We determine the four-point correlation function and amplitude in planar, maximally supersymmetric Yang-Mills theory to 12 loops. We find that the recently introduced “double-triangle” rule in fact implies the previously described square and pentagon rules; and when applied to 12 loops, it fully determines the 11-loop correlator and fixes all but 3 of the (619,981,403) 12-loop coefficients; these remaining coefficients can be subsequently fixed using the “(single-)triangle” rule. Not only do we confirm the Catalan conjecture for antiprism graphs, but we discover evidence for a greatly generalized Catalan conjecture for the coefficients of all polygon-framed fishnet graphs. We provide all contributions through 12 loops as Supplemental Material to this work.

In gauge-gravity duality, the Hawking-Page (HP) process plays the important role of representing a confined-deconfined phase transition. For spaces that are asymptotically anti–de Sitter with a planar spatial boundary, there is no HP transition, unless some infrared energy scale is introduced. Massive gravity theories have been applied in the context of holography in order to represent systems with momentum dissipation. In this work, we study the HP transition for massive gravity in an asymptotically anti–de Sitter space with ${\mathbb{R}}^n\times {\mathrm{S}}^1$ boundary. It is shown that the graviton mass term produces an HP transition at a finite critical temperature.

The interaction between quantum gravitational waves (GWs) and electromagnetic (EM) fields is investigated within the open quantum system formalism, where GWs are considered as a heat bath reservoir occupying a generic state ${\widehat{\rho }}_{\mathrm{gws}}$. Following the quantum Langevin equations, it turns out that the correlations of the Langevin noise operator associated with the GW background directly determine the statistical properties of the EM phasor $\varphi (t)$. We apply this formalism to the background of inflationary-generated primordial gravitational waves (PGWs). Since this background has an astronomically large correlation time, of the order of the Hubble time $H_0^{-1}$, we show that it leads to a non-Markovian dynamics of the EM field, which causes memory effects. As a result of the Gaussianity of PGW, it turns out that the EM phasor goes through a stochastic process, which is a manifestation of the fluctuation dissipation in the EM-GW system. The variance of the EM phase smears out as ${\mathrm{\Delta }}^2\phi (t)={\mathrm{\Delta }}^2{\phi }_0+4(t/{\tau }_c{)}^4$, where the characteristic timescale ${\tau }_c$ is associated with the diffusion rate caused by PGWs. The specific quartic growth of the phase noise is thus attributed to the two-mode squeezed nature of PGWs, which is inherently different from the phase diffusion induced by vacuum fluctuations of spacetime or a thermal heat bath of gravitons.

We show that for Horndeski theories it is possible to derive mathematically compact consistency relations (CR) between physically observable quantities, valid for different classes of theories defined by the behavior of the braiding function ${\alpha }_B$, independent of all other property functions. The CRs establish a parametrization-independent direct relation between the effective gravitational constant, the slip parameter, the gravitational and electromagnetic waves (EMW) luminosity distances, the speed of gravitational waves (GW), and the sound speed. The no-braiding CR is also satisfied by general relativity (GR) and allows one to estimate the gravitational coupling from GWs observations, independently from large scale structure (LSS) observations. A general, less mathematically compact, consistency condition is also derived, valid for any form of the function ${\alpha }_B$ and the other property functions. We apply the CRs to map the large scale structure observational constraints on the effective gravitational constant and the slip parameter to GW-EMW distance ratio constraints, showing that LSS and GWs give independent constraints consistent with no-braiding. Beside allowing one to perform parametrization and model-independent tests of the consistency between different constraints on modified gravity, the CRs allow one to probe the value of the effective gravitational constant with multimessenger observations, independently from LSS observations.

