We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that a nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay rate of the false vacuum for a generic nucleation site. We find that the decay rate becomes larger when the nucleation site is close to the black hole horizon and coincides with that in Minkowski spacetime when the nucleation site goes to infinity.

We characterize the correspondence between the twisted $N=2$ super-Yang-Mills theory and the Baulieu-Singer topological theory quantized in the self-dual Landau gauges. While the first is based on an on-shell supersymmetry, the second is based on an off-shell Becchi-Rouet-Stora-Tyutin symmetry. Because of the equivariant cohomology, the twisted $N=2$ in the ultraviolet regime and Baulieu-Singer theories share the same observables, the Donaldson invariants for 4-manifolds. The triviality of the Gribov copies in the Baulieu-Singer theory in these gauges shows that working in the instanton moduli space on the twisted $N=2$ side is equivalent to working in the self-dual gauges on the Baulieu-Singer one. After proving the vanishing of the $\beta$ function in the Baulieu-Singer theory, we conclude that the twisted $N=2$ in the ultraviolet regime, in any Riemannian manifold, is correspondent to the Baulieu-Singer theory in the self-dual Landau gauges—a conformal gauge theory defined in Euclidean flat space.

We study odd parity perturbations of spherically symmetric black holes with time-dependent scalar hair in shift-symmetric higher-order scalar-tensor theories. The analysis is performed in a general way without assuming the degeneracy conditions. Nevertheless, we end up with second-order equations for a single master variable, similarly to cosmological tensor modes. We thus identify the general form of the quadratic Lagrangian for the odd parity perturbations, leading to a generalization of the Regge-Wheeler equation. We also investigate the structure of the effective metric for the master variable and refine the stability conditions. As an application of our generalized Regge-Wheeler equation, we compute the quasinormal modes of a certain nontrivial black-hole solution. Finally, our result is extended to include the matter energy-momentum tensor as a source term.

We consider the following question: may two different black holes (BHs) cast exactly the same shadow? In spherical symmetry, we show the necessary and sufficient condition for a static BH to be shadow-degenerate with Schwarzschild is that the dominant photonsphere of both has the same impact parameter, when corrected for the (potentially) different redshift of comparable observers in the different spacetimes. Such shadow-degenerate geometries are classified into two classes. The first shadow-equivalent class contains metrics whose constant (areal) radius hypersurfaces are isometric to those of the Schwarzschild geometry, which is illustrated by the Simpson and Visser (SV) metric. The second shadow-degenerate class contains spacetimes with different redshift profiles and an explicit family of metrics within this class is presented. In the stationary, axi-symmetric case, we determine a sufficient condition for the metric to be shadow degenerate with Kerr for far-away observers. Again we provide two classes of examples. The first class contains metrics whose constant (Boyer-Lindquist-like) radius hypersurfaces are isometric to those of the Kerr geometry, which is illustrated by a rotating generalization of the SV metric, obtained by a modified Newman-Janis algorithm. The second class of examples pertains BHs that fail to have the standard north-south ${\mathbb{Z}}_2$ symmetry, but nonetheless remain shadow degenerate with Kerr. The latter provides a sharp illustration that the shadow is not a probe of the horizon geometry. These examples illustrate that nonisometric BH spacetimes can cast the same shadow, albeit the lensing is generically different.

The Dvali-Gabadadze-Porrati (DGP) braneworld model is employed to study the gravitational collapse of dust, with a Gauss-Bonnet (GB) term present in the five-dimensional bulk. We find that, within the normal (nonself-accelerating) DGP branch and due to the curvature effects from the GB component on the brane, the black hole singularity acquires modified features. More precisely, during collapse and for a finite comoving time, before a singularity would emerge at the zero physical radius, the first time derivative of the Hubble rate diverges, whereas the brane energy density and the Hubble rate remain finite. This is a peculiar behavior which displays similar properties to the sudden singularity occurring in particular late-time cosmological frameworks. Furthermore, the question of whether this altered singularity can be viewed by an external observer or will be hidden by a black hole horizon is addressed. We establish that, depending on the given induced-gravity parameter and the GB coupling constant, there exists a threshold mass for the collapsing dust, below which no trapped surfaces evolve as the collapse proceeds toward the singularity. In other words, a naked sudden singularity may form.

