Heavy neutral leptons (HNLs) are motivated by attempts to explain neutrino masses and dark matter. If their masses are in the MeV to several GeV range, HNLs are light enough to be copiously produced at collider and accelerator facilities, but also heavy enough to decay to visible particles on length scales that can be observed in particle detectors. Previous studies evaluating the sensitivities of experiments have often focused on simple but not particularly well-motivated models in which the HNL mixes with only one active neutrino flavor. In this work, we accurately simulate models for HNL masses between 100 MeV and 10 GeV and arbitrary couplings to $e$, $\mu$, and $\tau$ leptons. We include over 150 HNL production channels and over 100 HNL decay modes, including all of the processes that can be dominant in some region of the general parameter space. The result is HNLCalc, a user-friendly, fast, and flexible library to compute the properties of HNL models. As examples, we implement HNLCalc to extend the FORESEE package to evaluate the prospects for HNL discovery at forward LHC experiments. We present sensitivity reaches for FASER and FASER2 in five benchmark scenarios with coupling ratios $|U_e{|}^2:|U_{\mu }{|}^2:|U_{\tau }{|}^2=1:0:0$, $0:1:0$, $0:0:1$, $0:1:1$, and $1:1:1$, where the latter two have not been studied previously. Comparing these to current constraints, we identify regions of parameter space with significant discovery prospects.

We study the scalar and Yukawa sectors of three Higgs doublets models with a generalized $CP$ symmetry. Imposing the symmetry on the quadratic and quartic couplings of the scalar potential, we show that there are only four classes of scalar potentials, merely one more than in two-Higgs-doublet models (2HDM). Two 3HDM cases are analogs of two 2HDM cases, while the other 2HDM case splits here into two distinct potentials. In 2HDM with generalized $CP$ symmetries extended to the Yukawa sector, there are only two possible cases: the usual $CP$, with 18 real Yukawa couplings; and a minimal generalized $CP$ model, with 12 real Yukawa parameters. In contrast, with three Higgs there is a rich variety of allowed models. We classify all possible Yukawa textures, showing that there are 40 possibilities, several of which have only 10 real Yukawa couplings.

In the context of the 2HDM, and assuming that neutrinos acquire masses via the Weinberg operator, we perform a systematic analysis to determine the minimal quark and lepton flavor patterns, compatible with masses, mixing and $CP$ violation data, realizable by Abelian symmetries. We determine four minimal models for quarks, where the number of independent parameters matches the number of observables. For the lepton sector, three minimal predictive models are identified. Namely, we find scenarios with a preference for the upper/lower octant of the ${\theta }_{23}$ atmospheric mixing angle, that exhibit lower bounds on the lightest neutrino masses currently probed by cosmology and testable at future neutrinoless double beta decay experiments, even for a normally ordered neutrino masses. We investigate the phenomenology of each model taking into account all relevant theoretical, electroweak precision observables, scalar sector constraints, as well as stringent quark flavor processes such as $\overline{B}\to X_s\gamma$, $B_s\to {\mu }^{-}{\mu }^{+}$ and meson oscillations, and the charged lepton flavor-violating decays $e_{\alpha }^{-}\to e_{\beta }^{-}{e}_{\gamma }^{+}{e}_{\delta }^{-}$ and $e_{\alpha }\to e_{\beta }\gamma$. We show that, in some cases, Abelian flavor symmetries provide a natural framework to suppress flavor-changing neutral couplings and lead to scenarios featuring heavy neutral/charged scalar masses below the TeV scale within the reach of current experiments.

The geometry of center vortices is studied in SU(3) gauge theory at finite temperature to capture the key structural changes that occur through the deconfinement phase transition. Visualizations of the vortex structure in temporal and spatial slices of the lattice reveal a preference for the vortex sheet to align with the temporal dimension above the critical temperature. This is quantified through a correlation measure. A collection of vortex statistics, including vortex and branching point densities, and vortex path lengths between branching points, are analyzed to highlight internal shifts in vortex behavior arising from the loss of confinement. We find the zero-temperature inclination of branching points to cluster at short distances vanishes at high temperatures, embodying a rearrangement of branching points within the vortex structure. These findings establish the many aspects of center vortex geometry that characterize the phase transition in pure gauge theory.