We justify the applicability of the background subtraction method to both Einstein’s gravity and its higher derivative corrections in five-dimensional asymptotically anti–de Sitter (AdS) spacetimes, where the corresponding higher derivative corrections to the expression for the Arnowitt-Deser-Misner mass and angular momentum are also worked out. Then we further apply the background subtraction method to calculate the first-order corrected Gibbs free energy by the quadratic curvature terms for the five-dimensional Kerr-AdS black hole, which is in exact agreement with the previous result obtained by the holographic renormalization method. Such an agreement in turn substantiates the applicability of the background subtraction method.

Primordial black holes (PBHs) are one of the most important tracers of cosmic history. In this work, we investigate the formation of PBHs around the time of the QCD phase transition from a broadly peaked inflationary scalar power spectrum, which naturally produces an extended PBH mass function. This scenario yields two distinct stochastic gravitational wave backgrounds (SGWB): (i) scalar-induced, second-order tensor perturbations generated at PBH formation, and (ii) a merger-driven SGWB from the subsequent PBH binary population. Using Bayesian analysis, we examine both SGWB channels with the data from the NANOGrav 15-year dataset and the first three observing runs of LIGO-Virgo-KAGRA (LVK). We also forecast continuous-wave signals from mini-extreme mass ratio inspirals (mini-EMRIs) for direct comparison with NANOGrav and LVK constraints. Our parameter scans identify regions of the parameter space where the combined SGWB is detectable in future ground-based and space-based detectors. A broad PBH mass distribution naturally gives rise to mini-EMRIs, which future ground-based observatories, such as LVK A+, Einstein Telescope (ET), and Cosmic Explorer (CE), can detect. For a large part of the PBH parameter space, the SGWB of astrophysical origin masks the primordial SGWB in the frequency band of ground-based detectors. Thus, for extended PBH mass distributions, we find that the detection of mini-EMRIs is a more robust channel for probing the PBH parameter space than the corresponding SGWB.

We numerically study the formation of the gauge-mediation type $Q$ balls in the logarithmic square potential on three-dimensional lattices. We obtain the broad charge distribution of the $Q$ ball of this type for the first time, to the best of our knowledge. The charge of the $Q$ ball at the peak of the distribution is smaller than what we estimated as the average of the largest tens of the $Q$ balls in the logarithmic potential for the same initial amplitude of the field at the onset of its oscillation. We also discuss some impacts of the broad distribution on cosmology and astrophysics. In the $B$ ball ($Q$ being the baryon number) case, the broad distribution would lead to the coexistence of both stable and unstable $B$ balls. We find that stable $B$ balls can account for the dark matter of the Universe without affecting successful big bang nucleosynthesis by the decay of the unstable $B$ balls, but the baryon number of the Universe cannot be explained by them. On the other hand, the large $L$ balls ($Q$ being the lepton number) would be the dark matter as well while avoiding the constraints on the x- and/or $\gamma$-rays from the decay of the smaller $L$ balls.

We consider a model of inflation in which the inflaton field is a rolling axion with a potential which is flat enough to support an intermediate phase of ultraslow-roll (USR) inflation. Because of the Chern-Simons interaction, one polarization of the gauge field experiences the tachyonic growth during the first slow-roll stage, inducing large corrections in curvature perturbations via the inverse decay effect. A nontrivial feature of our setup is that, once the system enters the USR phase, the instability parameter falls off rapidly, terminating the gauge field production efficiently. Consequently, the power spectrum involves two separate peaks; the first peak is induced by the gauge field particle production, while the second peak is due to the standard USR mechanism. We show that the power spectrum at the intermediate scales develops strong scale dependence $\propto k^m$ with the index $m>4$. Calculating the bispectrum, we demonstrate that non-Gaussianities with nontrivial shapes and multiple peaks are generated in this setup.

We present a search for boosted dark matter from primordial black hole (PBH) evaporation using the DarkSide-50 ionization-signal-only dataset corresponding to the experiment’s $(12202\pm 180)\mathrm{kg}\mathrm{d}$ exposure. We focus on evaporation of PBHs with masses in the range $[{10}^{14},{10}^{16}]\mathrm{g}$ producing Dirac fermionic dark matter particles with sub-GeV kinetic energy. These relativistic particles, with energies up to hundreds of MeV, can generate detectable signals for masses below $\mathcal{O}(100)\mathrm{MeV}$. The absence of a signal enables setting complementary limits to those derived from cosmological observations and direct detection searches for cosmic-ray-boosted dark matter.

