The evaluation of effective potentials is critical for a range of phenomenological applications, including inflation, vacuum stability, and phase transitions. A drawback arises from the gauge dependence of the effective potential. Furthermore, in theories with spontaneous symmetry breaking, the effective potential exhibits infrared (IR) divergences in the limit of vanishing Goldstone masses. By considering the multiplicative anomaly that arises due to nonfactorization of elliptic operators in the Fermi gauge when computing the effective potential at one-loop order, we demonstrate that its gauge independence and IR behavior are improved to the corresponding findings of Landau gauge calculations simultaneously. The latter are straightforwardly and transparently reproduced using an approach that employs the heat kernel technique, thereby providing a shortcut to reflect anomaly-related cancellations from the outset. Our findings generalize to the treatment of the effective potential at finite temperature. In particular, the heat kernel extends gauge independence to any value of the expansion in mass over temperature.

We investigate two-particle scattering and two-particle scattering with a bare basis state using Hamiltonian effective field theory. We analyze the distribution of two-body scattering poles in the momentum and energy planes under relativistic conditions. Compared to the nonrelativistic case, there are significant differences in the distribution of bound state poles and resonance poles in the relativistic case, primarily due to the square root term in the relativistic formula. By considering pure two-particle scattering, we examine the relationship between the form factor and the number of poles. Additionally, we clearly elucidate the effects of attractive and repulsive interactions on the bound state poles and resonance poles. More importantly, we extend our model by including a bare state and explore the poles originating from the bare state or coupled channels through the trajectories of pole positions, as well as the compositeness of bound states.

Scenarios with multiple pseudoscalars are interesting as they usually tend to provide a framework to naturally realize a light axion with a large decay constant which has rich applications in cosmology, especially in the context of inflation and light dark matter physics. On the other hand, from a particle physics perspective, this facilitates a solution to the strong $CP$ problem with a low Peccei-Quinn symmetry breaking scale. One such realization is afforded within the framework of the clockwork mechanism where the axion can have suppressed couplings with the gluons or photons while its companion axionlike particles (ALPs) have relatively unsuppressed couplings, thereby facilitating detectability. We study a minimal clockwork model for the QCD axion invoking a Kim–Shifman–Vainshtein–Zakharov (KSVZ)-like setup and examine the visibility of its unique multi-ALP $(a_n)$ signature at the LHC, the most sensitive channel being $pp\to a_n(+\mathrm{additional}\mathrm{jets})$ followed by $a_n\to \gamma \gamma$. In congruence with the astrophysical and cosmological bounds for the axion, a striking feature emerges for the case of light ALPs $(m\sim \mathcal{O}(10\mathrm{GeV}))$ wherein the mass splittings among the former are so small that the signal profile mimics that of a single broad resonance, or an axion iceberg. The scenario is found to be imminently testable by the end of LHC’s Run 3 phase for an integrated luminosity of $\sim 300{\mathrm{fb}}^{-1}$. A larger average ALP mass, on the other hand, results in multiple closely spaced peaks with a characteristic signal profile, and would be expected to be seen at the forthcoming HL-LHC. Possible additional signals are also listed.

We investigate radiative corrections to electroweak precision observables, specifically the Peskin-Takeuchi parameters $S$, $T$, and $U$, in the $SU(3{)}_C\times SU(3{)}_L\times U(1{)}_X$ model (also known as the 331 model) with $\beta =-\sqrt{3}$. Using the sarah and spheno packages, we compute the mass spectrum and low-energy observables. We show that these parameters place strong constraints on the model, requiring most of the scalar masses to lie in the TeV range or below, and impose indirect bounds on the newly predicted gauge bosons. Furthermore, we demonstrate that the model can accommodate the $W$ boson mass anomaly reported by the CDF Collaboration, should future measurements confirm its persistence.

