We revisit the traditional type I, II, and III seesaw mechanisms in the presence of a complex scalar field charged under a global $U(1)$ symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axionlike particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyze two matching orders: first removing the radial mode and then the seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode, and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured nonunitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number-breaking scale, of the order of 1–10 TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is, thus, falsifiable even when the new states lie far beyond experimental reach.

The Standard Model prediction for the rare $K_L\to {\mu }^{+}{\mu }^{-}$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$, $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1/m_c^2$, are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancellation, this three-flavor theory contains additional low-energy constants that depend on $m_c$. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators, introduced in [Extraction of spectral densities from lattice correlators, Phys. Rev. D 99, 094508 (2019).], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinize the performance and systematics of this approach either as a stand-alone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.

We investigate the pion gravitational form factors (GFFs) at intermediate and large momentum transfer within the framework of QCD factorization. Our analysis centers on the non-Abelian $TJJ$ correlator, which couples the local QCD energy-momentum tensor to two external gluon fields and explicitly encodes the perturbative effects of the trace anomaly. We demonstrate how this quantum anomaly induces a scalar, dilatonlike contribution to the hard-scattering kernel. To ensure field-theoretic consistency, a careful separation of the quark and gluon sectors is performed, accounting for the modifications introduced by gauge-fixing terms and Slavnov-Taylor identities on the off-shell gluonic structure. To obtain realistic phenomenological predictions and regulate soft-gluon endpoint divergences in the hard kernel, we implement the Sudakov resummation framework coupled with a Gaussian model for the pion’s transverse-momentum-dependent wave function. We show that the resulting anomaly-induced corrections significantly modify the behavior of the pion GFFs at large momentum transfer, leaving a unique imprint on the trace sector and the $D$-term.

We investigate the dynamics and mass spectra of charged pseudoscalar (${\pi }^{+}$) and vector (${\rho }^{+}$) mesons in a background magnetic field at finite temperature using the two-flavor Nambu-Jona–Lasinio model. By employing a quark propagator that isolates the Schwinger phase from its Landau level expansion, we formulate an analytically controlled phase-space framework utilizing the Wigner-Weyl transform and the Moyal star product. This approach enables the algebraic diagonalization of the Bethe-Salpeter equations for composite states with asymmetric fractional constituent charges. For the pseudoscalar channel, we analytically verify the exact cancellation between the dynamical random phase approximation spatial sum rules and the vacuum gap equation. This identity preserves the generalized Goldstone theorem, causing the ${\pi }^{+}$ pole mass to track the kinematic zero-point energy drift at order of $eB$. In the vector channel, our full phase-space evaluation reveals that the Zeeman spin-splitting emerges dynamically from microscopic threshold truncations governed by the chiral Dirac algebra. Notably, we find that the tachyonic instability of the spin-aligned ${\rho }^{+}$ state is quenched. The magnetic catalysis of the chiral condensate drives the continuum threshold ($2M$) upwards, overtaking the Zeeman attraction and preventing vector meson condensation within this mean-field framework. Furthermore, finite-temperature evaluations show a monotonic thermal suppression of the meson masses driven by Pauli blocking, yet all modes remain bound without undergoing Mott dissociation prior to chiral symmetry restoration.

We present a dispersive amplitude analysis of the low-energy ${\pi }^0{\pi }^0$ system in the radiative decay $J/\psi \to \gamma {\pi }^0{\pi }^0$, using the mass-independent BESIII $0^{++}$ and $2^{++}$ intensities, the total spectrum, and the measured $0^{++}-2^{++}E1$ phase difference. The isoscalar $S$-wave is described by a coupled-channel $\pi \pi /K\overline{K}$ Muskhelishvili–Omnès representation, which implements the strong final-state interactions associated with the $f_0(500)$ and $f_0(980)$. The $D$-wave is treated with a single-channel $\pi \pi$ Muskhelishvili-Omnès representation, where we identify all kinematic constraints of helicity amplitudes before transforming them to the experimental $E1$, $M2$, and $E3$ multipoles. Smooth short-distance production of a pseudoscalar-meson pair is encoded in subtraction polynomials, while left-hand-cut effects are estimated and found to be numerically subleading. We identify the negative solution of the BESIII $0^{++}-2^{++}E1$ phase ambiguity, after using the modulo-$\pi$ freedom of production amplitudes, as the phase solution compatible with unitarity constraints, showing that the measured phase information can be accommodated with the Omnès phase motion without requiring large additional phases. By normalizing the BESIII intensities with the extracted branching fraction, we fix the absolute scale of the fitted amplitudes, making them suitable as input for future dispersive studies of two-pion contributions to gravitational form factors.

