We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric space-times, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations are of second order; this fact allows for analytic solutions and considerably simplifies the derivation of results of previous studies based on the original Harada equations. In particular, we prove the equivalence of the known third-order field equations, with the second-order ones obtained by us in the conformal Killing parametrization. The structure of the Ricci tensor and of the conformal Killing tensor are compatible with both anisotropic fluid sources and (non)linear electrodynamics. We reobtain covariantly and in simple steps the general static spherical solutions for vacuum and linear electrodynamics. Moreover we recover the purely magnetic Lagrangian functions that induce metrics of interest for black holes.

In Einstein-Aether gravity, we revisit the issue of linear stabilities of black holes against odd-parity perturbations on a static and spherically symmetric background. In this theory, superluminal propagation is allowed and there is a preferred timelike direction along the unit Aether vector field. If we choose the usual spherically symmetric background coordinates with respect to the Killing time $t$ and the areal radius $r$, it may not be appropriate for unambiguously determining the black hole stability because the constant $t$ hypersurfaces are not necessarily always spacelike. Unlike past related works of black hole perturbations, we choose an Aether-orthogonal frame in which the timelike Aether field is orthogonal to spacelike hypersurfaces over the whole background spacetime. In the short wavelength limit, we show that no-ghost conditions as well as radial and angular propagation speeds coincide with those of vector and tensor perturbations on the Minkowski background. Thus, the odd-parity linear stability of black holes for large radial and angular momentum modes is solely determined by constant coefficients of the Aether derivative couplings.

Recent advances in high-energy and high-peak-power laser systems have opened up new possibilities for fundamental physics research. In this work, the potential of twisted light for the generation of gravitational waves in the high frequency regime is explored for the first time. Focusing on Bessel beams, novel analytic expressions and numerical computations for the generated metric perturbations and associated powers are presented. The gravitational peak intensity is shown to reach $1.44\times {10}^{-5}{\mathrm{W}\mathrm{m}}^{-2}$ close to the source, and $1.01\times {10}^{-19}{\mathrm{W}\mathrm{m}}^{-2}$ ten meters away. Compelling evidence is provided that the properties of the generated gravitational waves, such as frequency, polarization states, and direction of emission, are controllable by the laser pulse parameters and optical arrangements.

We propose a new method to investigate signatures of a quantum gravity phase in the primordial state of cosmological perturbations. We formulate and study a quantum model of a perturbed Friedmann-Lemaître-Robertson-Walker universe beyond a tensor-product Born-Oppenheimer-like factorization, that is, without restricting the wave function of the universe to the product of the background and perturbation wave functions. We show that the quantum dynamics generically does not preserve the product form of the universe’s wave function, which spontaneously evolves into a more general entangled state. Upon expanding this state in a suitable basis of background wave functions and setting Gaussian initial conditions for the perturbations, we numerically find that each of these wave functions becomes associated with a non-Gaussian state of an inhomogeneous perturbation.

This paper explores the use of low-dimensional parametric representations of neutron-star equations of state that include discontinuities caused by phase transitions. The accuracies of optimal piecewise-analytic and spectral representations are evaluated for equations of state having first- or second-order phase transitions with a wide range of discontinuity sizes. These results suggest that the piecewise-analytic representations of these nonsmooth equations of state are convergent, while the spectral representations are not. Nevertheless, the lower-order ($2\le N_{\text{parms}}\le 7$) spectral representations are found to be more accurate than the piecewise-analytic representations with the same number of parameters.

This study investigates the first-order phase transition within neutron stars, leveraging the deep neural network (DNN) framework alongside contemporary astronomical measurements. The equation of state (EOS) for neutron stars is delineated in a piecewise polytropic form, with the speed of sound ($c_s$) serving as a pivotal determinant. In the phase transition region, $c_s$ is presumed to be zero, while in other intervals, it is optimized utilizing the DNN. Various onset energy densities of phase transition (${ϵ}_{pt}$), spanning from $2{ϵ}_0$ to $3{ϵ}_0$ (where ${ϵ}_0$ denotes the energy density at nuclear saturation density), as well as phase transition widths ($\mathrm{\Delta }ϵ$) ranging from $0.5{ϵ}_0$ to ${ϵ}_0$, are examined. Our findings underscore that smaller values of ${ϵ}_{pt}$ lead to a more substantial impact of $\mathrm{\Delta }ϵ$ on neutron star properties, encompassing maximum mass, corresponding radius, tidal deformability, phase transition mass, and trace anomaly. Conversely, when ${ϵ}_{pt}$ exceeds $2.5{ϵ}_0$, the influence of $\mathrm{\Delta }ϵ$ diminishes, resulting in a stiffer EOS compared to scenarios lacking a phase transition. Furthermore, the trace anomaly at high density shifts to negative values upon the commencement of the phase transition. It is noteworthy that the correlations between the average speed of sound at different energy density segments demonstrate a notably weak connection. The discernment of whether a phase transition has occurred with the present observables of neutron stars poses a challenging task.