Upon their evaporation via Hawking radiation, primordial black holes (PBHs) deposit energy in the ambient plasma on scales that can be smaller than the typical distance between two black holes, leading to the formation of hot spots around them. We investigate how such hot spots may act as a shield against the release of low-energy photons, affecting PBH’s capacity to dissociate light nuclei after big bang nucleosynthesis through photo-dissociation. We find that this shielding effect is particularly relevant for PBHs with masses between ${10}^{11}\mathrm{g}$ and $4\times {10}^{12}\mathrm{g}$. We emphasize that the magnitude of this effect is highly dependent on the specific shape of the temperature profile around PBHs and its time evolution, stressing the necessity for a comprehensive study of PBH hot spots and their dynamics in the future.

Gravitational waves from core-collapse supernovae provide a unique probe of the equation of state (EOS) of high density matter. In this work, we focus on the bounce signal from numerical simulations of rotating supernovae and explore its potential for EOS inference. We employ a support vector machine, previously shown to perform best among tested methods, to classify GW signals simulated for 18 EOS models. For optimally oriented sources, we estimate that the Advanced LIGO A+ detector can probe the EOS for Galactic events, while third-generation observatories such as the Einstein Telescope and Cosmic Explorer can reach substantially farther. For randomly oriented sources, only these next-generation detectors are expected to have sufficient sensitivity. These results represent the potential observational range for probing the nuclear EOS, although, due to the simplifying assumptions adopted, they should be regarded as approximate upper limits.

We study two general $U(1)$ extensions of the Standard Model (SM) those generate tiny neutrino masses via the seesaw mechanism after general $U(1)$ breaking. These models predict a new neutral gauge boson ($Z^{\prime }$) and right-handed neutrinos (RHNs), the latter introduced for anomaly cancellation and neutrino mass generation. In both scenarios, left- and right-handed fermions couple differently to the $Z^{\prime }$, and RHNs mix with light neutrinos, enabling variety of decay modes. Focusing on the high-luminosity LHC (HL-LHC) and the future FASER2 experiment, we explore RHN pair production from $Z^{\prime }$ decays in two cases; (i) long-lived $Z^{\prime }$ decays to visible modes and long-lived RHNs, and (ii) short-lived $Z^{\prime }$ decays to long-lived RHNs, which further decay visibly inside FASER2. We estimate projected limits on the general $U(1)$ gauge coupling, $Z^{\prime }$ mass, RHN mass, and light-heavy neutrino mixing for various $U(1)$ charge assignments, and compare them with current experimental bounds.

We propose new methods for optimizing the integration-by-parts (IBP) reduction of Feynman integrals, an important computational bottleneck in modern perturbative calculations in quantum field theory. Using the simple example of one-loop massive bubble integrals, we pose the problem of minimizing the number of arithmetic operations in reducing a target integral to master integrals via the Laporta algorithm. This is a nontrivial combinatorial optimization problem over the ordering of IBP equation generation (from pairs of seed integrals and IBP operators) and the ordering of integral elimination. Our first proposed method is reinforcement learning, which involves an agent interacting with an environment in a step-by-step manner and learning the best actions to take given an observation of the environment (in this case, the current state of the IBP reduction process). The second method is using metaheuristics, e.g., simulated annealing, to minimize the computational cost as a black-box function of numerical priority values that control the orderings. For large-scale problems, the number of free parameters can be compressed by using a small neural network to assign priority values. Remarkably, with almost no human guidance, both methods lead to IBP reduction schemes that are competitive with the most efficient human-designed algorithms. We also found interpretable features in the AI results that may be applicable to more complicated problems.