Through the black hole (BH) superradiance, ultralight bosons can form dense clouds around rotating Kerr BHs. Certain ultralight bosons, such as axions and axionlike particles (promising dark matter candidates), naturally possess self-interactions, and thus may significantly modify the dynamics of the superradiance process. Previous studies on the detection or constraint of ultralight bosons through superradiance have usually neglected the self-interaction effects of bosons. In this work, we investigate the formation and evolution of self-interacting boson clouds in the full Kerr spacetime during BH superradiance. Using numerical methods, we compute the superradiant growth rate of boson clouds with self-interactions around Kerr BHs and quantitatively evaluate how the self-interaction strength of scalar bosons affects the growth rate. We also assess the evolution of the BH’s mass and spin. Our results reveal that, in addition to the superradiance-imposed upper bound on the boson cloud mass, self-interaction of ultralight bosons introduces a new, lower critical mass limit, beyond which the growth rate of the boson cloud approaches zero. This implies that the superradiance process terminates earlier when self-interaction is considered. Furthermore, we explore how self-interaction affects both the oscillation frequency of boson clouds in gravitational atoms and the frequency of gravitational waves (GWs) emitted through cloud annihilation. The anticipated frequency shift might be detectable by the GW observatories. Given that self-interaction substantially alters the evolution of BH superradiance, its effects can significantly relax existing constraints on scalar bosons derived from superradiance. Taking the spin measurements from GW190412 and GW190517 as examples, we discuss the impact of self-interaction on the constraint results in detail.

We present lattice results for the flavor diagonal charges of the proton from the analysis of eight ensembles generated using $2+1+1$-flavors of highly improved staggered quarks by the MILC Collaboration. The calculation includes all the needed connected and disconnected contributions to nucleon three-point function. For extracting matrix elements using fits to the spectral decomposition of these correlation functions, two strategies to remove excited state contributions are employed and compared. To renormalize these charges, the $2+1$-flavor mixing matrix is calculated in the regularization independent symmetric momentum subtraction intermediate scheme on the lattice. The final results are presented in the $\overline{\mathrm{MS}}$ scheme at scale 2 GeV. The axial charges for the proton are $g_A^u=0.781(25)$, $g_A^d=-0.440(39)$, and $g_A^s=-0.055(9)$; the tensor charges are $g_T^u=0.782(28)$, $g_T^d=-0.195(16)$, and $g_T^s=-0.0016(12)$; and the scalar charges are $g_S^u=9.39(88)$, $g_S^d=8.84(93)$, and $g_S^s=0.37(14)$. Results for the neutron are given by the $u\leftrightarrow d$ interchange. Results for the sigma terms are ${\sigma }_{\pi N}{|}_{\text{standard}}=42(6)\mathrm{MeV}$ from a “standard” analysis and ${\sigma }_{\pi N}{|}_{N\pi }=61(6)\mathrm{MeV}$ from an “$N\pi$” analysis that includes the contributions of multihadron $N\pi$ excited states as motivated by chiral perturbation theory. Our preferred value ${\sigma }_{\pi N}{|}_{N\pi }$ is consistent with the phenomenological extraction from $\pi -N$ scattering data. The strangeness content of the proton, for which the standard analysis is appropriate, is ${\sigma }_s{|}_{\text{standard}}=35(13)\mathrm{MeV}$.

A rigidly rotating body in unbounded space is usually considered a pathological system since it leads to faster-than-light velocities and associated breaches of causality. However, numerical results on chiral symmetry breaking in rotating plasmas of interacting fermions reveal surprisingly close correspondence in predictions between the rigorous bounded and formal unbounded approaches. To provide insight into this correlation, we consider the linear sigma model coupled to quarks, undergoing rigid rotation in unbounded Minkowski space-time. Within the mean-field approach, we adopt three consecutive levels of approximation to the ground state of the system that feature uniform (model 1), weakly inhomogeneous (model 2), and fully inhomogeneous (model 3) condensates. Models 1 and 2 that do not take into account spatial gradients of the condensate show agreement with the Tolman-Ehrenfest law. Model 3 exhibits a deviation from the Tolman-Ehrenfest prediction due to the appearance of a new energy scale set by the inhomogeneity of the ground state. Its boundary conditions are fixed by imposing regularity at the rotation axis and by demanding the global minimization of the grand potential. We dub the latter as “firewall boundary conditions,” translating into the requirement of vanishing condensate on the light cylinder, which follows from the fact that the system state formally diverges at the light cylinder. In all models, we present the phase diagram of the system and point out that in models 2 and 3, the system resides either in a chirally restored phase, or in a mixed phase that possesses spatially separated chirally restored and chirally broken phases. Finally, we discuss the properties of the system under inhomogeneous rotation using the relativistic version of the Rankine vortex model.