We consider a scalar quantum field theory with global $O(N{)}^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-$N$ limit. For imaginary tetrahedral coupling the theory is asymptotically free, with stable and real quantum effective action. We demonstrate the dynamical build-up of a strong interaction as the correlation length increases in a regime where the coupling renormalization flow remains well defined in the infrared. This is in contrast to perturbative results of asymptotically free theories, which predict that the coupling becomes ill defined in the infrared, like in quantum chromodynamics. These properties make the model an important laboratory for the study of strong-coupling phenomena in quantum field theory from first principles.

We propose a hybrid scoto-seesaw model based on the $A_4\times Z_4\times Z_3\times Z_2$ non-Abelian discrete flavor symmetry. Light neutrino masses come from the tree-level type-I seesaw mechanism, and from the one-loop scotogenic contribution accommodating viable dark matter candidates responsible for the observed relic abundance of dark matter (DM). These contributions restore the atmospheric and solar neutrino mass scales, respectively. With only one right-handed neutrino, the model features specific predictions with the normal ordering of light neutrino masses, the lightest neutrino being massless, and only one relevant $CP$ Majorana phase. Further, an experimentally favorable ${\mathrm{TM}}_1$ mixing scheme is realized with concrete correlations and constraints on the mixing angles and associated $CP$ phases. The model predicts the atmospheric mixing angle to be in the upper octant with specific ranges $0.531(0.580)\le {\sin }^2{\theta }_{23}\le 0.544(0.595)$, and the Dirac $CP$ phase is restricted within the range $\pm (1.44–1.12)\mathrm{rad}$. The Majorana phase is also tightly constrained, with the ranges 0.82–0.95 and 1.58–1.67 rad, which are otherwise unconstrained from neutrino oscillations. Strict predictions on the Majorana phases also yield an accurate prediction for the effective mass parameter for neutrinoless double beta within the range of 1.61–3.85 meV. The model offers a rich phenomenology regarding DM relic density and direct-search constraints, and the fermionic DM scenario has been discussed in detail, estimating its possible connection with the neutrino sector. As an example of the model studies at colliders, the SM Higgs in the diphoton decay channel is examined. The model predicts strictly vanishing $\tau \to e\gamma$, $\tau \to 3e$ decays and testable signals by MEG-II and SINDRUM/Mu3e experiments for the $\mu \to e\gamma$ and $\mu \to 3e$ decays, respectively.

Wen study the renormalization of a complete set of gauge-invariant gluon nonlocal operators in lattice perturbation theory. We determine the mixing pattern under renormalization of these operators using symmetry arguments, which extend beyond perturbation theory. Additionally, we derive the renormalization factors of the operators within the modified minimal subtraction $(\overline{\mathrm{MS}})$ scheme up to one loop. To enable a nonperturbative renormalization procedure, we investigate a suitable version of the modified regularization-invariant (${\mathrm{RI}}^{\prime }$) scheme, and we calculate the conversion factors from that scheme to $\overline{\mathrm{MS}}$. The computations are performed by employing both dimensional and lattice regularizations, using the Wilson gluon action. This work is relevant to nonperturbative studies of the gluon parton distribution functions (PDFs) on the lattice.

The lattice SU(2) gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations that have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism. In this paper, we reexamine this phase structure in a gauge-independent way based on the numerical simulations performed without any gauge fixing. This is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanism for generating the mass of the gauge field without relying on any spontaneous symmetry breaking. For this purpose, we investigate correlations between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field which is constructed from the gauge field based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. Consequently, we reproduce gauge independently the transition line separating the confinement phase and the Higgs phase, and show surprisingly the existence of a new transition line that completely divides the confinement phase into two parts. Finally, we discuss the physical meaning of the new transition and the implications of the confinement mechanism.

