates. The results suggest that endogenous inputs to cingulate, occipital, and inferior frontal cortex are essential modulators of resting-state alpha power. Moreover, endogenous input and inhibitory and excitatory neural populations play varied roles in mediating alpha power in different resting-state sub-networks. The framework can be applied to arbitrary neural mass models and has broad applicability to image neural processes of different brain states.

Enhanced Stark effect in Dirac materials

The Stark effect in confined geometries is sensitive to boundary conditions. The vanishing wave function required on the boundary of nanostructures described by the infinite-barrier Schrödinger equation means that such states are only weakly polarizable. In contrast, materials described by the Dirac equation are characterized by much less restrictive boundary conditions. Focusing on honeycomb-lattice armchair nanoribbons, we demonstrate an enhancement by more than an order of magnitude. This result follows from an exact Dirac polarizability valid for arbitrary mass, momentum and ribbon width. Moreover, an exact expression for the frequency-dependent dynamic polarizability has been derived. Our analytic Dirac results have been validated by comparison to numerical results from atomistic models.

Cosmological scattering equations at tree-level and one-loop

We recently proposed a formula for tree-level n-point correlators of massive ϕ4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of n-point correlators. Finally, we propose a similar formula for 1-loop n-point correlators in terms of an integral over (n + 2) punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space.

Measuring quasinormal mode amplitudes with misaligned binary black hole ringdowns

In recent work, we examined how different modes in the ringdown phase of a binary coalescence are excited as a function of the final plunge geometry. At least in the large mass ratio limit, we found a clean mapping between angles describing the plunge and the amplitude of different quasi-normal modes (QNMs) which constitute the ringdown. In this study, we use that mapping to construct a waveform model expressed as a sum of QNMs where the mode amplitudes and phases are determined by the source plunge parameters. We first generate a large number of calibration waveforms and interpolate between fits of each mode amplitude and phase up to $\ell \leq 8$ and $\ell - |m| \leq 4$. The density of our calibration data allows us to resolve important features such as phase transition discontinuities at large misalignments. Using our ringdown waveform model, we then perform Bayesian parameter estimation with added white Gaussian noise to demonstrate that, in principle, the mode amplitudes can be measured and used to constrain the plunge geometry. We find that inferences are substantially improved by incorporating prior information constraining mode excitation, which motivates work to understand and characterize how the QNM excitation depends on the coalescence geometry. These results are part of a broader effort to map the mode excitation from arbitrary masses and spins, which will be useful for characterizing ringdown waves in upcoming gravitational-wave measurements.

Topological susceptibility and fourth cumulant in a uniform magnetic field

We study the topological susceptibility and fourth cumulant of the QCD vacuum in a background magnetic field (H) using three-flavor chiral perturbation theory (χPT) for arbitrary quark masses and n-flavor χPT with degenerate quark masses. We find that the enhancement by the magnetic field of the topological susceptibility relative to the H=0 vacuum value is larger in the three-flavor χPT compared to two-flavor χPT. Additionally, in comparing the fourth cumulant, we find that its suppression is comparable for magnetic fields, eH≲0.8mπ2, and weaker for larger magnetic fields in three-flavor χPT with its enhancement beginning at a significantly lower critical magnetic field compared to two-flavor χPT. We also find that the enhancement of the topological susceptibility in n-flavor χPT with degenerate quarks is significantly larger and the suppression of the topological cumulant significantly greater at weak fields with the critical magnetic field pushed out to larger magnetic fields compared to both two and three-flavor χPT.