Besides the ordinary hadrons, quantum chromodynamics (QCD) allows the existence of states in which excitations of the gluonic field can play the role of valence particles, either alone in a glueball, or coupled to quarks in a hybrid. So, hybrid baryons, made of three quarks and a gluon, can a priori exist. Till now, there is no experimental evidence for such exotic hadrons but experimental efforts are being made to search for them at CEBAF Large Acceptance Spectrometer. In this work, a hybrid baryon is considered as a two-body system composed of a color octet three-quark core and a gluon, interacting via a QCD-inspired interaction. A semirelativistic potential model is built in which the dominant interaction is a potential simulating the flux tube confinement, and the Casimir scaling is assumed to link interactions between triplet and octet color sources. This picture is similar to the quark-diquark description for baryons. It is chosen in order to take properly into account the helicity of the gluon. Only $cccg$ and $bbbg$ states are considered because the strong mass asymmetry between the quark core and the gluon is expected to favor the formation of the core. As the results for heavy hybrid baryons seem relevant, we consider this paper as a proof of concept which can be extended for the study of light hybrid baryons.

We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalized tensor networks. This class specifically includes spin networks, the kinematic states of lattice gauge theory, and discrete quantum gravity. We employ an algebraic, operatorial definition of holography based on quantum information channels, an approach which is particularly valuable in settings, such as the one we consider, where the relevant Hilbert space of states does not factorize into subsystem Hilbert spaces due to gauge invariance. We apply random tensor network techniques (successfully used in the AdS/CFT context) to analyze information transport properties of the bulk-to-boundary and boundary-to-boundary maps associated with this superposition of quantum geometries and produce typicality results about the average over the geometric data coloring the fixed graph structure. In this context, one naturally obtains a nontrivial area operator encoding the dominant contribution to entropy calculations. Among our main results is the requirement that one can only isometrically map a bulk region onto boundaries with fixed total area. We furthermore inquire about similar state-induced mappings between segments of the boundary and discuss related conditions for isometric behavior. These generalizations make further steps toward quantum gravity implementations of tensor network holography.

We work toward the general solution of the two-body problem in $2+1$-dimensional general relativity with a negative cosmological constant. The Bañados-Teitelboim-Zanelli (BTZ) solutions corresponding to black holes, point particles and overspinning particles can be considered either as objects in their own right, or as the exterior solution of compact objects with a given mass $M$ and spin $J$, such as rotating fluid stars. We compare and contrast the metric approach to the group-theoretical one of characterizing the BTZ solutions as identifications of $2+1$-dimensional anti–de Sitter spacetime under an isometry. We then move on to the two-body problem. In this paper, we restrict the two objects to the point particle range $|J|-1\le M<-|J|$, or their massless equivalents, obtained by an infinite boost. (Both anti–de Sitter space and massless particles have $M=-1$, $J=0$). We derive analytic expressions for the total mass $M_{\mathrm{tot}}$ and spin $J_{\mathrm{tot}}$ of the system in terms of the six gauge-invariant parameters of the two-particle system: the rest mass and spin of each object, and the impact parameter and energy of the orbit. Based on work of Holst and Matschull on the case of two massless, nonspinning particles, we conjecture that the black hole formation threshold is $M_{\mathrm{tot}}=|J_{\mathrm{tot}}|$. The threshold solutions are then extremal black holes. We determine when the global geometry is a black hole, an eternal binary system, or a closed universe.