The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble function is considered and sometimes it is argued that, as the interaction function is a local property, the inclusion of the Hubble function may influence the overall dynamics. This is the starting point of the present article where we consider a very simple interacting cosmic scenario between vacuum energy and the cold dark matter characterized by various interaction functions originated from a general interaction function: $Q=\mathrm{\Gamma }{\rho }_c^{\alpha }{\rho }_x^{1-\alpha -\beta }({\rho }_c+{\rho }_x{)}^{\beta }$, where ${\rho }_c$, ${\rho }_x$ are respectively the cold dark matter density and vacuum energy density; $\alpha$, $\beta$ are real numbers and $\mathrm{\Gamma }$ is the coupling parameter with dimension equal to the dimension of the Hubble rate. We investigate four distinct interacting cosmic scenarios and constrain them both theoretically and observationally. Our analyses clearly reveal that the interaction models should be carefully handled.

We pursue a novel strategy toward a first detection of continuous gravitational waves from rapidly rotating deformed neutron stars. Computational power is focused on a narrow region of signal parameter space selected by a strategically chosen benchmark. We search data from the second observing run of the LIGO Observatory with an optimized analysis run on graphics processing units. While no continuous waves are detected, the search achieves a sensitivity to gravitational wave strain of $h_0=1.01\times {10}^{-25}$ at 90% confidence, 24%–69% better than past searches of the same parameter space. Constraints on neutron star deformity are within theoretical maxima; thus, a detection by this search was not inconceivable.

This paper investigates the feasibility of simulating fuzzy dark matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in ($1+1$)-dimensional space time, that—under well controlled system conditions—is capable of realizing important aspects of the full-fledged ($3+1$)-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal ($3+1$)-Schrödinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for nonexpanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modeling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them.

The space-based gravitational-wave observatory LISA relies on a form of synthetic interferometry (time-delay interferometry, or TDI) where the otherwise overwhelming laser phase noise is canceled by linear combinations of appropriately delayed phase measurements. These observables grow in length and complexity as the realistic features of the LISA orbits are taken into account. In this paper we outline an implicit formulation of TDI where we write the LISA likelihood directly in terms of the basic phase measurements, and we marginalize over the laser phase noises in the limit of infinite laser-noise variance. Equivalently, we rely on TDI observables that are defined numerically (rather than algebraically) from a discrete-filter representation of the laser propagation delays. Our method generalizes to any time dependence of the armlengths; it simplifies the modeling of gravitational-wave signals; and it allows a straightforward treatment of data gaps and missing measurements.

We revisit the problem of the gauge invariance in the Coleman-Weinberg model in which a $U(1)$ gauge symmetry is driven spontaneously broken by radiative corrections. It was noticed in previous work that masses in this model are not gauge invariant at one-loop order. In our analysis, we use the dressed propagators of scalars which include a resummation of the one-loop self-energy correction to the tree-level propagator. We calculate the one-loop self-energy correction to the vector meson using these dressed propagators. We find that the pole mass of the vector meson calculated using the dressed propagator is gauge invariant at the vacuum determined using the effective potential calculated with a resummation of daisy diagrams.

We systematically investigate the effects made by the anomalous magnetic moment (AMM) of quark in the magnetized QCD matter, including the magnetic susceptibility, the inverse magnetic catalysis around the critical temperature and the modified neutral and or charged pion and rho meson’s spectra. The dynamical AMM of quark, coupling with magnetic field, causes Zeeman splitting in the energy dispersion of quark and thus changes the magnetism properties and masses of magnetized mesons. Unfortunately, we found that the lattice results of the quark matter under magnetic fields cannot fully be explained via including the AMM interaction. It is observed that the AMM of quark reduces the dynamical quark mass and therefore induces the inverse magnetic catalysis around $T_c$. The neutral pion is very sensitive to the AMM term and its mass decreases with magnetic field quickly. On the contrary, the charged pion mass shows a nontrivial behavior, i.e., linearly increases with the weak and moderate magnetic fields and then saturates at strong region. For rho mesons, AMM coupling modifies the masses of neutral rho particles for all $s_z$ consistently, while it reduces the masses of charged rho mesons for $s_z=+1$, 0 but enhances the mass of $s_z=-1$ state. The magnetic susceptibility at low temperatures can be either positive or negative with different strengths of AMM interaction.