This paper investigates the double strangeness heavy flavor baryons ${\mathrm{\Omega }}_c^0$ and ${\mathrm{\Omega }}_b^{-}$, which contain two strange quarks. Using QCD light-cone sum rules (LCSRs), we calculate the form factors for the Cabibbo-suppressed processes ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{-}$ and ${\mathrm{\Omega }}_b^{-}\to {\mathrm{\Xi }}^0$, corresponding to the heavy quark transitions $c\to d$ and $b\to u$, respectively. Combining these with the helicity amplitude formalism for semileptonic decay differential widths, we computed the branching fractions of their corresponding semileptonic decay processes. Our analysis reveals significant discrepancies between two versions of QCD LCSRs: one using the light-cone distribution amplitudes (LCDAs) of the final-state $\mathrm{\Xi }$ baryon and the other using the LCDAs of the initial-state double strangeness heavy flavor baryons. The results obtained with the $\mathrm{\Xi }$ baryon’s LCDAs show excellent agreement with other theoretical calculations. However, when using the LCDAs of the double strangeness heavy flavor baryons, the results differ by orders of magnitude, warranting further investigation.

Kaon physics can be used to independently determine three out of the four parameters of the CKM matrix, without any B physics input. Treating one parameter, $|V_{us}|$, or alternatively Wolfenstein $\lambda$, as well known, we show that the natural plane for the presentation of kaon CKM information is spanned by the combinations $[A^2(1-\widehat{\rho }),A^2\widehat{\eta }]$. In this way, the use of B physics inputs is avoided, as well as the artificial inflation of errors due to parametric uncertainties, mainly due to $|V_{cb}|$. We show that the current status of kaon CKM constraints, impacted by recent advances in measurement and theory, is characterized by four allowed regions, and find that incoming data will inevitably disfavor a number of them, either confirming the CKM paradigm as dominant, or discovering a departure from the Standard Model.

Based on a sample of $(1.0087\pm 0.0044)\times {10}^{10}J/\psi$ events collected at BESIII, the transition form factor of the $\eta$ meson is extracted by analyzing $J/\psi \to \gamma {\eta }^{\prime },{\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$ and $\eta \to \gamma l^{+}{l}^{-}$ ($l=e$, $\mu$) events. The measured slope of the transition form factor is ${\mathrm{\Lambda }}^{-2}=1.668\pm 0.093_{\mathrm{stat}}\pm 0.024_{\mathrm{sys}}(\mathrm{GeV}/c^2{)}^{-2}$ for the di-electron channel and ${\mathrm{\Lambda }}^{-2}=1.645\pm 0.343_{\mathrm{stat}}\pm 0.017_{\mathrm{sys}}(\mathrm{GeV}/c^2{)}^{-2}$ for the di-muon channel. The branching fractions for $\eta \to \gamma e^{+}{e}^{-}$ and $\eta \to \gamma {\mu }^{+}{\mu }^{-}$ are measured to be $\mathcal{B}(\eta \to \gamma e^{+}{e}^{-})=(6.79\pm 0.05_{\mathrm{stat}}\pm 0.36_{\mathrm{sys}})\times {10}^{-3}$ and $\mathcal{B}(\eta \to \gamma {\mu }^{+}{\mu }^{-})=(2.97\pm 0.12_{\mathrm{stat}}\pm 0.07_{\mathrm{sys}})\times {10}^{-4}$. By combining with the results based on the $J/\psi \to \gamma \eta$ and $\eta \to \gamma e^{+}{e}^{-}$ events from the previous BESIII measurement, we determine ${\mathrm{\Lambda }}^{-2}=1.707\pm 0.076_{\mathrm{stat}}\pm 0.029_{\mathrm{sys}}(\mathrm{GeV}/c^2{)}^{-2}$ and $\mathcal{B}(\eta \to \gamma e^{+}{e}^{-})=(6.93\pm 0.28_{\mathrm{tot}})\times {10}^{-3}$. In addition, we search for the dark photon ($A^{\prime }$) using the combined events. No significant signal is observed, and the upper limits on $\mathcal{B}(\eta \to \gamma A^{\prime },A^{\prime }\to e^{+}{e}^{-})$ are set at the 90% confidence level for different $A^{\prime }$ mass hypotheses.

