We propose a solution to the supersymmetry (SUSY) $\mu$ problem within the framework of modular flavor symmetry. The explicit $\mu$ term is prohibited by modular symmetry, and an effective $\mu$ term is regenerated following the stabilization of the modulus field. We examine the stabilization mechanism of a single modulus field with the presence of SUSY breaking contributions described by the nonlinear SUSY realization scheme involving a nilpotent Goldstino ${\mathbf{X}}_{nl}$ superfield. A natural small ${\mu }_{\mathrm{eff}}$, significantly smaller than the SUSY scale, can result from either the expansion of typical modular forms using a small deviation parameter near the fixed point $\omega$, or from the combined effects of suppression by powers of $q^{1/24}$ [or $(2\Im \tau {)}^{-1}$] along with the asymptotic suppression behavior of typical modular forms away from the fixed point $i\infty$, taking the form of appropriate power of the tiny deviation parameter. A natural small ${\mu }_{\mathrm{eff}}$ can also be achieved by a weightonlike mechanism for $H_u{H}_d$ bilinear.

To investigate the three-dimensional quantum electrodynamics in the radial quantization on the lattice, the lattice action is constructed and the free limit is studied on $S^2\times \mathbb{R}$. With the overlap fermion, it is numerically verified that the important symmetries of the theory can be realized on the lattice. The analytic correlators are derived and compared to the lattice results, which agree including the overall normalization. The $O(a^2)$ scaling is confirmed toward the analytic value in the continuum limit, and the number of reproduced excited states is estimated heuristically for the first few refinement levels. Our study helps us identify the features of the theory that we can study on the icosahedral lattice without fine-tuning.

We perform a global QCD analysis of the pion electromagnetic form factor (FF) data from pion electroproduction and elastic pion scattering to extract the valence pion generalized parton distributions (GPDs) at zero skewness. The analysis uses three different sets of pion parton distribution functions (PDFs), namely, xFitter, JAM21, and MAP23, to construct the GPD ansatz. Through a ${\chi }^2$ minimization and a careful parametrization scan, we determine the profile function parameters and find that only two parameters are sufficient to describe the data. The extracted valence pion GPDs from different analyses have similar $x$-dependence, with minor differences at small momentum transfer. The resulting theoretical predictions for the pion electromagnetic FF and its squared magnitude show good agreement with experimental measurements. Among the three analyses, the one using the MAP23 PDFs provides the best overall fit and is adopted as the final GPD set. Our results offer a consistent determination of the valence pion GPDs, indicating a minor impact of the choice of pion PDFs. The present study provides a solid foundation for future investigations of pion structure, including its charge radius, tomography, and mechanical properties.

Extending our study of the vector meson-nucleon scattering lengths, we are focusing on the $\rho$-meson case using recent CLAS threshold data for the reaction $\gamma p\to \rho p$ within the meson–baryon reaction model. The total ${\sigma }_t(\gamma p\to \rho p)$ and ${\sigma }_t(\gamma p\to \omega p)$ cross sections are close to the momentum of the vector meson in CM $q=0.2\mathrm{GeV}/\mathrm{c}$. Then the $\rho p$ photoproduction cross section grows rapidly. Our result for $\rho N$ scattering length is a factor of 4 smaller than the size of the hadron and the phenomenological determination of the $\omega$ nucleon scattering length using threshold photoproduction cross sections. The observed difference between $\rho N$ and $\omega N$ scattering lengths is of interest for further understanding within hadron structure theory.

We search for a possible ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Sigma }}}_c$ bound state, denoted as $H_c^{\pm }$, via the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}$ process for the first time. This analysis utilizes 207.8 and $159.3{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data at the center-of-mass energies of 4918.02 and 4950.93 MeV, respectively, collected with the BESIII detector at the BEPCII collider. No statistically significant signal is observed. The upper limits of the product of Born cross section and branching fraction $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{H}_c^{-}+\mathrm{c}.\mathrm{c}.)\times \mathcal{B}(H_c^{-}\to {\pi }^{-}{\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-})$ at a 90% confidence level are reported at each energy point and for various $H_c$ mass hypotheses (4715, 4720, 4725, 4730, and $4735\mathrm{MeV}/c^2$) and widths (5, 10, or 20 MeV), with the upper limits ranging from 1.1 pb to 6.4 pb.

