Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes—while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

We analyze contributions to the electric dipole moment (EDM) and Schiff moment of deuteron induced by the $CP$-violating three-pseudoscalar meson couplings using phenomenological Lagrangian approach involving nucleons and pseudoscalar mesons $P=\pi ,K,\eta ,{\eta }^{\prime }$. Deuteron is considered as a proton-neutron bound state and its properties are defined by one- and two-body forces. One-body forces correspond to a picture there; proton and neutron are quasifree constituents of deuteron and their contribution to the deuteron EDM (dEDM) is simply the sum of proton and neutron EDMs. Two-body forces in deuteron are induced by one-meson exchange between nucleons. They produce a contribution to the dEDM, which is estimated using corresponding potential approach. From numerical analysis of nucleon and deuteron EDMs, we derive stringent limits on $CP$-violating hadronic couplings and $\overline{\theta }$ parameter. We showed that proposed measurements of proton and deuteron EDMs at level of $\sim {10}^{-29}$ by the Store Ring EDM and JEDI Collaborations will provide more stringent upper limits on the $CP$-violating parameters.

In this paper, we propose a scotogenic model of neutrino masses with flavor-dependent $U(1{)}_{B-3L_{\alpha }}(\alpha =e,\mu ,\tau )$ gauge symmetry, in which neutrinos are generated at one-loop level and a fermion dark matter is naturally accommodated. In this model, three one-zero-texture structures of neutrino mass matrix, denoted as patterns A, B and C, are successfully realized by appropriate charge assignment for inert fermions and scalar fields. For each predicted texture, a detailed numerical analysis is carried out to find the allowed regions of neutrino mixing and masses. We find three scenarios (A for normal mass hierarchy and B and C for inverted mass hierarchy) favored by the latest data of neutrino oscillation experiments and Planck 2018 limit on the sum of neutrino masses. Other phenomenologies such as lepton flavor violation, dark matter, and collider signatures are also discussed.

We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides information about the sensitivity of experimental observables to physics beyond the standard model that is not accessible in the Fisher-information method. In principle, the SVD method can also have computational advantages over diagonalization of the Fisher information matrix. We demonstrate the SVD method by applying it to the dimension-6 coefficients for the process of top-quark decay to a $b$ quark and a $W$ boson and use this example to illustrate some pitfalls in widely used fitting procedures. We also outline an iterative procedure for applying the SVD method to dimension-8 SMEFT coefficients.

Topological lumps are known to be present in gluonic fields of $SU(3)$ gluodynamics. Near the transition temperature they were classified either as constituents of nondissociated (anti)calorons, or as constituents of (anti)dyon pairs, or as isolated (anti)dyons. In this paper we study the density and correlation functions of these objects at temperature $T/T_c=0.96$.

We discuss the status of resummation of large logarithmic contributions to groomed event shapes of hadronic final states in electron-positron annihilation. We identify the missing ingredients needed for next-to-next-to-next-to-leading logarithmic (NNNLL) resummation of the modified mass mass drop tagger (mMDT) groomed jet mass in $e^{+}{e}^{-}$ collisions: the low-scale collinear-soft constants at two-loop accuracy, $c_{S_c}^{(2)}$, and the three-loop noncusp anomalous dimension of the global soft function, ${\gamma }_S^{(2)}$. We present a method for extracting those constants using fixed-order codes: the event2 program to obtain the color coefficients of $c_{S_c}^{(2)}$, and mccsm for extracting ${\gamma }_S^{(2)}$. We present all necessary formulae for resummation of the mMDT groomed heavy jet mass distribution at NNNLL accuracy.