This study investigates photon entanglement generated from parapositronium decay by analyzing azimuthal correlations after the double Compton scattering with stationary electrons. We introduce a normalized correlation observable ${\mathcal{O}}_1=\cos (2{\varphi }_1-2{\varphi }_2)/C_1$ to witness entanglement. In the absence of decoherence, $⟨{\mathcal{O}}_1⟩=-1$, corresponding to a maximally entangled Bell state. With decoherence parametrized by $\rho$, the expectation becomes $-(1-\rho )$, allowing direct experimental quantification of coherence loss. A prior symmetry analysis of the Compton scattering process within the quantum field theory (QFT) is provided, which establishes the mirror-symmetric nature of the single-photon angular distribution. We further examine a local hidden-variable theory (LHVT) under the angular-momentum conservation and the rotation invariance. Imposing the mirror symmetry with respect to the plane defined by the photon spin and momentum leads to a non-negative LHVT prediction for $⟨{\sin }^2{\theta }_1{\sin }^2{\theta }_2\cos (2{\varphi }_1-2{\varphi }_2)⟩$, contradicting the negative QFT prediction value for any $\rho <1$. Thus, mirror symmetry serves as a novel criterion to exclude LHVT descriptions of the entangled state, whereas without preserving this symmetry, LHVTs can reproduce the correlations.

We study holographic defect conformal field theories which are dual to probe branes with bottom-up methods. First, we determine the embedding of codimension-1 interface branes in anti–de Sitter space. Then, we compute defect one- and two-point functions of heavy scalar operators at strong coupling. We use geodesic approximations to compute reflected two-point functions in two ways as well as ambient and defect-channel two-point functions. In appropriate limits, our results agree with the operator product expansion and the boundary operator expansion.

Classical causal set theory models spacetime causality by locally finite partial orders. Because partial orders are antisymmetric, they cannot represent distinct elements that are mutually causally related, as would occur in a discrete analog of a chronology-violating region. We develop a locally finite discrete framework that allows closed causal loops and yields a locally finite partial order upon identifying mutually related elements. Each class of mutually related elements is collapsed to one point in the induced poset, and its cardinality is assigned as a finite weight to the corresponding point. Within this setting we define maximum causal time using simple finite paths and prove an equidistance characterization: members of one chronology-violating class have the same discrete proper-time distance from any event in their common past or future, with a finite correction for the closed path inside the class. We also study the special case in which the relation is generated by iterating a single self-map $f:X\to X$; cycles of $f$ then give explicit finite closed causal loops. Finally, we define two finite counting invariants: the proportion of elements in chronology-violating classes and the normalized mean of $|I(x,x)|-1$. We study the mathematical properties of these discrete causal structures; no equations of motion or probabilities for their occurrence are specified. The construction does not assert a continuum-discrete correspondence in the chronology-violating case, and ordinary causets are recovered when all equivalence classes are singletons.

Although asymptotically flat black holes generically lack thermodynamic phase transitions, we show that curvature-induced scalarization of electrically charged black holes in Einstein-Maxwell-scalar-Gauss-Bonnet theory provides a natural setting for nontrivial thermodynamic behavior, without invoking external confining mechanisms or an extended thermodynamic formalism. Working within the canonical ensemble and employing the Euclidean approach, we identify the coexistence of locally stable scalarized and Reissner-Nordström thermal states, which promotes free-energy crossings to bona fide phase transitions between equilibrium phases. For weak coupling, a second-order phase transition coincides with the second bifurcation point, at which the scalarized branch reconnects with the Reissner-Nordström branch and scalar hair is spontaneously shed. As the coupling strength increases, this transition becomes zeroth order, the scalarized branch shrinks, and a fishlike structure develops in its Helmholtz free energy, rendering locally stable thermal states partially metastable, and yielding up to three phase transitions. In the strong-coupling limit, the scalarized branch reduces to a Schwarzschild-like solution, and the Reissner-Nordström phase ultimately emerges as the sole thermodynamically preferred configuration.

In the Kerr-Schild double copy, static and spherically symmetric black hole solutions of general relativity are mapped to purely electric solutions of Maxwell’s theory in flat spacetime. We demonstrate that, for these configurations, the thermodynamic Smarr formula is structurally identical to the single-copy Gauss’s law. Extending this to asymptotically anti–de Sitter spacetimes, we prove that the thermodynamic pressure-volume term naturally emerges from a gauge-theoretic background subtraction. This relationship establishes a novel connection between the classical double copy and black hole thermodynamics.

