We present a systematic framework for computing frequency-domain gravitational waveforms from relativistic binary scattering in different asymptotic regimes. The method yields a controlled series expansion that can in principle be extended to arbitrary order in the relevant kinematic parameter. By combining differential-equation techniques with restriction theory and algebraic-geometry methods for impact-parameter-space Fourier integrals, we derive recursion relations that generate the leading-order (tree-level) waveform in both the soft-emission and post-Newtonian regimes, establishing a proof of principle for extending the approach to higher-loop computations. Finally, following constraints from rapid-decay homology, we show that the Fourier integrals underlying the waveform satisfy $ϵ$-form differential equations mixing Bessel- and exponential-type kernels, marking a first step toward uncovering the analytic structure of the exact solution.

The ingoing and outgoing null expansions associated to a spatial 2-sphere are quantized in the spherically symmetric model of loop quantum gravity. It is shown that the resulting expansion operators are self-adjoint in the kinematical Hilbert space with generalized eigenstates. It turns out that the outgoing and ingoing expansion operators have the same spectrum consisting of a continuous band and discrete points. In the subspaces with fixed quantum numbers on the edges of the graphs underlining the quantum states, the two operators still share the common continuous spectrum, while their discrete spectra can be different from each other. These results provide new insights on the avoidance of the singularities in classical general relativity and the establishment of a certain notion of quantum horizons.

In previous work, we introduced the $\ell$-boson stars, a generalization of standard boson stars, which are parametrized by an angular momentum number $\ell$, while still preserving the spacetime’s spherical symmetry. In this article, we present and study the properties of $\ell$-boson stars in spacetimes with a negative cosmological constant, such that they are asymptotically anti–de Sitter.

In this paper, we study several models and parametrizations of dynamical dark energy (DE) that have been studied already in the past, in conjunction with the recently proposed model $w\mathrm{XCDM}$, the running vacuum model (RVM) with and without a threshold at $z=1$ and two variants of it, the RRVM and the “flipped RVM,” and compare them all with the concordance $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model and the popular $w_0{w}_a\mathrm{CDM}$ parametrization. We use two standard sets of cosmological data, one including distant supernovae from $\mathrm{Pantheon}+$ and the other from DES-Y5. The rest of the data (BAO from DESI DR2 and CMB from Planck PR4) are shared by the two sets. They are analyzed using the state-of-the-art techniques. No structure formation data are utilized for this analysis and no use is made of the SH0ES calibration of $H_0$. Even so, we find that the flipped RVM and to a lesser extent the $w\mathrm{XCDM}$ and the RVM with threshold, point to significant evidence of dynamical DE, at a level comparable to $w_0{w}_a\mathrm{CDM}$, more conspicuously for the dataset that involves DES-Y5 observations. We also find that while more traditional models studied in the past, in which there is an exchange between vacuum energy and cold dark matter (through, e.g., an interactive source proportional either to the density of dark matter or to that of vacuum) still hint at dynamical DE, the strength of the statistical signal (which we assess through information criteria and other estimators) is nevertheless less pronounced. Finally, we discuss the ability of the various models to explain the data by performing an analysis of their effective equation-of-state parameters and corresponding evolution of their dark energy densities.

We investigate how the cosmological Euler equation can be tested in the presence of viscous dark matter, violations of the equivalence principle (EP), and modifications of gravity, while relying on minimal theoretical assumptions. Extending the analysis of Castello et al. Phys. Rev. D 111, 123559 (2025)., we generalize the observable $E_P$, which quantifies EP violation, to ${\tilde{E}}_P$, discuss the degeneracy between bulk and shear viscosities and EP-violating effects, and explicitly show that the EP can still be tested in the small-viscosity limit. In addition, we identify a model-independent observable, $C_{\mathrm{vis},0}$, which characterizes the present-day dark matter viscosity and can be measured from relativistic galaxy number counts by cross-correlating two galaxy populations. We perform forecasts for three forthcoming stage-IV surveys: DESI, Euclid, and SKA Phase 2 (SKA2), and find that $C_{\mathrm{vis},0}$ can be tightly constrained, at the level of $\mathcal{O}({10}^{-6})$ or better in all cases. Among these surveys, SKA2 provides the tightest constraint, with a $1\sigma$ uncertainty of $1.08\times {10}^{-7}$ on $C_{\mathrm{vis},0}$.