We construct a new family of quantum chaotic models by combining multiple copies of integrable commuting SYK models. As each copy of the commuting SYK model does not commute with others, this construction breaks the integrability of each commuting SYK and the family of models demonstrates the emergence of quantum chaos. We study the spectrum of this model analytically in the double-scaled limit. As the number of copies tends to infinity, the spectrum becomes compact and equivalent to the regular SYK model. For finite $d$ copies, the spectrum is close to the regular SYK model in UV but has an exponential tail $e^{E/T_c}$ in the IR. We identify the reciprocal of the exponent in the tail as a critical temperature $T_c$, above which the model should be quantum chaotic. $T_c$ monotonically decreases as $d$ increases, which expands the chaotic regime over the nonchaotic regime. We propose the existence of a new phase around $T_c$, and the dynamics should be very different in two phases. We further carry out numeric analysis at finite $d$, which supports our proposal. Given any finite dimensional local Hamiltonian, by decomposing it into $d$ groups, in which all terms in one group commute with each other but terms from different groups may not, our analysis can give an estimate of the critical temperature for quantum chaos based on the decomposition. We also comment on the implication of the critical temperature to future quantum simulations of quantum chaos and quantum gravity.

This paper demonstrates how the Veneziano partial amplitude of Bosonic string theory admits a generalization to world-(hyper)surfaces of any dimension $d$. In particular, for $d=2$, by carving up the worldsheet integral according to stipulations imposed on conformal cross ratios, the Virasoro-Shapiro full amplitude can be decomposed into a sum of three partial amplitudes. The amplitudes obtained on generalizing the Veneziano amplitude all contain tachyons. To explore candidate tachyon-free and supersymmetric versions of these amplitudes, a new bootstrap principle is introduced and applied, which demands that towers of residues alternate between all-even and all-odd spin partial waves.

This work introduces a field-theoretical model designed to simulate the presence of material layers with magnetoelectric properties. The model comprises the standard Maxwell field coupled to a Chern-Simons field confined to a planar layer. The electromagnetic behavior of the boundary is emulated through the interaction between the Chern-Simons and Maxwell fields, governed by two parameters: the Chern-Simons mass and the coupling constant between the fields. Both parameters can be adjusted to reflect the specific properties of different materials. We compute the exact propagator of the theory and employ it to investigate several physical properties. Our analysis focuses on phenomena that arise from the presence of external sources coupled to both the Maxwell and Chern-Simons fields, considering various scenarios. In the Chern-Simons sector, the sources emulate defects in the crystal lattice of the material layer. The main objective of this paper is to present the proposed model and to explore its behavior in the simple context of a single planar material interface. We also suggest possible extensions of the model to more general configurations.

The Minkowski vacuum in an accelerated frame behaves like a fluid that has not only a finite temperature due to the Unruh effect, but also a finite shear viscosity. Moreover, the ratio of this viscosity to the entropy density exactly satisfies the Kovtun-Son-Starinets bound, inspired by the string theory $\eta /s=1/4\pi$. The origin of this viscosity is purely kinematical and is believed to be related to entanglement introduced by the Rindler horizon. We directly calculate the viscosity, entropy density, and their ratio for massless fields with spins $1/2$ and 1. We show that locally the ratio of viscosity to entropy density can be below the limiting value $1/4\pi$ at distances of the order of the thickness of the membrane corresponding to the stretched horizon, and is described by the universal function for different spins. In particular, on the membrane surface $\eta /s=1/8\pi$.

We investigate the classical stability of two coupled scalar fields with opposite-sign kinetic terms evolving in $1+1$ dimensional Minkowski spacetime. In the first part, we characterize unquenched ghostly interactions and present numerical solutions that support the following statements. First, the classical instability is not instantaneous and can even be benign, i.e., free of finite-time singularities. Second, while the classical instability can cascade toward higher frequency excitations, it is not driven by high frequency modes: At fixed amplitude, high-frequency modes are more stable than low-frequency modes. In the second part, we demonstrate that the classical instability can be quenched by mass terms. In particular, we exemplify that heavy high-frequency ghost fields seem to not violate the decoupling theorem and can be integrated out classically. In the third part, we demonstrate how self-interactions can quench the instability, for instance, by postponing its onset to parametrically large times. Extrapolating numerical results at large but finite evolution time to infinite evolution time, we demonstrate that classical fluctuations around trivial and nontrivial field-theory vacua are increasingly long-lived with (i) smaller initial amplitude of fluctuations, (ii) higher initial frequency of fluctuations, (iii) larger masses of the fields, or (iv) weaker interaction coupling. Moreover, our numerical simulations for field-theoretical generalizations of some globally stable ghostly mechanical models do not feature any instability.