There is a growing interest in investigating top-quark systems using tools from quantum information theory. A key peculiarity of the top quark is that it decays before hadronization or spin decorrelation occurs, thereby preserving its spin information. This unique property enables direct access to spin correlations, making the top quark an ideal candidate for probing fundamental quantum correlations in high-energy physics processes. A wide range of concepts from quantum information theory, such as entanglement, Bell nonlocality, quantum steering, quantum discord, and fidelity, have been investigated in this context. Several of these measures have been employed as diagnostic tools to test the Standard Model and to search for possible signatures of physics beyond. However, the nonlocal advantage of quantum coherence (NAQC) has remained largely unexplored in this context. In this work, we present a detailed investigation of the NAQC in top quark pair production. We employ two complementary NAQC measures based on the $l_1$ norm and the relative entropy of coherence. We also study the effect of angular averaging on these measures and assess the sensitivity of current LHC spin-correlation measurements to NAQC. Our findings reveal rich coherence structures and highlight NAQC as potentially a novel and complementary quantum signature in high-energy physics systems.

We explore phase structures and hadron mass spectra in cold and dense two-color quantum chromodynamics (QCD) with $2+2$ flavors where the sign problem disappears. We particularly focus on $U(1)$ axial anomaly effects. We employ an $N_f=2+2$ linear sigma model based on the $SU(8)$ Pauli-Gürsey symmetry to describe negative-parity as well as positive-parity hadrons, for which low-energy excitations are appropriately described particularly in the baryon superfluid phase with light diquark condensates. As a result, the strange chiral condensate is found to be enhanced in the superfluid phase owing to the flavor-mixing structure of $U(1)$ axial anomaly effects. We also confirm this enhancement by means of the Nambu–Jona-Lasinio model. Besides, our present analysis predicts the existence of a novel superfluid phase where heavy diquarks condense in dense regime. The topological susceptibility with $2+2$ flavors from the viewpoints of the anomaly effects and chiral-symmetry restoration is investigated. Furthermore, we derive a complete inverse mass hierarchy for negative-parity diquarks with sufficient anomaly effects. Our findings are expected to provide future lattice simulations with useful information on flavor-symmetry violation from the $U(1)$ axial anomaly aspects in cold and dense two-color QCD medium.

We consider mixed strong-electroweak corrections to Higgs production via gluon fusion, in which the Higgs boson couples to the top quark. Using the method of differential equations, we compute all of the master integrals that contribute to this process at two loops through $\mathcal{O}({ϵ}^2)$ in the dimensional regularization parameter $ϵ=(d-4)/2$, keeping full analytic dependence on the top quark, Higgs, $W$, and $Z$ boson masses. We present the results for these master integrals in terms of iterated integrals whose kernels depend on elliptic curves.

Based on a sample of $(10.087\pm 0.044)\times {10}^{9}J/\psi$ events collected by the BESIII detector at the BEPCII collider, we perform the first search for the lepton number violating decay $\eta \to {\pi }^{+}{\pi }^{+}{e}^{-}{e}^{-}+\mathrm{c}.\mathrm{c}$. No signal is found, and an upper limit on the branching fraction of $\eta \to {\pi }^{+}{\pi }^{+}{e}^{-}{e}^{-}+\mathrm{c}.\mathrm{c}.$ is set to be $4.6\times {10}^{-6}$ at the 90% confidence level.

In general relativity and gauge field theory, one often encounters a claim, which may be called the boundary problem, according to which “boundaries break diffeomorphism and gauge symmetries”. We argue that this statement has the same conceptual structure as the hole argument, and is thus likewise defused by the point-coincidence argument: We show that the boundary problem dissolves once it is understood that a physical region, thus its boundary, is relationally and invariantly defined. This insight can be technically implemented via the dressing field method, a systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories, whereby physical field-theoretical degrees of freedom co-define each other and define, coordinatize, the physical spacetime. We illustrate our claim with a simple application to the case of general relativity.

The Klein-Gordon and Dirac equation for a massive charged field in a uniform electric field has a symmetry of two-dimensional global de Sitter (dS) and anti–de Sitter (AdS) space. In the in-out formalism the mean numbers of spinors (spin-$1/2$ fermions) and scalars (spin-0 bosons) spontaneously produced by the uniform electric field are exactly found from the Bogoliubov relations both in the global and planar coordinates of (A)${\text{dS}}_2$ space. We show that the uniform electric field enhances the production of charged spinor and scalar pairs in the planar and global dS space while the AdS space reduces the pair production in which weak electric fields below the Breitenlohner-Freedman bound prohibits pair production. The leading Boltzmann factor in dS space can be written as the Gibbons-Hawking radiation or Schwinger effect enhanced by e-folding factors less than one that give the QED effect or the curvature effect. We observe that ${\mathrm{dS}}_2$ and ${\mathrm{AdS}}_2$ spaces are connected by QED, such as a reciprocal relation between the mean number of spinors and scalars provided that the spacetime curvature is analytically continued. The leading behavior of the mean numbers for spinors and scalars is explained as a residue sum of contour integrals of the frequency or momentum in the phase-integral formulation.