We use numerical relativity to study the scalar field evolution sourced by hyperbolic encounters of black holes in quadratic scalar Gauss-Bonnet gravity. In this theory, single black holes are known to acquire a scalar hair through scalarization for certain values of their mass and spin. We work in the decoupling limit and evolve the scalar field on top of a background metric. Seeding binary black holes with an initial scalar field, we find that configurations which initially cannot sustain a scalar hair temporarily scalarize during an encounter and thereby exhibit dynamical scalarization. This is possible for both positive and negative couplings between the scalar field and curvature in black hole binaries with zero and nonzero initial spins, respectively. Furthermore, we find that the change in the spin magnitude of black holes during certain hyperbolic encounters can lead to permanent spin-induced scalarization (or descalarization), which we refer to as spin-up (de)scalarization.

Gravity-induced entanglement (GIE) experiments have been proposed as a theory-independent test of the quantum nature of gravity, on the strength of several no-go theorems concluding that GIE detection implies the gravitational interaction is either nonlocal or nonclassical. This is in apparent tension with a growing number of papers claiming that theories with a classical gravitational field do predict GIE. This article resolves the tension by reviewing the assumptions of the no-go theorems and highlighting the information-theoretic, rather than spatiotemporal, nature of the locality assumption. This makes violating locality not particularly problematic. Indeed, quantum electrodynamics and perturbative quantum gravity are nonlocal in the sense of the theorems. Given that GIE detection is not sufficient to rule out a classical gravitational field, the quantitative comparison of theoretical predictions in the low-energy quantum gravity regime will allow us to test whether the gravitational field is quantum or classical.

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective quantum-gravity solutions that admit a Birkhoff-type theorem, rendering them unique within the considered framework. We show that such inner-extremal horizon configurations exist only for a finely tuned value of the mass determined by the parameters of the theory. Building on this construction, together with the corresponding nondegenerate regular black hole solutions, we perform a generic analysis of the mass inflation phenomenon in four-dimensional spacetimes using a colliding null-shell setup near the inner horizon. We identify the conditions under which mass inflation becomes significant and examine how the presence of a minimal length scale affects this behavior, with particular emphasis on the case where such a scale is motivated by loop quantum gravity. Finally, we comment on the stability of these configurations under the null-shell perturbations considered in our analysis.

Recently, a new family of asymptotically flat black-hole solutions endowed with primary scalar hair has been discovered in beyond-Horndeski gravity. We study in detail the quasinormal modes spectra, graybody factors, and Hawking radiation of this class of black holes. We demonstrate that the presence of primary scalar hair leaves characteristic imprints on the ringdown properties and shifts the quasinormal frequencies, inducing overtone rearrangements and the rise of echoes. While the fundamental modes associated with the light ring are affected moderately, higher overtones are highly sensitive to the small near-horizon deformation produced by the scalar field. In certain parameter regimes, the graybody factors exhibit resonant-tunneling behavior, which leads to an oscillatory frequency dependence of the Hawking emission rate. Thus, both black-hole spectroscopy and Hawking radiation may provide complementary and distinctive probes of the beyond-Horndeski gravity. Additionally, we demonstrate that the corresponding naked singularities are quantum mechanically singular, and wave dynamics is ill posed.

The deflection angles of rays diverge logarithmically near outside and inside of a photon sphere in usual strong deflection limits and the rays near the photon sphere could be detected by near-future space observations on black hole shadows. On the other hand, we show that the deflection angles of the rays near the photon sphere at a throat of a $Z_2$-symmetric wormhole, as an example among some commonly used types of wormholes or simple wormholes, which is often studied by the Event Horizon Telescope collaborations, diverge in power law but not logarithmically. This is because the $Z_2$-symmetric wormhole has a marginally unstable photon sphere at the throat and it has neither a common nor simple but special property. We investigate gravitational lensing of the rays nearly outside and inside of the marginally unstable photon sphere at the throat in a class of $Z_2$-symmetric wormholes in the strong deflection limits. We use a numerical method to calculate the deflection angles diverging in power law and we apply it to the commonly used simple wormhole spacetime, a Damour-Solodukhin wormhole spacetime, and a Simpson-Visser black-bounce spacetime. Our numerical results imply universal property of the deflection angle of the rays near the marginally unstable photon sphere on $Z_2$-symmetric wormhole throat in the strong deflection limits as similar to the deflection angles of ray bent by a marginally unstable photon sphere off a throat in the strong deflection limits which have a different power. We also correct the coefficients of power-law divergent terms of the deflection angles of the rays bent nearly outside of the marginally unstable photon sphere at the $Z_2$-symmetric wormhole throat in a semianalytic approach investigated by the author and others.