We study exact Wentzel–Kramers–Brillouin analysis (EWKB) for a $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics (QM) defined by the potential $V_{\mathcal{P}\mathcal{T}}(x)={\omega }^2{x}^2+g{x}^{2K}(ix{)}^{ϵ}$ with $\omega \in {\mathbb{R}}_{\ge 0}$, $g\in {\mathbb{R}}_{>0}$ and $K,ϵ\in \mathbb{N}$ to clarify its perturbative/nonperturbative structure. In our analysis, we mainly consider the massless cases, i.e., $\omega =0$, and derive the exact quantization conditions (QCs) for arbitrary $(K,ϵ)$ including all perturbative/nonperturbative corrections. From the exact QCs, we clarify full transseries structure of the energy spectra with respect to the inverse energy level expansion, and then formulate the Gutzwiller trace formula, the spectral summation form, and the Euclidean path integral. For the massive cases, i.e., $\omega >0$, we show the fact that, by requiring the existence of the solution of the exact QCs, the path of analytic continuation in EWKB is uniquely determined for a given $N=2K+ϵ$, and in consequence the exact QCs, the energy spectra, and the three formulas are all perturbative. Similarities to Hermitian QMs and resurgence are also discussed as additional remarks.

Many six-dimensional (1, 0) superconformal field theories (SCFTs) are known to fall into families labeled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form global symmetries of a theory labelled by a nilpotent orbit $O$ of $\mathfrak{g}$ can be determined from the anomalies of the theory associated to the trivial nilpotent orbit (the parent theory), together with the data of $O$. In particular, knowledge of the tensor branch field theory is bypassed completely. We show that the known anomalies, previously determined from the geometric/atomic construction, are reproduced by analyzing the Nambu-Goldstone modes inside of the moment map associated to the $\mathfrak{g}$ flavor symmetry of the parent SCFT. This provides further evidence for the physics underlying the labeling of the SCFTs by nilpotent orbits. We remark on some consequences, such as the reinterpretation of the 6D $a$-theorem for such SCFTs in terms of group theory.

We use Fourier neural operators (FNOs) to study the relation between the modulus and phase of amplitudes in $2\to 2$ elastic scattering at fixed energies. Unlike previous approaches, we do not employ the integral relation imposed by unitarity, but instead train FNOs to discover it from many samples of amplitudes with finite partial wave expansions. When trained only on true samples, the FNO correctly predicts (unique or ambiguous) phases of amplitudes with infinite partial wave expansions. When also trained on false samples, it can rate the quality of its prediction by producing a true/false classifying index. We observe that the value of this index is strongly correlated with the violation of the unitarity constraint for the predicted phase and present examples where it delineates the boundary between allowed and disallowed profiles of the modulus. Our application of FNOs is unconventional: it involves a simultaneous regression-classification task and emphasizes the role of statistics in ensembles of neural operators. We comment on the merits and limitations of the approach and its potential as a new methodology in theoretical physics.

The $U(1)$ gauge-invariant scalar-vector-tensor theories, which catches 5 degrees of freedom, are valuable for its implications to inflation problems, generation of primordial magnetic fields, new black hole (BH), and neutron star solutions, etc. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities of nontrivial BH solutions dressed with scalar hair against both odd- and even-parity perturbations on top of the static and spherically symmetric background in the most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. In addition to some general discussions, several typical concrete models are investigated. Specially, we show that the stability against even-parity perturbations is ensured outside the event horizon under certain constraints to these models. This is a crucial step to check the self-consistency of the theories and to shed light on the physically accessible models of such theories for future studies.

Within the context of the effective field theory (EFT) framework to gravitational dynamics, we compute the Hamiltonian, source quadrupole moment, and gravitational-wave energy flux for (nonspinning) inspiralling compact binaries at next-to-next-to-next-to leading order (${\mathrm{N}}^3\mathrm{LO}$) in the post-Newtonian (PN) expansion. We use the recently developed $d$-dimensional multipole-expanded effective theory, and explicitly perform the matching to the (pseudo) stress-energy tensor. The calculation involves Feynman integrals up to three- (conservative) and two-loop (radiative) orders, evaluated within dimensional regularization. Our (ambiguity-free) results confirm (for the first time) the value of the gravitational-wave flux for quasicircular orbits at 3PN order, while paving the way forward to the inclusion of spin effects as well as higher-order computations.