Critical collapse is a well-studied subject for a variety of self-gravitating matter. One of the most intensively examined models is that of perfect fluids, which have been used extensively to describe compact objects such as stars, as well as being of cosmological interest. However, neutron stars are believed to possess an elastic crust, thus departing from a perfect fluid body, and critical collapse with elastic materials is an entirely unexplored topic. In this work, we employ a scale-invariant elastic matter model to study self-similar collapse with elasticity. As with perfect fluid models, we show that including elasticity allows for continuous self-similar configurations, which we determine numerically by solving the associated boundary value problem. The set of solutions is discrete and we focus on the fundamental mode, but also present some results for overtones. Similarly to the perfect fluid case, the existence of a sonic point plays a central role. We find that the addition of elasticity, by either increasing the shear index $\mathrm{s}$ or decreasing the Poisson ratio $\nu$, leads to an increase in compressibility and can yield negative radial pressures around the sonic point. Simultaneously, the elastic longitudinal wave speed ceases to be constant, while the two possible transverse wave speeds grow further apart. The departure from the perfect fluid case can be so dramatic as to generate a second sonic point, which does not seem to be regular. This, in turn, imposes bounds on the elasticity parameters of the material. This study represents the first step in the analysis of critical collapse with elastic materials.

Gravitational waves (GWs) emanated by stellar-mass compact binary coalescences (CBCs), and lensed by galaxy- or cluster-scale lenses, will produce two or more copies of the GW signal. In the geometric-optics limit, these signals will have similar phase evolution but differing amplitudes. Such lensing signatures are expected to be detected by the end of the LIGO-Virgo-KAGRA Collaboration’s fifth observing run. In this work, we propose a novel ${\chi }_{\mathrm{lens}}^2$ statistic to segregate pairs of detected GW events as lensed or unlensed, using templates typically used in GW searches. The statistic is an application of the generalized ${\chi }^2$ discriminator, tailored to probe the similarity (or lack thereof) between the phase evolutions of two CBC signals. We assess the performance of ${\chi }_{\mathrm{lens}}^2$ on an in-part astrophysically motivated dataset of lensed and unlensed CBCs detectable in the fourth observing run, assuming a single LIGO-like detector at design sensitivity. Our results show that ${\chi }_{\mathrm{lens}}^2$ correctly identifies lensed events with efficiencies comparable to existing Bayesian and machine learning methods, while being orders of magnitude faster to evaluate than Bayesian methods. Moreover, the statistical properties of ${\chi }_{\mathrm{lens}}^2$ in stationary Gaussian noise are fully understood, in contrast to machine learning methods. ${\chi }_{\mathrm{lens}}^2$ can, therefore, be used to rapidly and accurately weed out the vast majority of unlensed candidate pairs and identify lensed pairs.

Gravitational models with nonminimal couplings involving the trace of the energy-momentum tensor have become increasingly popular. The idea of coupling the trace of the matter tensor to the geometry can be applied to various matter models, including relativistic perfect fluids. However, it is well known that the variational formulation of perfect fluids involves some technicalities. We carefully derive the field equations including the trace coupling of a perfect fluid using two different approaches, namely, that given by Brown using Lagrange multipliers and that given by Schutz using velocity potentials. We show that previous results involving such trace couplings do not match the results presented here. We demonstrate that our fluid’s equations of motion are consistent with the gravitational field equations. Moreover, we present a simple on-shell argument which further supports the correctness of our results. Our work implies that a vast amount of the $f(R,T)$ literature using perfect fluids needs to be revisited.

In this work, we develop a generalized perturbative framework for gravitational shadows in static, spherically symmetric spacetimes. Building upon the recent two-parameter perturbative framework of K. Kobialko et al. [Perturbation theory for gravitational shadows in static spherically symmetric spacetimes, Phys. Rev. D 111, 044071 (2025).], this work extends the expansion in particle energy and metric deviation to encompass arbitrary, simultaneous deformations of all metric functions. By relaxing the common restriction of a fixed area radius $(\beta (r)=r^2)$, our formalism applies to a significantly broader class of alternative gravity theories and exotic compact objects. We derive analytical formulas for the massive shadow radius up to the second order in the deformation parameter, explicitly revealing the phenomenological signatures that arise from the coupling between temporal and spatial metric perturbations. The key result is that the distinct energy dependence of the massive shadow provides a powerful method to disentangle these different types of geometric deformations, breaking observational degeneracies inherent in the photon shadow alone. We demonstrate this principle with applications to traversable wormholes and canonical scalar-tensor solutions, showing how each produces a unique, distinguishable energy-dependent fingerprint. This generalized framework provides a robust, theory-agnostic tool for testing strong-field gravity. It offers a clear methodology for reconstructing metric parameters from potential multimessenger observations of massive particle shadows.