We present a unified Bayesian assessment of model comparison and dataset consistency for $\mathrm{\Lambda }\mathrm{CDM}$ (cold dark matter plus a cosmological constant) and minimal extensions (neutrino mass, spatial curvature, and constant or evolving dark energy) using cosmic microwave background (CMB), baryon acoustic oscillation (BAO), and type Ia supernova (SN) data. The major results are summarized in the first three figures. We quantify model preference with Bayesian evidence and assess consistency with complementary evidence- and likelihood-based diagnostics applied uniformly across dataset combinations. For the models considered, updated planck processing systematically improves internal CMB consistency (low-$\ell$ versus high-$\ell$, and primary CMB versus CMB lensing). The preference for a closed geometry and an associated “curvature tension” with BAO and/or CMB lensing are largely confined to earlier planck likelihood implementations and weaken substantially when using updated CMB processing and more recent BAO measurements. Apparent evidence for evolving dark energy in $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SN}$ combinations depends sensitively on the specific pairing of CMB and SN likelihoods: plausible alternatives shift inferred tensions by more than $1\sigma$ and can completely reverse the preferred model. Allowing a free neutrino mass tends to absorb residual shifts without introducing new inconsistencies, and we do not find robust evidence for a standalone $\tau$-driven discrepancy once the full likelihood context is accounted for. We conclude that claims of a required update of our standard cosmological model from $\mathrm{\Lambda }\mathrm{CDM}$ to $w_0{w}_a\mathrm{CDM}$ are premature.

Wide-field optical imaging surveys are efficient at identifying galaxy clusters, but optically identified clusters suffer from projection effects—physically unassociated galaxies along the line of sight are often included as cluster members due to distance uncertainties. Previous studies have used spectroscopic follow-up observations of cluster members to quantify projection effects; however, such follow-up efforts cannot keep pace with the rapidly growing cluster samples. On the other hand, spectroscopic surveys designed for large-scale structure studies collect tens of millions of spectra but tend to have sparse spectra in cluster regions. To bridge this gap, we develop a clustering redshift approach that cross-correlates cluster members with sparse, noncluster-targeted spectroscopic galaxy samples. We validate this approach using the Cardinal simulation, recovering the correct spectroscopic redshift distribution and projection effect parameters of cluster members identified by the red-sequence Matched-filter Probabilistic Percolation algorithm. Our approach is insensitive to the selection of the spectroscopic sample and paves the way for calibrating projection effects in the upcoming Legacy Survey of Space and Time clusters using Dark Energy Spectroscopic Instrument and Roman spectroscopic samples.

We investigate nonminimal Higgs inflation in a no-scale-inspired supergravity framework and confront its predictions with the latest cosmic microwave background (CMB) constraints from ACT DR6 and Planck. Working within a shifted hybrid inflation scenario, we construct an effective single-field description in which the grand unified theory Higgs direction serves as the inflaton after stabilization of the orthogonal scalar fields. We show that the inclusion of the leading nonrenormalizable operator in the superpotential induces a controlled deformation of the Starobinsky attractor, allowing the scalar spectral index to be shifted into the range favored by recent ACT and related CMB datasets while maintaining a small tensor-to-scalar ratio, $r\sim {10}^{-3}–{10}^{-2}$. The resulting inflationary dynamics remain theoretically consistent, with controlled supergravity corrections and sub-Planckian inflaton field values. We perform a detailed numerical analysis of the model parameter space, including reheating and nonthermal leptogenesis, and identify regions that simultaneously satisfy current observational constraints and yield a viable postinflationary cosmological history.

The population of binary black hole (BBH) mergers observed by the LIGO-Virgo-KAGRA (LVK) collaboration offers a window into the cosmic evolution of compact binaries and the physical mechanisms that drive their formation. We employ the semianalytic population-synthesis code b-pop to model BBHs assembled through isolated binary evolution and dynamical interactions in young, globular, and nuclear star clusters. Our framework self-consistently incorporates star formation history, metallicity evolution, and single and binary stellar evolution to quantify their impact on the observable properties of the BBH population and on the relative contribution of distinct formation channels. Our models are characterized by a merger rate, $\mathcal{R}=17.5–24.1{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$, broadly consistent with LVK constraints. Moreover, the predicted distributions of primary mass, mass ratio, and effective inspiral spin parameter are compatible with those inferred from current LVK observations. Our primary-mass distribution is dominated by isolated binaries at $m_1\lesssim 20M_{\odot }$, while dynamically assembled first- and higher-generation mergers dominate at larger masses. As a consequence, the subpopulation of mergers with $m_1\gtrsim 45M_{\odot }$ exhibits a nearly flat mass-ratio distribution and distinctive spin properties. We leverage our models to explore how: (i) the fraction of stars in isolated binaries and the fraction of stellar mass bound in clusters regulate the overall merger rate; (ii) common-envelope physics shapes the primary-mass distribution and its redshift evolution; (iii) the inclusion of stellar-collision products enhances the formation of higher-generation mergers; and (iv) the natal spin distribution of stellar-mass black holes influences the effective spin of merging BBHs. Using our models to assess possible origins of selected gravitational waves events, we illustrate how the complexity of the underlying astrophysical processes can hinder the possibility to draw definitive conclusions.