Motivated by recent experimental evidence for apparent $cc\overline{c}\overline{c}$ states by LHCb, CMS and ATLAS, we consider how the mass spectrum and decays of such states can be used to discriminate among their possible theoretical interpretations, with a particular focus on identifying whether quarks or diquarks are the most relevant degrees of freedom. Our preferred scenario is that $X(6600)$ and its apparent partner state $X(6400)$ are the tensor $(2^{++})$ and scalar $(0^{++})$ states of an S-wave multiplet of $cc\overline{c}\overline{c}$ states. Using tetraquark mass relations which are independent of (or only weakly dependent on) model parameters, we give predictions for the masses of additional partner states with axial and scalar quantum numbers. Additionally, we give predictions for relations among decay branching fractions to $J/\psi J/\psi$, $J/\psi {\eta }_c$, ${\eta }_c{\eta }_c$, and $D^{(*)}{\overline{D}}^{(*)}$ channels. The scenario we consider is consistent with existing experimental data on $J/\psi J/\psi$, and our predictions for partner states and their decays can be confronted with future experimental data, to discriminate between quark and diquark models.

By utilizing a background field effective theory, we compute the collisional energy loss of a heavy quark moving through a semiquark-gluon plasma characterized by nontrivial holonomy for Polyakov loops. We consider the elastic scatterings between the incident heavy quark and the thermal partons with both hard and soft momentum transfers. As compared to the energy loss obtained from the perturbation theory, the hard processes get modified through the thermal distribution functions that depend on the background field, while the proper treatment of the soft processes strongly relies on the use of the hard-thermal-loop resummed gluon propagator derived from the background field effective theory. Our results show that the heavy quark energy loss is significantly suppressed in the semiquark-gluon plasma due to a background field that is self-consistently generated in the effective theory. On the other hand, the suppression has a strong dependence on the temperature of the plasma, which becomes negligible above 2–3 times the critical temperature. For a realistic coupling constant, ignoring a relatively weak dependence on the heavy quark velocity, the suppression on the collisional energy loss can be approximated by an overall factor determined solely by the background field. This simple conclusion is expected to be useful for phenomenological applications in the heavy flavor physics.

A search for the nonresonant production of Higgs boson pairs in the $HH\to b\overline{b}{\tau }^{+}{\tau }^{-}$ channel is performed using $140{\mathrm{fb}}^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The analysis strategy is optimized to probe anomalous values of the Higgs boson self-coupling modifier ${\kappa }_{\lambda }$ and of the quartic $HHVV$ ($V=W,Z$) coupling modifier ${\kappa }_{2V}$. No significant excess above the expected background from Standard Model processes is observed. An observed (expected) upper limit ${\mu }_{HH}<5.9(3.3)$ is set at 95% confidence-level on the Higgs boson pair production cross section normalized to its Standard Model prediction. The coupling modifiers are constrained to an observed (expected) 95% confidence interval of $-3.1<{\kappa }_{\lambda }<9.0$ ($-2.5<{\kappa }_{\lambda }<9.3$) and $-0.5<{\kappa }_{2V}<2.7$ ($-0.2<{\kappa }_{2V}<2.4$), assuming all other Higgs boson couplings are fixed to the Standard Model prediction. The results are also interpreted in the context of effective field theories via constraints on anomalous Higgs boson couplings and Higgs boson pair production cross sections assuming different kinematic benchmark scenarios.

With the current precision of measurements by the ATLAS and CMS experiments, it cannot be excluded that a standard model (SM)-like Higgs boson is a $CP$ violating mixture of $CP$-even and $CP$-odd states. We explore this possibility here, assuming Higgs boson production in ZZ-fusion, at 1 TeV ILC, with unpolarized beams. The full simulation of SM background and fast simulation of the signal is performed, simulating $8{\mathrm{ab}}^{-1}$ of data collected with the ILD detector. We demonstrate that the $CP$ mixing angle ${\mathrm{\Psi }}_{CP}$ between scalar and pseudoscalar states can be measured with the statistical uncertainty of 3.8 mrad at 68% CL, corresponding to $1.44\times {10}^{-5}$ for the $CP$ parameter $f_{CP}$, for the pure scalar state. This is the first result on sensitivity of an $e^{+}{e}^{-}$ collider to measure $f_{CP}$ in the Higgs production vertex in vector boson fusion.

We report new limits on the kinetic mixing strength of the dark photon spanning the mass range $0.21-1.24\mathrm{\mu }\mathrm{eV}$ corresponding to a frequency span of 50–300 MHz. The Dark E-field Radio experiment is a wideband search for dark photon dark matter. In this paper we detail changes in calibration and upgrades since our proof-of-concept pilot run. Our detector employs a wide-bandwidth E-field antenna moved to multiple positions in a shielded room, a low noise amplifier, wideband analog-to-digital converter, followed by a $2^{24}$-point fast Fourier transform. An optimal filter searches for signals with $\mathrm{Q}\approx {10}^6$. In nine days of integration, this system is capable of detecting dark photon signals corresponding to a kinetic mixing strength $\epsilon$ several orders of magnitude lower than previous limits. We find a 95% exclusion limit on $\epsilon$ over this mass range between $6\times {10}^{-15}$ and $6\times {10}^{-13}$, tracking the complex resonant mode structure in the shielded room.