We study a class of Sachdev, Ye, and Kitaev (SYK) models with $\mathcal{N}=2$ supersymmetry, described by $N$ fermions in chiral Fermi multiplets, as well as $\alpha N$ first-order bosons in chiral multiplets. The interactions are characterized by two integers $(p,q)$. We focus on the large $N$ and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use $\mathcal{I}$-extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large $p$ and large $p$, $q$ limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.

The characteristic oscillations of black holes, as described by their quasinormal mode (QNM) spectrum, play a fundamental role in testing general relativity with gravitational waves. The so-called parametrized QNM framework was introduced to predict perturbative changes in the spectrum due to small deviations from general relativity. In this work, we extend the framework to model time-domain signals and study the excitation of quasinormal modes from the time evolution of initial data. Specifically, we quantify whether the perturbative eigenvalue predictions agree with extracting excited quasinormal modes from such simulations. Addressing this issue is particularly important in the context of agnostic ringdown tests and the possible presence of spectral instabilities, which may diminish the promises of black hole spectroscopy. We find that the extracted quasinormal modes agree well with the perturbative predictions, underlining that these types of modifications can, in principle, be robustly tested from real observations. Moreover, we also report the importance of including late-time tails for accurate mode extractions. Finally, we provide a WKB-inspired analysis supporting the importance of the peak of the scattering potential and show robust scaling relations.

In the nanohertz band, the spatial correlations in pulsar timing arrays (PTAs) produced by interfering gravitational waves (GWs) from multiple sources likely deviate from the traditional ones without interference under the assumption of an isotropic Gaussian ensemble. This work investigates the impact of such interference within the framework of massive gravity. Through simulations, we show that while the resulting correlation patterns can be described by Legendre expansions with coefficients that depend on the interference configuration, they remain predominantly quadrupolar ($l=2$), with this feature becoming more pronounced as the graviton mass increases—reflecting both the tensorial polarizations and the modified GW dispersion. However, the interference introduces significant variability in the angular correlation, making it difficult to distinguish massive gravity from general relativity based on a single realization of the Universe. We conclude that beyond a fundamental constraint set by the PTA observation time, achieving a substantially tighter bound on the graviton mass is statistically challenging and observationally limited under realistic conditions.

We study black hole imaging in the context of geometrically thick accretion disks in Schwarzschild spacetime. By decomposing the emitting region into a set of one-dimensional luminous segments, each characterized by its inclination angle and inner radius, we construct transfer functions that capture key image features—namely, the direct image, lensing ring, and photon ring. This approach allows a unified treatment of disk geometry and viewing angle. We explore three regimes: optically thin, optically thick, and partially optically thick disks. For optically thin flows, increasing the disk thickness (characterized by the half-opening angle ${\psi }_0$) broadens the lensing ring, gradually bridging the photon ring and the direct image. The photon ring remains narrow, but its position robustly defines the innermost edge of the lensing structure. In the optically thick case, image features are primarily determined by the first intersection of traced light rays with the disk, and we provide analytical criteria for the presence of lensing and photon rings based on the critical deflection angles. For partially optically thick disks, we adopt a simplified radiative transport model and find a critical absorption coefficient $\chi \sim (6M{\psi }_0{)}^{-1}$ beyond which the image rapidly transitions from an optically thin- to thick-disk appearance. These results help clarify the respective roles of the photon and lensing rings across different disk configurations, and may offer a useful framework for interpreting future high-resolution black hole observations.

We investigate the gravitational lensing of a Schwarzschild–de Sitter black hole with a global monopole at finite distances. In this asymptotically nonflat spacetime, the deflection angle of light is decomposed into two parts: the first derives from the orbit differential equation, and the second originates from the metric itself. By absorbing the cosmological constant into the effective impact parameter, we derive an analytical expression for the first part using elliptic integrals. Combined with the second part, we obtain a complete exact solution for the deflection angle in this context. Additionally, considering that the distances from the source to the observer are large, we derive expressions for the light deflection angle in both the weak- and the strong-field limits. In both cases, we find that the deflection is enhanced by the presence of the global monopole, further supporting its potential role as an alternative to elusive dark matter.