The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics and magnetohydrodynamics have benefited from a large number of evolution schemes that are able to enforce these constraints and are easily applicable to curvilinear coordinates, unstructured meshes, or $N$-body simulations, many of these techniques cannot be straightforwardly applied to existing formulations of the Einstein equations. We develop a $3+1$ a formulation of the Einstein equations that shows a striking resemblance to the equations of relativistic magnetohydrodynamics and to electrodynamics in material media. The fundamental variables of this formulation are the frame fields, their exterior derivatives, and the Nester-Witten and Sparling forms. These mirror the roles of the electromagnetic four potential, the electromagnetic field strengths, the field excitations and the electric current. The role of the lapse function and shift vector, corresponds exactly to that of the scalar electric potential. The formulation is manifestly first order and flux-conservative, which makes it suitable for high-resolution shock capturing schemes and finite-element methods. Being derived as a system of equations in exterior derivatives, it is directly applicable to any coordinate system and to unstructured meshes, and leads to a natural discretization potentially suitable for the use of machine-precision constraint propagation techniques such as the Yee algorithm and constrained transport. Due to these properties, we expect this new formulation to be beneficial in simulations of many astrophysical systems, such as binary compact objects and core-collapse supernovae as well as cosmological simulations of the early Universe.

In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by massive geodesic particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a distant observer. Furthermore, we incorporate the gravitational dragging effect generated by the rotating nature of the Kerr black hole into the analysis and elucidate its nontrivial contribution to the expression for the light bending parameter and the frequency shifts of photons emitted by orbiting particles that renders simple symmetric expressions for the kinematic redshift and blueshift. We also incorporate the dependency of the frequency shift on the azimuthal angle, a fact that allows one to express the total redshift/blueshift at any point of the orbit of the revolving particle for the cases when the black hole is both static or moving with respect to us. These formulas allow one to compute the Kerr black hole parameters by applying this general relativistic formalism to astrophysical systems like the megamaser accretion disks orbiting supermassive black holes at the core of active galactic nuclei. Our results open a new window to implement parameter estimation studies to constrain black hole variables, and they can be generalized to black hole solutions beyond Einstein’s gravity.

We study the motion of a spinning particle with gravimagnetic moment in Schwarzschild-like spacetimes with a metric $d{s}^2=-f(r)d{t}^2+f^{-1}(r)d{r}^2+r^{2}d{\mathrm{\Omega }}^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom black holes as well as Ayon-Beato-Garcia and Bardeen regular spacetimes. First, we introduce the Hamiltonian system of equations which describes such kind of particles. In the case of null gravimagnetic moment, the equations are equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. Working in the equatorial plane, using the constants of motion generated by the symmetries of the considered spacetimes and the spin supplementary conditions (SSC), we change the problem of solving six differential equations for the momenta and the nonvanishing spin-tensor components to solving six algebraic equations. We show that the equation for the $P_0(r)$ component totally decouples, $P_0(r)$ can be found by solving a 6th order polynomial. We analyze the conditions for existence of solutions of this algebraic system for the relevant cases of gravimagnetic moment equal to unit, which corresponds to a gravimagnetic particle, and zero which corresponds to the MPTD system. A numerical algorithm to generate solutions of the momenta $P_{\mu }$ is provided and some solutions are generated.

We present a validation of the Dark Energy Survey Year 3 (DES Y3) $3\times 2$-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the $3\times 2$-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy–galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

Precise reconstruction of the cosmic microwave background lensing potential can be achieved with deep polarization surveys by iteratively removing lensing-induced $B$ modes. We introduce a lensing spectrum estimator and its likelihood for such optimal iterative reconstruction. Our modeling shares similarities to the state-of-the-art likelihoods for quadratic estimator (QE)-based lensing reconstruction. In particular, we generalize the $N^{(0)}$ and $N^{(1)}$ lensing biases, and design a realization-dependent spectrum debiaser, making this estimator robust to uncertainties in the data modeling. We demonstrate unbiased recovery of the cosmology using map-based reconstructions, focussing on lensing-only cosmological constraints and neutrino mass measurement in combination with CMB spectra and acoustic oscillation data. We find this spectrum estimator is essentially optimal and with a diagonal covariance matrix. For a CMB-S4 survey, this likelihood can double the constraints on the lensing amplitude compared to the QE on a wide range of scales, while at the same time keeping numerical cost under control and being robust to errors.

