In this paper, we present a detailed analysis of first-order perturbations of the Kerr metric in the slow-rotation limit. We perform the calculation by perturbing the Schwarzschild metric plus up to second-order corrections in the spin in the Regge-Wheeler gauge. The apparent coupling between different angular momentum axial-led and polar-led modes can be removed by suitably combining the perturbation equations and projecting them onto spin-weighted spherical harmonics. In this way, we derive the corrections to the Regge-Wheeler and the Zerilli equations up to second order in the spin. We show that the two potentials remain isospectral as in the nonrotating limit. However, it is easy to demonstrate it only for a precise choice of the tortoise coordinate. The isospectrality with a slowly rotating Teukolsky equation is also verified. We discuss the main implication of this result for the problem of vacuum metric reconstruction, providing the transformation rule between slow-spinning Teukolsky variables and metric perturbations. The existence of this relation leaves us with the conjecture that a resummation of the expansion in the spin is possible, leading to two decoupled differential equations for perturbations of the Kerr metric.

Black holes have a unique sensitivity to the presence of ultralight matter fields or modifications of the underlying theory of gravity. In the present paper we combine both features by studying an ultralight, dynamical scalar field that is nonminimally coupled to the gravitational Chern-Simons term. In particular, we numerically simulate the evolution of such a scalar field around a rotating black hole in the decoupling approximation and find a new kind of massive scalar hair anchored around the black hole. In the proximity of the black hole, the scalar exhibits the typical dipolar structure of hairy solutions in (massless) dynamical Chern-Simons gravity. At larger distances, the field transitions to an oscillating scalar cloud that is induced by the mass term. Finally, we complement the time-domain results with a spectral analysis of the scalar field characteristic frequencies.

Strong lensing of gravitational-wave signals can produce three types of images, denoted as type-I, type-II, and type-III, corresponding to the minima, saddle, and maxima, respectively, of the lensing potential of the lensed images. Type-II images, in particular, receive a nontrivial phase shift of $\pi /2$. This phase shift can introduce additional distortions in the strains produced by the type-II image of the binary black hole signals depending on the morphology of the signals, e.g., when they have contributions from higher harmonics, precession, eccentricity, etc. The probability of observing type-II images is nearly the same as that of strong lensing itself, and, thus, these signals are likely to be observed in the near future. In this work, we investigate the potential applicability of these distortions in helping identify type-II signals from a single detection and the systematic biases that could arise in the inference of parameters if they are recovered with gravitational-wave templates that do not take the distortion into account. We show that the lensing distortions will allow us to confidently identify the type-II images for highly inclined binaries: At network signal-to-noise ratio (SNR) $\rho =20(50)$, individual type-II images should be identifiable with ln Bayes factor $\ln \mathcal{B}>2$ for inclinations $\iota >5\pi /12(\pi /3)$. Furthermore, based on the trends we observe in these results, we predict that, at high SNRs ($\gtrsim 100$), individual type-II images would be identifiable even when the inclination angle is much lower ($\sim \pi /6$). We then show that neglecting physical effects arising from these identifiable type-II images can significantly bias the estimates of source parameters (such as sky location, distance, inclination, etc.). Thus, in the future, using templates that take into account the lensing deformation would be necessary to extract source parameters from type-II lensed signals.

New probes of neutrino mixing are needed to advance precision studies. One promising direction is via the detection of low-energy atmospheric neutrinos (below a few hundred MeV), to which a variety of near-term experiments will have much-improved sensitivity. Here we focus on probing these neutrinos through distinctive nuclear signatures of exclusive neutrino-carbon interactions—those that lead to detectable nuclear-decay signals with low backgrounds—in both neutral-current and charged-current channels. The neutral-current signature is a line at 15.11 MeV and the charged-current signatures are two or threefold coincidences with delayed decays. We calculate the prospects for identifying such events in the Jiangmen Underground Neutrino Observatory (JUNO), a large-scale liquid-scintillator detector. A five-year exposure would yield about 16 neutral-current events (all flavors) and about 16 charged-current events (mostly from ${\nu }_e+{\overline{\nu }}_e$, with some from ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$), and thus roughly 25% uncertainties on each of their rates. Our results show the potential of JUNO to make the first identified measurement of sub-100 MeV atmospheric neutrinos. They also are a step towards multi-detector studies of low-energy atmospheric neutrinos, with the goal of identifying additional distinctive nuclear signatures for carbon and other targets.

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale $Q^2$) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale $Q_0^2$) by data that has a finite $Q^2$ range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that $Q^2$ evolution, given empirical data over a wide range of skewness ($\xi$) and $Q^2$ scales, constrains the SGPDs studied at low $x$ and low $\xi$. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of $x$ and $\xi$.