The Newman-Janis algorithm, which involves complex-coordinate transformations, establishes connections between static and spherically symmetric black holes and rotating and/or axially symmetric ones, such as between Schwarzschild black holes and Kerr black holes, and between Schwarzschild black holes and Taub-NUT black holes. However, the transformations in the two samples are based on different physical mechanisms. The former connection arises from the exponentiation of spin operators, while the latter from a duality operation. In this paper, we mainly investigate how the connections manifest in the dynamics of black holes. Specifically, we focus on studying the correlations of quasinormal frequencies among Schwarzschild, Kerr, and Taub-NUT black holes. This analysis allows us to explore the physics of complex-coordinate transformations in the spectrum of quasinormal frequencies.

Future gravitational-wave detectors, especially the Laser Interferometer Space Antenna (LISA), will be sensitive to black hole binaries formed in astrophysical environments that promote large eccentricities and spin-induced orbital precession. Approximate models of gravitational waves that include both effects have only recently begun to be developed. The efficient fully precessing eccentric (EFPE) family is one such model, covering the inspiral stage with small-eccentricity-expanded gravitational-wave amplitudes accurate for initial time eccentricities $e<0.3$ at 4 years before reaching an orbital frequency of 1 Hz. In this work, we extend this model to cover a larger range of initial eccentricities. The new EFPE for moderate eccentricities (EFPE_ME) model is able to accurately represent the leading-order gravitational-wave amplitudes to $e\le 0.8$. Comparing the EFPE and the EFPE_ME models in the LISA band, however, reveals that there is no significant difference when the eccentricity at four years before merger, $e_0$, is less than or equal to 0.5, as radiation reaction circularizes supermassive black hole binaries too quickly. This suggests that the EFPE model may have a larger regime of validity in eccentricity space than previously thought, making it suitable for some inspiral parameter estimation with LISA data. On the other hand, for systems with $e_0>0.5$, the deviations between the models are significant, particularly for binaries with total masses below ${10}^5{M}_{\odot }$. This suggests that the EFPE_ME model will be crucial to avoid systematic bias in parameter estimation with LISA in the future, once this model has been hybridized to include the merger and ringdown and the computation of the amplitudes is optimized.

Cosmological observables are particularly sensitive to key ratios of energy densities and rates, both today and at earlier epochs of the Universe. Well-known examples include the photon-to-baryon and the matter-to-radiation ratios. Equally important, though less publicized, are the ratios of pressure-supported to pressureless matter and the Thomson scattering rate to the Hubble rate around recombination, both of which observations tightly constrain. Preserving these key ratios in theories beyond the $\mathrm{\Lambda }$ Cold-Dark-Matter ($\mathrm{\Lambda }\mathrm{CDM}$) model ensures broad concordance with a large swath of datasets when addressing cosmological tensions. We demonstrate that a mirror dark sector, reflecting a partial ${\mathbb{Z}}_2$ symmetry with the Standard Model, in conjunction with percentage level changes to the visible fine-structure constant and electron mass which represent a phenomenological change to the Thomson scattering rate, maintains essential cosmological ratios. Incorporating this ratio-preserving approach into a cosmological framework significantly improves agreement to observational data ($\mathrm{\Delta }{\chi }^2=-35.72$) and completely eliminates the Hubble tension with a cosmologically inferred $H_0=73.80\pm 1.02\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ when including the $\mathrm{S}{H}_0\mathrm{ES}$ calibration in our analysis. While our approach is certainly nonminimal, it emphasizes the importance of keeping key ratios constant when exploring models beyond $\mathrm{\Lambda }\mathrm{CDM}$.

We study the thermodynamic properties of the color-flavored-locked (CFL) quark matter in finite temperature and strong magnetic field cases within the confined-isospin-density-dependent-mass model. We find that considering the CFL phase in quark star (QS) matter can significantly influence the equation of state as well as the properties of QSs at finite temperature or under strong magnetic fields. In particular, our results indicate that the polytropic index becomes anisotropic under magnetic fields and decreases with the increment of the star mass at different isentropic stages of QSs.