We analyze the clustering of galaxies using the $z=1.006$ snapshot of the CosmoDC2 simulation, a high-fidelity synthetic galaxy catalog designed to validate analysis methods for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We present subpercent measurements of the galaxy autocorrelation and galaxy-dark matter cross correlations in Fourier space and configuration space for a magnitude-limited galaxy sample. At these levels of precision, the statistical errors of the measurement are comparable to the systematic effects present in the simulation and measurement procedure; nevertheless, using a hybrid-PT model, we are able to model nonlinear galaxy bias with 0.5% precision up to scales of $k_{\max }=0.5h/\mathrm{Mpc}$ and $r_{\min }=4\mathrm{Mpc}/h$. While the linear bias parameter is measured with 0.01% precision, other bias parameters are determined with considerably weaker constraints and sometimes bimodal posterior distributions. We compare our fiducial model with lower dimensional models, where the higher-order bias parameters are fixed at their coevolution values and find that leaving these parameters free provides significant improvements in our ability to model small scale information. We also compare bias parameters for galaxy samples defined using different magnitude bands and find agreement between samples containing equal numbers of galaxies. Finally, we compare bias parameters between Fourier space and configuration space and find moderate to significant tension between the two approaches. Although our model is often unable to fit the CosmoDC2 galaxy samples within the 0.1% precision of our measurements, our results suggest that the hybrid-PT model used in this analysis is capable of modeling nonlinear galaxy bias within the percent level precision needed for upcoming galaxy surveys.

Searching for gravitational waves in pulsar timing array data is computationally intensive. The data is unevenly sampled, and the noise is heteroscedastic, necessitating the use of a time-domain likelihood function with attendant expensive matrix operations. The computational cost is exacerbated when searching for individual supermassive black hole binaries, which have a large parameter space due to the additional pulsar distance, phase offset and noise model parameters needed for each pulsar. We introduce a new formulation of the likelihood function which can be used to make the Bayesian analysis significantly faster. We divide the parameters into projection and shape parameters. We then accelerate the exploration of the projection parameters by more than four orders of magnitude by precomputing the expensive inner products for each set of shape parameters. The projection parameters include nuisance parameters such as the gravitational wave phase offset at each pulsar. In the new scheme, these troublesome nuisance parameters are efficiently marginalized over using multiple-try Markov chain Monte Carlo sampling as part of a Metropolis-within-Gibbs scheme. The acceleration provided by our method will become increasingly important as pulsar timing datasets rapidly grow. Our method also makes sophisticated analyses more tractable, such as searches for multiple binaries, or binaries with non-negligible eccentricities.

Two photo-neutron sources, ${}^{88}\mathrm{Y}$${}^9\mathrm{Be}$ and ${}^{124}\mathrm{Sb}$${}^9\mathrm{Be}$, have been used to investigate the ionization yield of nuclear recoils in the CDMSlite germanium detectors by the SuperCDMS collaboration. This work evaluates the yield for nuclear recoil energies between 1 and 7 keV at a temperature of $\sim 50\mathrm{mK}$. We use a geant4 simulation to model the neutron spectrum assuming a charge yield model that is a generalization of the standard Lindhard model and consists of two energy dependent parameters. We perform a likelihood analysis using the simulated neutron spectrum, modeled background, and experimental data to obtain the best fit values of the yield model. The ionization yield between recoil energies of 1 and 7 keV is shown to be significantly lower than predicted by the standard Lindhard model for germanium. There is a general lack of agreement among different experiments using a variety of techniques studying the low energy range of the nuclear recoil yield, which is most critical for interpretation of direct dark matter searches. This suggests complexity in the physical process that many direct detection experiments use to model their primary signal detection mechanism and highlights the need for further studies to clarify underlying systematic effects that have not been well understood up to this point.

The total cross section of the process $e^{+}{e}^{-}\to \mathrm{\Lambda }\overline{\mathrm{\Lambda }}$ is calculated within the energy range close to the mass of the $\psi (3770)$ charmonium state. Two different contributions were considered: the $D$-meson loop and the three gluon charmonium annihilation one. Both of them contribute noticeably and in sum, fairly reproduce the data. Large relative phase for these contributions are generated with respect to the pure electromagnetic mechanism. As a by-product, the fit for the electromagnetic form factor of $\mathrm{\Lambda }$ hyperon is obtained for the large momentum transferred region.

We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments. Our investigation corrects and builds upon previous studies by carefully accounting for the gauge dependence of relevant quantities. We work in a preferred frame for the laboratory, the proper detector frame, and show how to resum short-wavelength effects to provide analytic results that are exact for GWs of arbitrary wavelength. This formalism allows us to firmly establish that, contrary to previous claims, cavity experiments designed for the detection of axion dark matter only need to reanalyze existing data to search for high-frequency GWs with strains as small as $h\sim {10}^{-22}–{10}^{-21}$. We also argue that directional detection is possible in principle using readout of multiple cavity modes. Further improvements in sensitivity are expected with cutting-edge advances in superconducting cavity technology.