Urgent theoretical progress is needed in order to provide an estimate in the Standard Model of the recent measurement by LHCb of direct $CP$ violation in charm-meson two-body decays. Rescattering effects must be taken into account for a meaningful theoretical description of the amplitudes involved in such category of observables, as signaled by the presence of large strong phases. We discuss the computation of the latter effects based on a two-channel coupled dispersion relation, which exploits isospin-zero phase shifts and inelasticity parametrizations of data coming from the rescattering processes $\pi \pi \to \pi \pi$, $\pi K\to \pi K$, and $\pi \pi \to K\overline{K}$. The determination of the subtraction constants of the dispersive integrals relies on the leading contributions to the transition amplitudes from the $1/N_C$ counting, where $N_C$ is the number of QCD colors. Furthermore, we use the measured values of the branching ratios to help in selecting the nonperturbative inputs in the isospin limit, from which we predict values for the $CP$ asymmetries. We find that the predicted level of $CP$ violation is much below the experimental value.

We formulate the path integral of two- and three-flavor Wilson fermion in two dimensions as a multilayer Grassmann tensor network by the matrix product decomposition. Thanks to this new description, the memory cost scaling is reduced from $\mathrm{O}({\mathrm{e}}^{N_f})$ for the conventional construction to $\mathrm{O}(N_f)$. Based on this representation, we develop a coarse-graining algorithm where spatially or temporally adjacent Grassmann tensors are converted into a canonical form along a virtual direction before we carry out the spacetime coarse-graining. Benchmarking with the lattice Gross-Neveu model at finite density, we see that the Silver Blaze phenomenon in the pressure and number density is captured with relatively small bond dimensions.

Using lattice QCD we extract $\pi \pi$ scattering amplitudes with isospin 0, 1, and 2 in low partial-waves at two values of the light quark mass corresponding to $m_{\pi }\sim 283$ and 330 MeV. We confirm expectations of weak repulsion in isospin-2, and the presence of a narrow $\rho$ resonance in isospin-1, and study the pion mass dependence of these channels. In isospin-0 we find that the two pion masses considered straddle the point at which the $\sigma$ transitions from being a stable bound state to being either a virtual bound state or a subthreshold resonance. We discuss the ability of lattice calculations like these to precisely determine the $\sigma$ pole location when it is a resonance, and propose an approach in which the full complement of amplitudes computed in this paper can be used simultaneously to provide more constraint.

We use a potential model to investigate the phenomenology of quarkonium in a thermal rotating medium, where vorticity and spin density are not necessarily in equilibrium. We find that the quarkonium spin density matrix, as well as the binding energy and melting temperature, are sensitive to both the vorticity and the lack of equilibrium between vorticity and spin. This means that quarkonium spin alignment is a sensitive probe for vorticity and spin within the hydrodynamic phase. Information unequivocally pointing to spin-orbit nonequilibrium dynamics can be obtained from a combined study of quarkonium relative abundance and spin alignment, as well as experimentally obtainable off-diagonal density matrix elements.

A search for flavor-changing neutral-current couplings between a top quark, an up or charm quark, and a $Z$ boson is presented, using proton–proton collision data at $\sqrt{s}=13\mathrm{TeV}$ collected by the ATLAS detector at the Large Hadron Collider. The analyzed data set corresponds to an integrated luminosity of $139{\mathrm{fb}}^{-1}$. The search targets both single-top-quark events produced as $gq\to tZ$ (with $q=u$, $c$) and top-quark-pair events, with one top quark decaying through the $t\to Zq$ channel. The analysis considers events with three leptons (electrons or muons), a $b$-tagged jet, possible additional jets, and missing transverse momentum. The data are found to be consistent with the background-only hypothesis and 95% confidence-level limits on the $t\to Zq$ branching ratios, assuming only tensor operators of the Standard Model effective field theory framework contribute to the $tZq$ vertices. These are $6.2\times {10}^{-5}$ ($13\times {10}^{-5}$) for $t\to Zu$ ($t\to Zc$) for a left-handed $tZq$ coupling, and $6.6\times {10}^{-5}$ ($12\times {10}^{-5}$) in the case of a right-handed coupling. These results are interpreted as 95% CL upper limits on the strength of the corresponding couplings, yielding limits for $|C_{uW}^{(13)*}|$ and $|C_{uB}^{(13)*}|$ ($|C_{uW}^{(31)}|$ and $|C_{uB}^{(31)}|$) of 0.15 (0.16), and limits for $|C_{uW}^{(23)*}|$ and $|C_{uB}^{(23)*}|$ ($|C_{uW}^{(32)}|$ and $|C_{uB}^{(32)}|$) of 0.22 (0.21), assuming a new-physics energy scale ${\mathrm{\Lambda }}_{\mathrm{NP}}$ of 1 TeV.