Gravitational-wave (GW) events are generally believed to originate in galaxies and can thus serve, like galaxies, as tracers of the Universe’s large-scale structure. In GW observations, waveform analysis provides direct measurements of luminosity distances; however, without relying on a specific cosmological model, the redshifts of GW sources cannot be determined due to the mass-redshift degeneracy. By cross-correlating GW events with galaxies, one can establish a correspondence between luminosity distance and redshift shells, enabling cosmological inference. In this work, we explore the scientific potential of cross-correlating GW sources detected by third-generation (3G) ground-based GW detectors with the photometric redshift survey of the China Space Station Survey Telescope (CSST). We find that the constraint precisions of the Hubble constant and the matter density parameter can reach 1.04% and 2.04%, respectively. Additionally, we have also constrained the precision of the GW clustering bias parameter. These results highlight the significant potential of the synergy between CSST and 3G ground-based GW detectors in constraining cosmological models and probing GW source formation channels using cross-correlation of dark sirens and galaxies.

We report that moderately eccentric flows around supermassive black holes (SMBHs), formed via either circumnuclear gas accretion or tidal disruption events, generate eccentricity cascades (from $>0.8$ to 0.2 outward), explaining multiwavelength emission and variability in active galactic nuclei (AGNs). The flows’ nonaxisymmetric temperature structure explains nonaxisymmetric dust sublimation fronts, distinct broad emission-line components, and their radial motions. The innermost broad-line region (BLR) links to the SMBH vicinity through highly eccentric streams that produce soft x-rays at periapsis. General relativistic precession further compresses these flows, generating a hard x-ray continuum near the SMBH. Precession of the eccentric flow drives optical/x-ray variability, reproducing the observed x-ray power spectral density and occasional x-ray quasiperiodic eruptions. We thus propose eccentric accretion disks as a physical AGN model that unifies the elusive BLRs and the x-ray corona. This model will enable detailed anatomy of AGNs and maximize their potential as cosmological standard candles.

It is known that about 60% of all Higgs bosons produced at the CERN-LHC decay into a pair of bottom quarks. Bottoms quickly hadronize, in most cases, into bottom-flavored (B) hadrons before they decay. Therefore, the study of scaled-energy distribution of B mesons in the decay process $H\to B+\mathrm{Jets}$ can be considered as a channel to search for the Higgs characteristics. In all previous studies, authors have ignored the mass effect of b quarks as well as B mesons by working in the massless scheme. In this work we, for the first time, study the mass effect of b quarks as well as produced mesons on the scaled-energy ($x_B$) distribution of B mesons by working in the massive scheme or general-mass variable-flavor-number scheme. We find that the meson mass is responsible for a significant enhancement of partial decay width in the low-$x_B$ region while the b quark mass leads to an enhancement of the partial decay rate in the peak region and above.

Primordial black holes (PBHs) are able to produce light dark matter (DM) particles via Hawking radiation, and yield a flux of boosted DM that can be probed at underground DM direct detection experiments. We analyze both galactic and extragalactic contributions to the differential flux of light DM from PBH evaporation, and then compute the expected event rate from PBH boosted DM scattering off electrons or nuclei after taking into account the attenuation effect. Using recent data from DM direct detection experiments XENONnT, PandaX-4T, and LZ, we set constraints on both DM-electron and DM-nucleus scattering cross sections, as well as the fraction of DM composed of PBHs $f_{\mathrm{PBH}}$ for $9\times {10}^{14}-1\times {10}^{16}\mathrm{g}$ PBHs that are not fully evaporated today. We also investigate the spectral evolution induced by Hawking evaporation throughout the evaporation and postevaporation regimes. The constraints on the PBH mass are then extended into the $1\times {10}^{13}-6\times {10}^{14}\mathrm{g}$ window for fully evaporated PBHs.

We investigate gravitational wave signals in a nonsupersymmetric grand unified model where the group $SO(10)$ is broken in two steps to the Standard Model gauge group. We calculate the analytical form of the one-loop effective potential responsible for the first step of symmetry breaking and show that it can lead to a first-order phase transition with gravitational wave production. We also determine the gravitational wave background produced by the primordial plasma of relativistic particles. The present experimental sensitivity is still far from the expected signals but could be in reach of novel detector concepts.