Single gravitational-wave detectors face inherent limitations in detecting the anisotropy of the stochastic background. In this work, we explore the sensitivity to anisotropic backgrounds with a network of space-borne detectors. We find that the separation between detectors plays an important role in determining the sensitivity. For the first time, we observe as large as three orders of magnitude enhancement in detection sensitivity for multipoles with $l=5$ and 6, compared to coinciding detectors. Coordinating and optimizing the separation between two space-borne detectors can significantly enhance the network’s sensitivity to the multipole components of the stochastic background. For the $\mathrm{TianQin}+\text{Laser}$ Interferometer Space Antenna (LISA) network, benefiting from detector separation, it is possible to achieve sensitivity levels of 2–3 orders of magnitude better than those when using the TianQin or LISA detector alone. These findings pave the way to uncover the underlying physics of anisotropy through gravitational-wave detections.

Composition measurement of cosmic rays (CRs) around the knee of the CR energy spectrum is crucial for studying the processes of particle acceleration and propagation of Galactic CRs. The Square Kilometer Array (KM2A) of the Large High Altitude Air Shower Observatory (LHAASO) can provide precise measurement of the muonic and electromagnetic (em) components in CR-induced extensive air showers, and hence a good chance to disentangle the CR composition. Here we propose an approach of decomposing CR compositions with the number ratio between muons and em particles ($N_{\mu }/N_{\mathrm{e}}$) observed by LHAASO-KM2A: We reconstruct the energy spectra of individual CR compositions by fitting the $N_{\mu }/N_{\mathrm{e}}$ distributions in each reconstructed energy bin using the template shapes of the $N_{\mu }/N_{\mathrm{e}}$ distributions of individual CR compositions based on Monte Carlo (MC) simulation. We evaluate the performance of this approach with MC tests where mock data of LHAASO-KM2A are generated by MC simulation. We show that the input composition model can be well recovered in this approach, independent of the CR composition model adopted in the MC simulation for the template distributions. The uncertainties of the reconstructed spectra at $<20\mathrm{PeV}$, mainly limited by simulation statistics, are $\le 7\%$ for the proton, He, and, Fe groups, and $\le 8\%$ and $\le 16\%$ for the carbon-nitrogen-oxygen and MgAlSi groups, respectively.

Time delay interferometry (TDI) is a key technique employed in gravitational wave (GW) space missions to mitigate laser frequency noise by combining multiple laser links and establishing an equivalent equal arm interferometry. The null frequencies will be introduced in noise spectra and GW response when the periodical signal/noise is canceled in synthesized laser links. These frequencies are characteristic frequencies of a TDI which related to its geometry of combination. In this work, we implement a second-generation TDI configuration referred to as hybrid relay to perform noise suppressions and data analysis, whose characteristic frequencies are only one-quarter that of the fiducial second-generation Michelson observables. We examine the performance of TDI configuration in laser noise cancellation and clock noise suppression and justify its essential capabilities. To assess its robustness for signal extraction, we simulate data containing GW signals from massive black hole binaries and perform parameter inferences with comparisons against the fiducial Michelson TDI configuration. The results demonstrate that the alternative TDI solution could be more robust than Michelson in fulfilling data analysis.

In this paper, we study the quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ [with $P=(\pi ,K,\eta ,{\eta }^{\prime })$] within framework of perturbative QCD (PQCD) factorization approach. With the help of $\pi -\pi$ distribution amplitude and scalar form factor $F_{\pi \pi }({\omega }^2)$, we calculate the $CP$ averaged branching fraction and the $CP$ asymmetry for the quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$. Taking the quasi-two-body decay $B^{+}\to {\pi }^{+}{f}_0(500)\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ as an explicit example, we present the behavior of differential branching fraction and direct $CP$ violation versus the $\pi \text{−}\pi$ invariant mass. The total branching fraction and direct $CP$ violation are $\mathcal{B}(B^{+}\to {\pi }^{+}[\sigma \to ]{\pi }^{+}{\pi }^{-})=(1.78\pm 0.41\pm 0.51)\times {10}^{-6}$ and ${\mathcal{A}}_{CP}(B^{+}\to {\pi }^{+}[\sigma \to ]{\pi }^{+}{\pi }^{-})=(29.8\pm 11.1\pm 13.0)\%$ respectively. Our results could be tested by further experiments.