Quantum study of supersymmetric theories on Euclidean two dimensional anti–de Sitter space (${\mathrm{AdS}}_2$) is invalid if we use the standard normalizable functional basis due to its incompatibility with supersymmetry. We cure this problem by demonstrating that supersymmetry requires a complexified spectrum and constructing the supersymmetric basis for scalar and spinor fields. Our new basis is free of fermionic zero modes, delta-function normalizable with respect to a newly defined inner product, and compatible with the supersymmetric asymptotic boundary condition. We also explore the one-loop evaluation using this basis and show that it agrees with the standard nonsupersymmetric basis up to a global contribution arising from the fermion zero mode.

We investigate the kinematic topologies of light rings (LRs) and massive particle rings (PRs) encircling spherical and axisymmetric black holes. Our results demonstrate that the global topology number of LRs is consistently $-1$ for asymptotically flat and (anti–)de Sitter spacetime. Additionally, we show that the global topology of PRs varies, with a value of 0 in asymptotically flat and anti–de Sitter spacetime but $-1$ in asymptotic de Sitter spacetime.

Extreme mass-ratio inspirals (EMRIs) are the most potential sources detectable by the Laser Interferometer Space Antenna (LISA). To analyze the influence of higher harmonics on parameter estimation for EMRIs efficiently, we use the waveform model that the phase trajectories are relativistic flux-based adiabatic trajectories and the waveforms are constructed by the augmented analytic kludge method. We perform a Fisher-matrix error analysis of the EMRI parameters using signals taking into account the motion of the LISA constellation and higher harmonics of gravitational waves. Our results demonstrate that including higher harmonics greatly reduces the errors on the exterior parameters such as inclination angle $\iota$, the luminosity distance $d_L$, the polarization angle $\psi$, and the initial phase ${\mathrm{\Phi }}_0$, except for source localization $\mathrm{\Delta }\mathrm{\Omega }$ when EMRIs face us. However, the influence of higher harmonics on parameters $(\iota ,d_L,\psi ,{\mathrm{\Phi }}_0)$ can be negligible when the inclination angle is above 1.0. For intrinsic parameters such as the spin of central black and the masses of binaries, the influence of higher harmonics can be negligible for any inclination angle. Our findings are independent of the mass or spin of the EMRI system.

Time delay interferometry (TDI) is primarily proposed for space-borne heterodyne interferometers to suppress the intrinsic laser phase noise. According to the TDI algorithm, the targeted sensitivity is achieved by constructing a virtual equal-arm interferometer through a linear combination of appropriately time-shifted independent Doppler measurements. To maximize the potential capability of the experimental apparatus, it is desirable to obtain the sensitivity limit of a specific detector among different TDI combinations. In this paper, we evaluate the detector’s sensitivity functions in terms of generators of the kernel of a homomorphism map determined by the underlying TDI equation. The analysis is based on decomposing an arbitrary second-generation TDI combination as a linear combination of independent first and zeroth-generation generators. As one ignores the difference in the armlengths, it is found that the sensitivity function can be classified in terms of a smaller set of independent generators. In particular, the equal armlength approximation simplifies the underlying TDI equation as well as the resultant analytic expressions of sensitivity functions. By enumerating all 45 distinct TDI combinations up to sixteen links obtained using the geometric TDI approach, eleven distinct elementary sensitivity curves are derived in terms of the relevant generators. The observed degeneracies in sensitivity curves are explained using algebraic arguments. The obtained analytic results are understood to be helpful in characterizing the quality and improving the implementation of specific TDI solutions.

We have investigated whether the Scalar-Tensor-Vector Gravity (STVG) theory may explain the kinematic of stars in dwarf spheroidal galaxies. STVG modifies general relativity by adding extra scalar and vector fields with the main aim of replacing dark matter in astrophysical self-gravitating systems. The weak-field limit of STVG brings a Yukawa-like modification to the Newtonian gravitational potential. The modification is modulated by two parameters, $\alpha$ and $\mu$, that represent a redefinition of the gravitational coupling constant and the mass of the additional vector fields, respectively. Thus, adopting the modified gravitational potential arising in the weak-field limit of STVG, we have solved the spherical Jeans equation to predict the line-of-sight velocity dispersion profiles of eight dwarf spheroidal galaxies orbiting around the Milky Way. The predicted profiles are then compared to the data using a Monte Carlo Markov chain algorithm. Our results pointed out some tensions on the $\alpha$ parameter within the dataset, while comparison with previous analysis shows the effectiveness of STVG in replacing dark matter with extra massive fields. Further improvements will require more sophisticated modeling of the line-of-sight velocity dispersion which will be possible as soon as high-precision astrometric data in dwarf spheroidals will become available.