In recent years, numerous experiments have been proposed and conducted to search for ultralight bosonic dark matter (ULBDM). Signals from ULBDM in such experiments are characterized by extremely narrow spectral widths. A near-optimal detection strategy is to divide the data based on the signal coherence time and sum the power across these segments. However, the signal coherence time can extend beyond a day, making it challenging to construct contiguous segments of such a duration due to detector instabilities. In this work, we present a novel detection statistic that can coherently extract ULBDM signals from segments of arbitrary durations. Our detection statistic, which we refer to as coherent SNR, is a weighed sum of data correlations, whose weights are determined by the expected signal correlations. We demonstrate that coherent SNR achieves sensitivity independent of segment duration and surpasses the performance of the conventional incoherent-sum approach, through analytical arguments and numerical experiments.

With the forthcoming deployment of the IceCube Upgrade, unprecedented statistics of atmospheric neutrinos in the energy range (1–100) GeV will become available, providing a valuable opportunity to probe physics beyond the Standard Model in the neutrino sector. In this study, we calculate the sensitivity of the IceCube Upgrade to sterile neutrinos with mass-squared splittings $\lesssim 1{\mathrm{eV}}^2$. We demonstrate that, particularly due to the (1–10) GeV energy window, ${\nu }_{\mu }-{\nu }_s$ mixing angles as small as $\sim 5°$ can be probed by the IceCube Upgrade for all mass-squared splittings below $1{\mathrm{eV}}^2$. Furthermore, we investigate the potential impact of a sterile neutrino state on the precision determination of standard atmospheric neutrino mixing parameters in the IceCube Upgrade.

In this work, we demonstrate the complete process of using space-based gravitational wave detectors to measure properties of the stochastic gravitational wave background arising from a first-order electroweak phase transition. Based on frequency-domain simulations of the Taiji mission, including instrumental noise and astrophysical foregrounds, we perform parameter inference using both the Fisher information matrix and Bayesian Markov Chain Monte Carlo sampling. We show how the reconstructed spectrum constrains the macroscopic parameters of the phase transition, and further how these constraints map onto the underlying particle-physics parameters in a singlet-extended Standard Model. Our results demonstrate that the Higgs cubic and quartic self-couplings can be significantly constrained using gravitational wave observations, despite limitations arising from parameter degeneracy.

Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for computing the low-lying spectrum of generic quantum Hamiltonians within a projection subspace. The method projects the thermal density matrix onto a subspace spanned by a chosen set of linearly independent states. It is free of Trotter discretization errors and systematically converges to the low-energy states which have finite overlap with the projection subspace as the $\beta$ parameter increases. While most effective for systems without a sign problem, the method also yields information about low-energy spectra when sign problems are present. We illustrate the approach on two problems. For the sign-free case, we compute the first four low-energy levels in the scaling limit of the one-dimensional Ising model with both transverse and longitudinal fields, demonstrating the flow from the conformal limit to the massive $E_8$ quantum field theory. For the sign-problem case, we apply the method to the frustrated Shastry-Sutherland model and benchmark it against exact diagonalization on small lattices. We also present results for larger systems beyond the lattice sizes accessible to exact diagonalization, while limited to small $\beta$ where sign problems occur. Our method provides a general route toward quantum Monte Carlo spectroscopy for lattice Hamiltonians.

We provide a nonperturbative determination of the scheme- and scale-independent low-energy constant ${\ell }_7$, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with $N_{\mathrm{f}}=2+1$ quark flavors. We adopt staggered fermions and extract ${\ell }_7$ from the pion mass splitting by suitably generalizing the method introduced by Frezzotti et al. [Phys. Rev. D 104, 074513 (2021)] for the Wilson discretization. Adopting 12 gauge ensembles with three different values of the pion mass, and four different values of the lattice spacing, we are able to achieve controlled extrapolations toward the continuum, infinite volume, and chiral limits. Our final result ${\ell }_7\times {10}^3=2.79(58{)}_{\mathrm{stat}}(19{)}_{\mathrm{syst}}=2.79(61{)}_{\mathrm{tot}}$ agrees with and substantially improves on previous determinations.