We propose a data-driven approach to extract the kaon leading-twist distribution amplitude (DA) from empirical information on the ratio of the neutral-to-charged kaon electromagnetic form factors, ${\mathcal{R}}_K$. Our study employs a two-parameter representation of the DA at $\zeta =2\mathrm{GeV}$, designed to capture the expected broadening and asymmetry of the distribution, as well as the soft endpoint behavior predicted by quantum chromodynamics (QCD). Our leading-order analysis of the latest experimental measurements of ${\mathcal{R}}_K$ reveals that the extracted DA exhibits a somewhat significant skewness, with the first symmetric moment being approximately $⟨1-2x{⟩}_K=0.082(7)$. On the other hand, the broadness and general shape of the produced distributions show a reasonable consistency with contemporary lattice and continuum QCD analyses. These findings highlight the importance of accurately determining the profile of the DA, especially the skewness and its relation to $S{U}_F(3)$ flavor symmetry breaking, as well as the inclusion of higher-order effects in the hard-scattering kernels for analyzing data at experimentally accessible scales.

We present R-ANODE, a new method for data-driven, model-agnostic resonant anomaly detection that raises the bar for both performance and interpretability. The key to R-ANODE is to enhance the inductive bias of the anomaly detection task by fitting a normalizing flow directly to the small and unknown signal component, while holding fixed a background model (also a normalizing flow) learned from sidebands. In doing so, R-ANODE is able to outperform all classifier-based, weakly supervised approaches as well as the previous ANODE method, which fit a density estimator to all of the data in the signal region instead of just the signal. We show that the method works equally well whether the unknown signal fraction is learned or fixed and is even robust to signal fraction misspecification. Finally, with the learned signal model, we can sample and gain qualitative insights into the underlying anomaly, which greatly enhances the interpretability of resonant anomaly detection and offers the possibility of simultaneously discovering and characterizing the new physics that could be hiding in the data.

This work implements the combined baryon chiral perturbation theory (BChPT) and $1/N_c$ expansions for pion-nucleon elastic scattering. The effective theory is based on the baryon sector dynamical spin-flavor $SU(4)$ symmetry emergent in the large $N_c$ limit, whose breaking is controlled by the $1/N_c$ expansion. The noncommutativity of the chiral and $1/N_c$ expansions in unitarity corrections (loops) requires a linking of both expansions. As it was shown in the case of baryon masses and currents, the natural linking is the $\xi$ expansion, in which $\mathcal{O}(p)=\mathcal{O}(1/N_c)=\mathcal{O}(\xi )$. The spin-flavor symmetry requires that the ground state baryons span an $SU(4)$ symmetric irreducible representation which implies that in particular $N$ and $\mathrm{\Delta }$ are active degrees of freedom in the effective theory. The scattering amplitude is expanded to the next-to-next-to leading order in the $\xi$ expansion, corresponding to the one-loop contributions with the leading-order Lagrangian. The results are given for generic $N_c$ in order to demonstrate the consistency of the framework. The spin-flavor symmetry plays a central role in maintaining the consistency of the effective theory with respect to the $1/N_c$ expansion. This consistency manifests itself in an improvement in the convergence of the low energy expansion with respect to the case of the ordinary BChPT without an explicit dynamical $\mathrm{\Delta }$, which is known to be inconsistent with the constraints of $N_c$ scaling. Fits to the $\pi N\to \pi N$, $S$, $P$, and $D$ partial wave amplitudes from the SAID data base are finally used to test the framework and to determine the energy range of its applicability.