We present a consistent one-loop calculation for the inflationary tensor power spectrum in the presence of an excited spectator scalar field using the in-in formalism. We find that the superhorizon primordial power spectrum of the tensor mode can be scale-invariantly enhanced or reduced by the loop effects of a subhorizon scalar field. Our calculation also includes the scalar-induced gravitational wave spectrum classically computed in the previous literature, which is significant only near the scales where the scalar field is amplified. The superhorizon enhancement is a higher-order effect of the interaction Hamiltonian, which can be understood as a Bogoliubov transformation introduced by nonlinear interactions. On the other hand, the scale-invariant reduction of the tensor power spectrum may occur due to the fourth-order scalar-scalar-tensor-tensor coupling. This phenomenon can be understood as the evolution of an anisotropic Bianchi type-I background in the separate universe approach. Our result suggests that large-scale measurements may indirectly test the dramatic effects of small-scale cosmological perturbations through loop corrections. This possibility opens a new ground in probing the small-scale physics of the primordial Universe through gravitational wave detectors of cosmological scales.

We study dark energy cosmological models, extensions of the standard model of particles, characterized by having an extra relativistic energy density at very early times, and that rapidly dilute after a phase transition occurs. These models generate well-localized features (or bumps) in the matter power spectrum for modes crossing the horizon during the phase transition epoch. This is because the presence of the additional energy component enhances the growth of matter fluctuations. Instead of considering a particular model, we focus on a parametric family of Gaussian bumps in the matter power spectrum, which otherwise would be a $\mathrm{\Lambda }\mathrm{CDM}$ one. We study the evolution of such bump cosmologies and their effects in the halo mass function and halo power spectrum using $N$-body simulations, the halo-model based hmcode method, and the peak background split framework. The bumps are subject to different nonlinear effects that become physically well understood, and from them we are able to predict that the most distinctive features will show up for intermediate halo masses ${10}^{12.3}{\mathrm{h}}^{-1}{M}_{\odot }<\mathrm{M}<{10}^{13.6}{\mathrm{h}}^{-1}{M}_{\odot }$. Out of this range, we expect halos are not significantly affected regardless of the location of the primordial bump in the matter power spectrum. Our analytical results are accurate and in very satisfactory agreement with the simulated data.

Stimulated emission is shown to be robust in stars. Through Bose enhancement this produces quantum states of aligned, monochromatic photons somewhat similar to a laser. The probability of creating such states is computed. We show that from the solar corona such quantum states would propagate outside of the solar region and through the Solar System without decoherence. For a $1\text{−}{\mathrm{m}}^2$ test detector at the distance of the Earth from the Sun, we estimate rates of such quantum states in the few per second thus potentially detectable. The same process should lead to such quantum states also arriving from stars at interstellar distances.

We calculate the leading twist pion unpolarized transverse momentum distribution $f_1(x,k_T^2)$ and the Boer-Mulders function $h_1^{\perp }(x,k_T^2)$, using leading Fock-state light front wave functions (LF-LFWFs) based on Dyson-Schwinger and Bethe-Salpeter equations (DS-BSEs). These DS-BSEs based LF-LFWFs provide dynamically generated s- and p-wave components, which are indispensable in producing the chirally odd Boer-Mulders function that has one parton spin flipped. Employing a nonperturbative SU(3) gluon rescattering kernel to treat the gauge link of the Boer-Mulders function, we thus obtain both transverse momentum dependent parton distribution functions at hadronic scale and then evolve them to the scale of ${\mu }^2=4.0{\mathrm{GeV}}^2$. We finally calculate the generalized Boer-Mulders shift and find it to be in agreement with the lattice quantum chromodynamics prediction.

In an axiverse with numerous axions, the cosmological moduli problem poses a significant challenge because the abundance of axions can easily exceed that of dark matter. The well-established stochastic axion scenario offers a simple solution, relying on relatively low-scale inflation. However, axions are typically subject to mixing due to mass and kinetic terms, which can influence the solution using stochastic dynamics. Focusing on the fact that the QCD axion has a temperature-dependent mass, unlike other axions, we investigate the dynamics of the QCD axion and another axion with mixing. We find that the QCD axion abundance is significantly enhanced and becomes larger than that of the other axion for a certain range of parameters. This enhancement widens the parameter regions accounting for dark matter. In addition, we also find a parameter region in which both axions have enhanced abundances of the same order, which result in multicomponent dark matter.