In an SU(2) gauge theory, if the gauge bosons turn out to be degenerate after spontaneous symmetry breaking, obviously these mass terms are invariant under a global SU(2) symmetry that is unbroken. The pure gauge terms are also invariant under this symmetry. This symmetry is called the custodial symmetry (CS). In $\mathrm{SU}(2)\times \mathrm{U}(1)$ gauge theories, CS implies a mass relation between the $W$ and the $Z$ bosons. The Standard Model, as well as various extensions of it in the scalar sector, possesses such a symmetry. In this paper, we critically examine the notion of CS and show that there may be three different classes of CS, depending on the gauge couplings and self-couplings of the scalars. Among old models that preserve CS, we discuss the two-Higgs-doublet model and the one-doublet plus two-triplet model by Georgi and Machacek. We show that for two-triplet extensions, the Georgi-Machacek model is not the most general possibility with CS. Rather, we find, as the most general extension, a new model with more parameters and hence a richer phenomenology. Some of the consequences of this new model have also been discussed.

We investigate the potential for searching and identifying the leptoquark (LQ) effects in the charm sector through the low-energy polarized scattering processes, ${\overrightarrow{e}}^{-}p\to e^{-}{\mathrm{\Lambda }}_c$, $e^{-}\overrightarrow{p}\to e^{-}{\mathrm{\Lambda }}_c$, and ${\overrightarrow{e}}^{-}\overrightarrow{p}\to e^{-}{\mathrm{\Lambda }}_c$. Considering only the longitudinally polarized processes, we show that the different LQ models can be disentangled from each other by measuring the four spin asymmetries, $A_L^e$, $A_L^p$, $A_{L3}^{ep}$, and $A_{L6}^{ep}$, constructed in terms of the polarized cross sections. Although it is challenging to accomplish the same goal with transversely polarized processes, we find that investing them in future experiments is especially beneficial since they can directly probe into the imaginary part of the Wilson coefficients in the general low-energy effective Lagrangian. With our properly designed experimental setups, it is also demonstrated that promising event rates can be expected for all these processes and, even in the worst-case scenario—no LQ signals observed at all—they can still provide a competitive potential for constraining the new physics, compared with those from the conventional charmed-hadron weak decays and the high-$p_T$ dilepton invariant mass tails at high-energy colliders.

We critically examine a number of theoretical uncertainties affecting the MiniBooNE short-baseline neutrino oscillation experiment in an attempt to better understand the observed excess of electronlike events. We reexamine the impact of fake charged current quasielastic events, the background due to neutral current ${\pi }^0$ production, and the single-photon background. For all processes, we compare the predictions of different event generators (genie, gibuu, nuance, and nuwro) and, for genie, of different tunes. Where MiniBooNE uses data-driven background predictions, we discuss the uncertainties affecting the relation between the signal sample and the control sample. In the case of the single-photon background, we emphasize the uncertainties in the radiative branching ratios of heavy hadronic resonances. We find that not even a combination of uncertainties in different channels adding up unfavorably (an “Altarelli cocktail”) appears to be sufficient to resolve the MiniBooNE anomaly. We finally investigate how modified background predictions affect the fit of a $3+1$ sterile neutrino scenario. We carefully account for full four-flavor oscillations not only in the signal but also in the background and control samples. We emphasize that, because of the strong correlation between MiniBooNE’s ${\nu }_e$ and ${\nu }_{\mu }$ samples, a sterile neutrino mixing only with ${\nu }_{\mu }$ is sufficient to explain the anomaly, even though the well-known tension with external constraints on ${\nu }_{\mu }$ disappearance persists.

Motivated by the prospect of quantum simulation of quantum field theories, we formulate the $O(N)$ nonlinear sigma model as a “qubit” model with an ($N+1$)-dimensional local Hilbert space at each lattice site. Using an efficient worm algorithm in the worldline formulation, we demonstrate that the model has a second-order critical point in ($2+1$) dimensions, where the continuum physics of the nontrivial $O(N)$ Wilson-Fisher fixed point is reproduced. We compute the critical exponents $\nu$ and $\eta$ for the $O(N)$ qubit models up to $N=8$, and find excellent agreement with known results in literature from various analytic and numerical techniques for the $O(N)$ Wilson-Fisher universality class. Our models are suited for studying $O(N)$ nonlinear sigma models on quantum computers up to $N=8$ in $d=2$, 3 spatial dimensions.

We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $\eta /s$. The pointlike interaction rates of hadrons are evaluated through the $S$-matrix approach in the presence of a magnetic field to obtain the temperature and magnetic-field-dependent relaxation time. We observe that the transport coefficients are anisotropic in the presence of the magnetic field. We calculate the temperature and magnetic-field-dependent anisotropic shear viscosity coefficients by incorporating the estimated relaxation time. The value of viscosity over entropy density is lower in the presence of a magnetic field than the value of it in a thermal medium. The behavior of the perpendicular components of the shear-viscous coefficient is also discussed. We consider the temperature-dependent hadron masses from mean-field effects in this work.