An extension of the van der Waals hadron resonance gas (VDWHRG) model which includes the in-medium thermal modification of hadron masses, the thermal VDWHRG (TVDWHRG) model, is considered in this paper. Based on the $2+1$ flavor Polyakov linear sigma model (PLSM) and the scaling mass rule of hadrons, we obtain the temperature behavior of all hadron masses for different fixed baryon chemical potentials ${\mu }_B$. We calculate various thermodynamic observables at ${\mu }_B=0\mathrm{GeV}$ in the TVDWHRG model. An improved agreement with the lattice data from the TVDWHRG model in the crossover region ($T\sim 0.16–0.19\mathrm{GeV}$) is observed as compared to those from the VDWHRG and ideal HRG (IHRG) models. We further discuss the effects of the in-medium modification of hadron masses and VDW interactions between (anti)baryons on the dimensionless transport coefficients, such as the shear viscosity to entropy density ratio ($\eta /s$) and scaled thermal ($\lambda /T^2$) and electrical (${\sigma }_{\mathrm{el}}/T$) conductivities in the IHRG model at different ${\mu }_B$ by utilizing quasiparticle kinetic theory with relaxation time approximation. We find in contrast to the IHRG model, the TVDWHRG model leads to a qualitatively and quantitatively different behavior of transport coefficients with $T$ and ${\mu }_B$.

Recent lattice QCD calculations showed that a $d_{N\mathrm{\Omega }}$ similar to the deuteron with baryon number $B=2$ and with a small binding energy might exist. In this work we propose a hadronic molecular approach to study the dynamical properties of this exotic state. We employed a phenomenological Lagrangian approach to describe the coupling of the $d_{N\mathrm{\Omega }}$ to its constituents and the strong decays into conventional hadrons, $d_{N\mathrm{\Omega }}\to \mathrm{\Lambda }\mathrm{\Xi }$ and $d_{N\mathrm{\Omega }}\to \mathrm{\Sigma }\mathrm{\Xi }$. Predictions for the sum of the decay rates are in the range of a few hundred keV. In addition, we find that the $d_{N\mathrm{\Omega }}\to \mathrm{\Lambda }\mathrm{\Xi }$ mode is dominant, preferably searched for in a future Relativistic Heavy Ion Collider (RHIC) experiment.

We dimensionally reduce the spacetime action of bosonic string theory, and that of the bosonic sector of heterotic string theory after truncating the Yang-Mills gauge fields, on a $d$-dimensional torus including all higher-derivative corrections to first order in ${\alpha }^{\prime }$. A systematic procedure is developed that brings this action into a minimal form in which all fields except the metric carry only first-order derivatives. This action is shown to be invariant under $\mathrm{O}(d,d,\mathbb{R})$ transformations that acquire ${\alpha }^{\prime }$-corrections through a Green-Schwarz type mechanism. We prove that, up to a global prefactor, the first-order ${\alpha }^{\prime }$-corrections are uniquely determined by $\mathrm{O}(d,d,\mathbb{R})$ invariance.

We present a conjecture for the leading $1/N$ anomalous dimension of the scalar primary operator in $U(N{)}_k$ Chern-Simons theories coupled to a single fundamental field, to all orders in the t’Hooft coupling $\lambda =\frac{N}{k}$. Following this we compute the anomalous dimension of the scalar in a Regular Bosonic theory perturbatively at two-loop order and demonstrate that matches exactly with the result predicted by our conjecture. We also show that our proposed expression for the anomalous dimension is consistent with all other existing two-loop perturbative results, which constrain its form at both weak and strong coupling thanks to the bosonization duality. Furthermore, our conjecture passes a novel nontrivial all loop test which provides a strong evidence for its consistency.

We renormalize a six-dimensional cubic theory to four loops in the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme where the scalar is in a bi-adjoint representation. The underlying model was originally derived in a problem relating to gravity being a double copy of Yang-Mills theory. As a field theory in its own right we find that it has a curious property in that while unexpectedly there is no one-loop contribution to the $\beta$ function the two-loop coefficient is negative. It therefore represents an example where asymptotic freedom is determined by the two-loop term of the $\beta$ function. We also examine a multi-adjoint cubic theory in order to see whether this is a more universal property of these models.