We generalize our recent analysis of hidden-strangeness tetraquarks within the dynamical diquark model from its adiabatic form (in which each state is described solely by a diquark-antidiquark potential) to its diabatic form (which incorporates effects of dihadron thresholds upon the states). We tabulate all relevant thresholds and compute the dihadron content of each predicted state. Our results produce no particular hidden-strange tetraquark candidate whose structure is dominated by dihadron structure, in contrast to the charm sector, where many exotic states are strongly associated with such thresholds: The hidden-strange states tend to remain compact and less influenced by dihadron thresholds. Multiple states above 2 GeV with peculiar decay properties, including $\varphi (2170)$, $f_2(2340)$, and $\eta (2370)$, continue to serve as excellent hidden-strange tetraquark candidates.

We present the first perturbative QCD calculations of the ${\mathrm{\Xi }}_b\to (\mathrm{\Lambda },\mathrm{\Sigma })$ transition form factors at leading order in ${\alpha }_s$, which govern the Cabibbo-suppressed semileptonic decays ${\mathrm{\Xi }}_b\to (\mathrm{\Lambda },\mathrm{\Sigma })\ell {\nu }_{\ell }$ with $\ell =e$, $\mu$, $\tau$. Using these form factors, we evaluate differential and integrated branching fractions and angular observables within the helicity formalism. The branching ratios are predicted to be of order ${10}^{-4}$ for $\mathrm{\Sigma }$ final states and ${10}^{-5}$ for $\mathrm{\Lambda }$ final states, making them accessible to ongoing experiments such as LHCb. Ratios of decay rates between $\tau$ and $e$ channels are also provided, offering new probes of lepton-flavor universality. Lepton-mass effects are found to significantly impact the integrated angular observables. Furthermore, a combined analysis of $b\to u$ and $b\to c$ transitions in ${\mathrm{\Xi }}_b$ decays yields subpercent precision for the ratios ${\mathcal{R}}_{\ell }(\mathrm{\Sigma }/{\mathrm{\Xi }}_c)$, enabling an independent determination of $|V_{ub}/V_{cb}|$ once the relevant decay-rate measurements become available.

We present a microscopic calculation of two-particle–two-hole meson-exchange current response functions in asymmetric nuclei, with particular emphasis on the ${}^{40}\mathrm{Ar}$ nucleus. Employing a relativistic mean-field and relativistic Fermi gas framework, we compute the nuclear response for ${}^{40}\mathrm{Ar}$ and compare it with that of the symmetric ${}^{40}\mathrm{Ca}$ nucleus, analyzing the role of proton-neutron imbalance. The model incorporates distinct proton and neutron Fermi momenta to accurately capture the nuclear dynamics of systems with $Z\ne N$. Our results indicate that using ${}^{40}\mathrm{Ca}$ as a proxy for ${}^{40}\mathrm{Ar}$ leads to a systematic error of approximately 10%. Additionally, we propose an asymmetric scaling formula to obtain the two-particle–two-hole response for arbitrary nuclei from the ${}^{12}\mathrm{C}$ response, improving the description of asymmetric nuclei. Finally, we benchmark our predictions against inclusive electron scattering and neutrino cross sections.

We present limits on spin-independent inelastic weakly interacting massive particle (WIMP)-nucleus scattering using the $737.1\mathrm{kg}·\mathrm{day}$ dataset from the CDEX-1B experiment. Expected nuclear recoil spectra for various inelastic WIMP masses $m_{\chi }$ and mass splittings $\delta$ are calculated under the standard halo model. An accurate background model of CDEX-1B is constructed by simulating all major background sources. The model parameters are then determined through maximum likelihood estimation and Markov chain Monte Carlo fitting. The resulting 90% confidence level upper limits on the WIMP-nucleon cross section ${\sigma }_{\mathrm{n}}$ exclude certain DAMA/LIBRA allowed regions: the ${\chi }^2<4$ regions for $\delta <30\mathrm{keV}$ at $m_{\chi }=250\mathrm{GeV}$ and the ${\chi }^2<9$ region for $\delta <50\mathrm{keV}$ at $m_{\chi }=500\mathrm{GeV}$. The method is applicable to other inelastic dark matter scenarios, and the upcoming CDEX-50 experiment is expected to improve sensitivity by four orders of magnitude.