We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium in theories with nontrivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large $N_c$, the reduced density matrices that “resum” the leading rapidity logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov-like evolution equations. We study their entanglement entropy in a simplified $1+1$ toy model and in 3D QCD. The entanglement entropy in these cases, after resummation, is shown to saturate the Kolmogorov-Sinai bound of 1. Remarkably, in 3D QCD the essential growth rate of the entanglement entropy is found to vanish at large rapidities, a result of kinematical “quenching” in transverse space. The one-body reduction of the entangled density matrix obeys a Balitsky-Fadin-Kuraev-Lipatov evolution equation, which can be recast as an evolution in an emergent AdS space, at large impact parameter and large rapidity. This observation allows the extension of the perturbative wee parton evolution at low $x$, to a dual nonperturbative evolution of string bits in curved ${\mathrm{AdS}}_5$ space, with manifest entanglement entropy in the confining regime.

We discuss quantum entanglement between fast and slow degrees of freedom, in a two-dimensional (2D) large $N_c$ gauge theory with Dirac quarks, quantized on the light front. Using the ’t Hooft wave functions, we construct the reduced density matrix for an interval in the momentum fraction $x$ space, and calculate its von Neumann entropy in terms of structure functions, that are measured by deep inelastic scattering on mesons (hadrons in general). We found that the entropy is bounded by an area law with logarithmic divergences, proportional to the rapidity of the meson. The evolution of the entanglement entropy with rapidity is fixed by the cumulative singlet parton distribution function (PDF), and bounded from above by a Kolmogorov-Sinai entropy of 1. At low $x$, the entanglement exhibits an asymptotic expansion, similar to the forward meson-meson scattering amplitude in the Regge limit. The evolution of the entanglement entropy in parton $x$ per unit rapidity measures the meson singlet PDF. The resummed entanglement entropy along the single meson Regge trajectory is stringlike. We suggest that its extension to multimeson states models deep inelastic scattering on a large 2D“nucleus.” The result is a large rate of change of the entanglement entropy with rapidity, that matches the current Bekenstein-Bremermann bound for maximum quantum information flow. This mechanism may be at the origin of the large entropy deposition and rapid thermalization, reported in current heavy ion colliders, and may extend to future electron-ion colliders.

We present next-to-leading order QCD corrections to $B_c\to {\eta }_c$ and $B_c\to J/\psi$ tensor form factors within the nonrelativistic QCD framework. The full analytical results for $B_c$ to $S$-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviors of tensor form factors in the hierarchy heavy quark limit, i.e., $m_b\to \infty$, $m_c\to \infty$, and $m_c/m_b\to 0$. A compact expression for tensor form factors is given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed, especially at the large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given at the end.

We present the first study of production of $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons in hadronic matter. Quark interchange between two colliding charmed mesons leads to the production of the three mesons. We calculate unpolarized cross sections for the reactions $D\overline{D}\to \rho R$, $D{\overline{D}}^{*}\to \pi R$, $D{\overline{D}}^{*}\to \rho R$, $D^{*}\overline{D}\to \pi R$, $D^{*}\overline{D}\to \rho R$, $D^{*}{\overline{D}}^{*}\to \pi R$, and $D^{*}{\overline{D}}^{*}\to \rho R$, where $R$ stands for $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$. In the temperature region covering hadronic matter, the peak cross sections of producing $\psi (4040)$ are similar to or larger than the ones of producing $\psi (4415)$, and the latter are generally larger than those of producing $\psi (4160)$. With the cross sections, we establish new master rate equations for $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$. The equations are solved for central Pb-Pb collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ at the Large Hadron Collider. Solutions of the equations show that the $\psi (4040)$ number density at kinetic freeze-out of hadronic matter is larger than the $\psi (4415)$ number density, which is larger than the $\psi (4160)$ number density.

Machine learning techniques have been employed for the high energy physics community since the early 80s to deal with a broad spectrum of problems. This work explores the prospects of using deep learning techniques to estimate elliptic flow ($v_2$) in heavy-ion collisions at the RHIC and LHC energies. A novel method is developed to process the input observables from particle kinematic information. The proposed deep neural network (DNN) model is trained with Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}$ minimum bias events simulated with a multiphase transport model. The predictions from the machine learning technique are compared to both simulation and experiment. The deep learning model seems to preserve the centrality and energy dependence of $v_2$ for the LHC and RHIC energies. The DNN model is also quite successful in predicting the $p_{\mathrm{T}}$ dependence of $v_2$. When subjected to event simulation with additional noise, the proposed DNN model still keeps the robustness and prediction accuracy intact up to a reasonable extent.