The ringdown phase of the binary black hole (BBH) merger provides a clean and direct probe of strong-field gravity and tests of the nature of black holes. The quasinormal mode frequencies in modified gravity theories, as well as their amplitudes and phases, might deviate from the Kerr ones in general relativity. Charged black holes (BHs) in Einstein-Maxwell theory provide an excellent example of a beyond-Kerr solution with direct astrophysical and fundamental physics applications. In this work, we extract the ringdown mode amplitudes and phases for charged BBH mergers based on fully general relativistic simulations with charge-to-mass ratio up to 0.3. Our results suggest that, even though the inspiral phase of charged BBHs can be significantly accelerated or decelerated, the ringdown mode excitation only changes mildly. We further explore the charge detectability with the ringdown-only signal for the Einstein Telescope and Cosmic Explorer. We find that previous studies may have overestimated the charge detectability and including higher modes in charged waveforms is necessary for future ringdown analysis. This constitutes the first such analysis based on waveforms generated by numerical relativity simulations of charged BHs in full Einstein-Maxwell theory.

Schwarzschild black-hole interiors, bounded by event horizons and terminated by spacelike singularities, are regions where all physical observers are inevitably destroyed. In the geometric optics approximation, waves follow null geodesics to the singularity. However, outside the geometric optics regime, the behavior of wave propagation can be rich and nuanced, even in such extreme habitats. In this work, we show that axial gravitational perturbations in the interior of a Schwarzschild black hole can form overdamped (nonoscillatory) quasibound states that decay before reaching the singularity. Using Kruskal-Szekeres coordinates to avoid coordinate ambiguities, we identify these modes and analyze their eigenfunctions. Contrary to earlier claims, we find that the Regge-Wheeler master function of these modes have nonzero amplitude at the future event horizon but decay before interacting with the singularity. We consider observations of the modes along timelike geodesics. This work suggests that certain gravitational fluctuations can hover transiently within the black-hole interior, challenging common assumptions about wave behavior in uncharted and extreme regions of spacetime.

The formation of primordial black holes or other dark matter relics from amplified density fluctuations in the early Universe may also generate scalar-induced gravitational waves (GW), carrying vital information about the primordial power spectrum and the early expansion history of our Universe. We present a Bayesian approach aimed at reconstructing both the shape of the scalar power spectrum and the Universe’s equation of state from GW observations, using interpolating splines to flexibly capture features in the GW data. The optimal number of spline nodes is chosen via Bayesian evidence, aiming at balancing complexity of the model and the fidelity of the reconstruction. We test our method using both representative mock data and recent pulsar timing array measurements, demonstrating that it can accurately reconstruct the curvature power spectrum as well as the underlying equation of state, if different from radiation.

We present parameter sets corresponding to new underlying event tunes for the herwig7.3 Monte Carlo event generator. The existing herwig tunes are in good agreement with LHC data, however, they are not typically designed for center-of-mass energies below $\sqrt{s}=300\mathrm{GeV}$. The tunes presented in this study can describe midrapidity data collected at the nominal RHIC energy of $\sqrt{s}=200\mathrm{GeV}$ as well as higher center-of-mass energies utilized by experiments at the LHC and Tevatron. The base “New Haven” tune is developed by fitting minimum-bias simulations of proton-proton ($pp$) collisions to midrapidity identified hadron and jet data from the STAR experiment. The “Nashville” tune includes a separate set of parameters developed by tuning to Tevatron proton-antiproton ($p\overline{p}$) data at $\sqrt{s}=300$, 900 and 1960 GeV from CDF, and LHC $pp$ measurements from CMS at $\sqrt{s}=7\mathrm{TeV}$, in addition to the STAR measurements. Both new tunes demonstrate significant improvements over the recommended default tune currently included in the latest version of herwig for minimum bias production. As such, we advocate using these tunes for future simulation studies at midrapidity by experimental collaborations at RHIC (STAR and sPHENIX) and the LHC (ALICE, ATLAS, and CMS).