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In $D=4$, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in $D=4$, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action.

The traditional Chern-Simons (CS) terms in $3+1$ dimensions that modify general relativity (GR), quantum chromodynamics (QCD), and quantum electrodynamics (QED), typically lack scale invariance. However, a locally scale invariant and geodesically complete framework for the Standard Model (SM) coupled to GR was previously constructed by employing a tailored form of local scale (Weyl) symmetry. This refined $\mathrm{SM}+\mathrm{GR}$ model closely resembles the conventional SM in subatomic realms where gravitational effects are negligible. Nevertheless, it offers an intriguing prediction: the emergence of new physics beyond the traditional SM and GR near spacetime singularities, characterized by intense gravity and substantial deviations in the Higgs field. In this study, we expand upon the enhanced $\mathrm{SM}+\mathrm{GR}$ by incorporating Weyl invariant CS terms for gravity, QCD, and QED in $3+1$ dimensions, thereby integrating CS contributions within the locally scale-invariant and geodesically complete paradigm. Additionally, we establish a holographic correspondence between the new CS terms in $3+1$ dimensions and novel ($4+2$)-dimensional CS-type actions within 2T physics. We demonstrate that the Weyl transformation in $3+1$ dimensions arises from $4+2$ general coordinate transformations, which unify the hidden extra $1+1$ large (not curled up) dimensions with the evident $3+1$ dimensions. By leveraging the newfound local conformal symmetry, the augmented and geodesically complete $\mathrm{SM}+\mathrm{GR}+\mathrm{CS}$ introduces innovative tools and perspectives for exploring classical field theory aspects of black hole and cosmological singularities in $3+1$ dimensions, while the ($4+2$)-dimensional connection unveils deeper facets of spacetime.

We study possible ways gravitational waves (GW) are sourced in a theory with minimal left-right symmetry breaking. Generically first order phase transitions (FOPT) lead to gravitational waves sourced by bubble dynamics, while second order phase transitions (SOPT) do not. However, due the presence of two degenerate fields, we obtain domain walls in the putative SOPT case, giving rise to GW via disintegrating domain walls, testable at experiments such as IPTA, DECIGO, and LISA. On the other hand, for the case of FOPT, we get the usual signal from spontaneously created bubbles, but there also arises a late forming domain wall structure separating the two types of vacua. The disintegration of these walls provides an additional source of GW. Thus the parameter range signaling FOPT case gives rise to two distinct peaks in the spectrum of GW. This is verifiable for the low symmetry breaking scales ${10}^4–{10}^6\mathrm{GeV}$, but a high scale such as $\sim {10}^{10}\mathrm{GeV}$ remains beyond the reach of currently planned experiments. Finally, we point out that a version of the left-right symmetric model which separates the scale of parity breaking from that of gauge symmetry breaking is also subject to domain wall formation and amenable to GW observations.

Dark matter relic density has been increasingly accurately measured by successive generations of experiments. The Boltzmann equation determines the yields using the dark matter annihilation cross section as one of the inputs; the accurate computation of the latter including thermal contributions thus assumes importance. We report here the next-to-leading-order (NLO) thermal corrections to the cross sections for (Majorana) dark matter annihilation of standard model fermions, $\chi \chi \to f\overline{f}$, via charged scalars. We use a novel approach, utilizing the technique of Grammer and Yennie, extended to thermal field theories, where the cancellation of soft infrared divergences occurs naturally. We present the NLO thermal cross sections in full detail both for the relativistic case and in the nonrelativistic limit. Our independent calculation verifies earlier results where the leading contribution at order $\mathcal{O}(T^2)$ was shown to be proportional to the square of the fermion mass in the nonrelativistic limit, just as at leading order. We find that the $\mathcal{O}(T^4)$ contributions have the same dependence on the fermion mass as well.

We have applied thermodynamic stability analysis to derive the stability and causality conditions for conventional relativistic viscous hydrodynamics and spin hydrodynamics. We obtain the thermodynamic stability conditions for second-order relativistic hydrodynamics with shear and bulk viscous tensors, finding them identical to those derived from linear mode analysis. We then derive the thermodynamic stability conditions for minimal causal extended second-order spin hydrodynamics in canonical form, both with and without viscous tensors. Without viscous tensors, the constraints from thermodynamic stability exactly match those from linear mode analysis. In the presence of viscous tensors, the thermodynamic stability imposes more stringent constraints than those obtained from linear mode analysis. Our results suggest that conditions derived from thermodynamic stability analysis can guarantee both causality and stability in linear mode analysis.