Evidences have been found that the weak cosmic censorship conjecture could be violated if test particles with charge and angular momentum are injected into a black hole. However, second-order corrections and fine-tunings on the particle’s parameters are required in previous studies, indicating that self-force and radiative effects must be taken into account. In this paper, we first consider a magnetically charged particle falling into an extremal Bardeen black hole, which is regular (with no singularity) and has a magnetic monopole at the center. We then investigate a general class of magnetic black holes associated with nonlinear electrodynamics. In all the cases, we show that the test particle with magnetic charge could overcharge the black hole, causing possible violation of the weak cosmic censorship conjecture. We also find that every spherically symmetric spacetime associated with a magnetic field can also be generated by an electric field. Moreover, if a magnetically charged black hole can be overcharged, the same spacetime containing an electrically charged black hole can also be overcharged. Although possible counterexamples to the weak cosmic censorship have been constructed previously in the literature, which always involved higher-order terms in particles’ parameters, we find, for the first time, that linear terms are enough to make counterexamples.

Riemann normal coordinates (RNC) at a regular event $p_0$ of a spacetime manifold $\mathcal{M}$ are constructed by imposing (i) $g_{\mathsf{ab}}{|}_{p_0}={\eta }_{ab}$, and (ii) ${{\mathrm{\Gamma }}^{\mathsf{a}}}_{\mathsf{bc}}{|}_{p_0}=0$. There is, however, a third, independent, assumption in the definition of RNC which essentially fixes the density of geodesics emanating from $p_0$ to its value in flat spacetime, viz.: (iii) the tangent space ${\mathcal{T}}_{p_0}(\mathcal{M})$ is flat. We relax (iii) and obtain the normal coordinates, along with the metric $g_{\mathsf{ab}}$, when ${\mathcal{T}}_{p_0}(\mathcal{M})$ is a maximally symmetric manifold ${\tilde{\mathcal{M}}}_{\mathrm{\Lambda }}$ with curvature length $|\mathrm{\Lambda }{|}^{-1/2}$. In general, the “rest” frame defined by these coordinates is noninertial with an additional acceleration $\mathit{a}=-(\mathrm{\Lambda }/3)\mathit{x}$ depending on the curvature of tangent space. Our geometric setup provides a convenient probe of local physics in a universe with a cosmological constant $\mathrm{\Lambda }$, now embedded into the local structure of spacetime as a fundamental constant associated with a curved tangent space. We discuss classical and quantum implications of the same.

We study the gravitational field of ultrarelativistic spinning objects (gyratons) in a modified gravity theory with higher derivatives. In particular, we focus on a special class of such theories with an infinite number of derivatives known as “ghost-free gravity” that include a nonlocal form factor such as $\exp (-\square {\ell }^2)$, where $\ell$ is the scale of nonlocality. First, we obtain solutions of the linearized ghost-free equations for stationary spinning objects. To obtain gyraton solutions we boost these metrics and take their Penrose limit. This approach allows us to perform calculations for any number of spacetime dimensions. All solutions are regular at the gyraton axis. In four dimensions, when the scale nonlocality $\ell$ tends to zero, the obtained gyraton solutions correctly reproduce the Aichelburg–Sexl metric and its generalization to spinning sources found earlier by Bonnor. We also study the properties of the obtained four-dimensional and higher-dimensional ghost-free gyraton metrics and briefly discuss their possible applications.

Newtonian gravitational potential sourced by a homogeneous circular ring in arbitrary dimensional Euclidean space takes a simple form if the spatial dimension is even. In contrast, if the spatial dimension is odd, it is given in a form that includes complete elliptic integrals. In this paper, we analyze the dynamics of a freely falling massive particle in its Newtonian potential. Focusing on circular orbits on the symmetric plane where the ring is placed, we observe that they are unstable in 4D space and above, while they are stable in 3D space. The sequence of stable circular orbits disappears at $1.6095\cdots$ times the radius of the ring, which corresponds to the innermost stable circular orbit (ISCO). On the axis of symmetry of the ring, there are no circular orbits in 3D space but more than in 4D space. In particular, the circular orbits are stable between the ISCO and infinity in 4D space and between the ISCO and the outermost stable circular orbit in 5D space. There exist no stable circular orbits in 6D space and above.