The Born-Oppenheimer approximation is widely used to investigate the properties of hydrogenlike systems and doubly heavy hadrons. However, the extent to which this approximation captures the features of such systems within potential models remains an open question. In this work, we adopt the results obtained with the Gaussian expansion method as a benchmark to assess the validity of the Born-Oppenheimer approximation within potential models for hadronic systems. We also investigate the dependence of the Born-Oppenheimer approximation results on the choice of trial wave functions. A comprehensive study of the Born-Oppenheimer approximation is carried out by performing calculations using Slater-type functions and Gaussian-type functions as trial wave functions, and by comparing the resulting predictions with those obtained from the Gaussian expansion method. We find that the calculations performed within the Born-Oppenheimer approximation are close to those obtained with the Gaussian expansion method when the heavy-quark mass is relatively small. However, as the heavy-quark mass increases, calculations employing Slater-type functions yield larger values than those from the Gaussian expansion method, whereas those using Gaussian-type functions lead to smaller ones. The use of Slater-type functions generally leads to an enhanced binding energy. The underestimation observed in Born-Oppenheimer approximation calculations with Gaussian-type functions primarily stems from the neglect of nonadiabatic corrections. This comparative study provides deeper insight into the structure of doubly heavy hadrons and helps clarify the applicability and limitations of the Born-Oppenheimer treatment within potential models.

The dynamics of a spinning colored particle in a background non-Abelian Yang-Mills field is of broad interest in many areas of physics. A physically important application arises in relativistic heavy-ion collisions, where hard probes such as heavy quarks and jets propagate through the strong early-time classical color fields collectively referred to as the glasma. The standard framework for describing the classical dynamics of colored particles in a background Yang-Mills field is provided by the Wong equations, but it does not incorporate spin degrees of freedom. Although several extensions of the Wong equations have been proposed to include spin, they generally fail to satisfy all the necessary requirements simultaneously, such as Lorentz covariance, allowance for an arbitrary chromomagnetic moment, and preservation of the required physical constraints. In this work, we extend the framework of a relativistic classical spinning particle in an electromagnetic field to describe spin-$1/2$ quarks propagating in a generic background non-Abelian Yang-Mills field. By systematically applying the Dirac-Bergmann algorithm, we derive a self-consistent set of equations of motion for the particle’s coordinates, momenta, spin, and color charge that satisfies all these requirements. This formalism provides a more complete and physically consistent description of spinning colored particles in background Yang-Mills fields and offers a suitable framework for studying momentum diffusion and spin polarization phenomena of hard probes in heavy-ion collisions, particularly in the glasma.

The IceCube Upgrade is an extension of the existing IceCube Neutrino Observatory and will be deployed in the 2025–2026 austral summer. It will significantly improve the sensitivity of the detector to atmospheric neutrino oscillations. The existing 86-string IceCube array contains a dense in-fill known as DeepCore which is optimized to measure neutrinos with energies down to a few GeV. The IceCube Upgrade will consist of seven new densely instrumented strings placed within the DeepCore volume to further enhance the performance in the GeV energy range. The additional strings will feature new optical modules, each containing multiple photomultiplier tubes (PMTs), in contrast to the existing modules that each contain a single PMT. This will more than triple the number of PMT channels with respect to the current IceCube configuration, allowing for improved detection efficiency and reconstruction performance at GeV energies. We describe necessary updates to simulation, event selection, and reconstruction to accommodate the higher data rates observed by the upgraded detector and the addition of multi-PMT modules. We determine the expected sensitivity of the IceCube Upgrade to the atmospheric neutrino oscillation parameters ${\sin }^2{\theta }_{23}$ and $\mathrm{\Delta }{m}_{32}^2$, the appearance of tau neutrinos and the neutrino mass ordering. The IceCube Upgrade will provide neutrino oscillation measurements that are of similar precision to those from accelerator experiments, while providing complementarity by probing higher energies and longer baselines, and with different sources of systematic uncertainties.

This paper investigates the fundamental issue of triangulation dependence in spinfoam quantum gravity. It introduces a novel framework, named spinfoam stack, to systematically sum spinfoam amplitudes over an infinite class of 2-complexes. These complexes are generated by stacking an arbitrary number of faces upon a simpler root complex. The central result is obtained by analyzing the amplitude of spinfoam stack in the limit where an upper cutoff on the area of internal faces is taken to infinity. In this limit, the amplitude as an integral localizes via a stationary phase mechanism onto a critical manifold. This manifold is shown to be the space of SU(2) flat connections on the underlying complex. This localization effectively reduces the bulk dynamics from a theory of quantum geometry to a topological theory akin to SU(2) BF theory. For spinfoams on topologically trivial manifolds, this result has a powerful consequence: the spinfoam stack amplitude factorizes into a triangulation-dependent normalization factor and a finite part that depends only on the boundary data. Renormalizing the amplitude yields a finite result that is manifestly independent of the bulk structure of the 2-complex. This provides a concrete realization of triangulation independence in a well-defined limit, suggesting the possibility of a nontrivial fixed point of quantum gravity existing within the spinfoam formalism.