Based on the geometric-optics correspondence between the parameters of a quasinormal mode and the conserved quantities along geodesics, we propose an equation to calculate the typical shadow radius for asymptotically flat and rotating black holes when viewed from the equatorial plane given by ${\overline{R}}_s=\sqrt{2}/2(\sqrt{r_0^{+}/f^{\prime }(r){|}_{r_0^{+}}}+\sqrt{r_0^{-}/f^{\prime }(r){|}_{r_0^{-}}})$, with $r_0^{\pm }$ being the radius of circular null geodesics for the corresponding mode. Furthermore we have explicitly related the shadow radius to the real part of QNMs in the eikonal regime corresponding to the prograde and retrograde mode, respectively. As a particular example, we have computed the typical black hole shadow radius for some well-known black hole solutions including the Kerr black hole, Kerr-Newman black hole and higher dimensional black hole solutions described by the Myers-Perry black hole.

Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory, and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the second-order corrections of general relativity, namely, $R^2$, $R^3$, and $R\square R$. Then, we explore spherically symmetric and static solutions in the weak-field regime and black holes context. All solutions in the weak-field regime due to a point mass are deduced, and by making a stability analysis of these solutions, we restrict them to Yukawa-type solutions. In regard to black hole solutions, we use the Lichnerovicz method to investigate the possibility of the existence of non-Schwarzschild black holes. The results obtained show that non-Schwarzschild solutions might exist. However, for reasonable values of the parameters of the theory, its horizon radii are extremely small making macroscopic black holes different from Schwarzschild unfeasible.

In this paper, we look for the vacuum static spherically symmetric solution in the mimetic gravity scenario based on the conformal invariance principle. The trivial solution is a stealth Schwarzschild black hole with scalar hair where the mimetic field does not contribute to the background. However, a solution with two naked singularities shows up when the mimetic scalar field contributes to the background. We show that one of these singularities is the same as the singularity at the center of standard Schwarzschild black hole while the other appears due to caustics formation. However, we construct the mimetic black hole solution by gluing the exterior static spherically symmetric solution to a time-dependent anisotropic spacetime describing the interior of the black hole. It is shown that these two solutions match continuously on the surface of the apparent horizon. Some physical properties of the corresponding mimetic black holes are discussed.

The scenario of constant-roll inflation in the frame of the Randall-Sundraum II (RS II) brane gravity model is considered. Based on the scenario, the smallness of the second slow-roll parameter is released and it is assumed as a constant which could be of the order of unity. Applying the Hamilton-Jacobi formalism, the constancy of the parameter gives a differential equation for the Hubble parameter which leads to an exact solution for the model. Reconsidering the perturbation equations, we show there are some modified terms appearing in the amplitude of the scalar perturbations and in turn in the scalar spectral index and tensor-to-scalar ratio. Comparing the theoretical results of the model with observational data, the free parameters of the model are determined. Then, the consistency of the model with the swampland criteria is investigated for the obtained values of the free parameters. As the final step, the attractor behavior of the model is considered.

Ultralight primordial black holes (PBHs) with masses $\lesssim {10}^{15}\mathrm{g}$ and subatomic Schwarzschild radii, produced in the early Universe, are expected to have evaporated by the current cosmic age due to Hawking radiation. Based on this assumption, a number of constraints on the abundance of ultralight PBHs have been made. However, Hawking radiation has thus far not been verified experimentally. It would, therefore, be of interest if constraints on ultralight PBHs could be placed independently of the assumption of Hawking radiation. In this paper, we explore the possibility of probing these PBHs, within a narrow mass range, using gravitational-wave (GW) data from the two LIGO detectors. The idea is that large primordial curvature perturbations that result in the formation of PBHs would also generate GWs through nonlinear mode couplings. These induced GWs would produce a stochastic background. Specifically, we focus our attention on PBHs of the mass range $\sim {10}^{13}-{10}^{15}\mathrm{g}$ for which the induced stochastic GW background peak falls in the sensitivity band of LIGO. We find that, for both narrow and broad Gaussian PBH mass distributions, the corresponding GW background would be detectable using presently available LIGO data, provided we neglect the existing constraints on the abundance of PBHs, which are based on Hawking radiation. Furthermore, we find that these stochastic backgrounds would be detectable in LIGO’s third observing run, even after considering the existing constraints on PBH abundance. A nondetection should enable us to constrain the amplitude of primordial curvature perturbations as well as the abundance of ultralight PBHs. We estimate that by the end of the third observing run, assuming nondetection, we should be able to place constraints that are orders of magnitude better than currently existing ones.