Covariant scalar field quantization, nicknamed $({\phi }^r{)}_n$, where $r$ denotes the power of the interaction term and $n=s+1$ where $s$ is the spatial dimension and 1 adds time. Models such that $r<2n/(n-2)$ can be treated by canonical quantization, while models such that $r>2n/(n-2)$ are nonrenormalizable, leading to perturbative infinities, or, if treated as a unit, emerge as ‘free theories’. Models such as $r=2n/(n-2)$, e.g., $r=n=4$, again using canonical quantization also become ‘free theories’, which must be considered quantum failures. However, there exists a different approach called affine quantization that promotes a different set of classical variables to become the basic quantum operators and it offers different results, such as models for which $r>2n/(n-2)$, which has recently correctly quantized $({\phi }^{12}{)}_3$. In the present paper we show, with the aid of a Monte Carlo analysis, that one of the special cases where $r=2n/(n-2)$, specifically the case $r=n=4$, can be acceptably quantized using affine quantization.

Recognizing the potential of effective field theories to posit multiple beyond Standard Model (BSM) scenarios in a similar footing with a possibility to compare them, we inspect the effects of 11 single scalar-multiplet extensions of the SM on the combined set of electroweak precision observables and Higgs signal strength data by systematically integrating out the heavy multiplets and computing the resulting Standard Model effective field theory operators and Wilson coefficients (WCs) up to one-loop level. Noting that multiple BSM models give rise to a degenerate set of WCs, we then perform Bayesian statistical inference both directly on the BSM parameters and on the associated set of independent WCs. Using the posteriors of the BSM parameters, we infer the respective (correlated) WC distributions and compare both the model-independent and -dependent analyses by overlaying the 2D marginal WC posteriors from both processes, thus laying the groundwork for a data-driven attempt to compare diverse BSM theories of different origins, and hopefully, a possible way to approach the intractable inverse problem. We also demonstrate, with an example model, the crucial role of theoretical constraints to rule out large chunks of BSM parameter spaces. All numerical results are available on GitHub.

Extensions of the Standard Model with an Abelian gauge group are constrained by gauge anomaly cancellation, so that only a limited number of possible charge assignments is allowed without the introduction of new chiral fermions. For flavor universal charges, couplings of the associated hidden photon to Standard Model fermions are flavor conserving at tree level. We show explicitly that even the flavor-specific charge assignments allowed by anomaly cancellation condition lead to flavor-conserving tree-level couplings of the hidden photon to quarks and charged leptons if the Cabibbo-Kobayashi-Maskawa or Pontecorvo-Maki-Nakagawa-Sakata matrix can be successfully reconstructed. Further, loop-induced flavor-changing couplings are strongly suppressed. As a consequence, the structure of the Majorana mass matrix is constrained and flavor-changing tree-level couplings of the hidden photon to neutrino mass eigenstates are identified as a means to distinguish the $U(1{)}_{B-L}$ gauge boson from any other anomaly-free extension of the Standard Model without new chiral fermions. We present a comprehensive analysis of constraints and projections for future searches for a $U(1{)}_{B-3L_i}$ gauge boson, calculate the reach of resonance searches in $B$ meson decays and comment on the implications for nonstandard neutrino interactions.

The electric charge transport in a weakly magnetized hot QCD medium has been investigated in the presence of an external inhomogeneous electric field. The current densities (electric and Hall) induced by the inhomogeneous electric field have been estimated in the regime where space-time inhomogeneity of the field is small so that the collisional effect in the medium cannot be neglected. The collisional aspect of the medium has been captured by employing both a relaxation-time approximation and a Bhatnagar-Gross-Krook collision kernel in the relativistic Boltzmann equation. The magnetic field, momentum anisotropy, and quark chemical potential dependences of the electric current and Hall current densities have been explored, and the impacts on the respective conductivities have been studied. The inhomogeneities of the field are seen to have sizable effects on the electromagnetic responses of the collisional medium.

Developing the calculation techniques to fivefold heavy hadrons, we perform the study of novel fully heavy $QQQQ\overline{Q}$ pentaquark states by the QCD sum rule approach that is firmly based on the QCD basic theory. Numerically, masses of fully heavy pentaquark states are calculated to be ${7.41}_{-0.31}^{+0.27}\mathrm{GeV}$ for $cccc\overline{c}$ and ${21.60}_{-0.22}^{+0.73}\mathrm{GeV}$ for $bbbb\overline{b}$, respectively. In experiment, these predicted all-heavy pentaquark states could be searched for in the ${\mathrm{\Omega }}_{QQQ}{\eta }_Q$ invariant mass spectrum.

We present a global analysis of the observed $Z_c$, $Z_{cs}$, and future $Z_{css}$-like spectra using (inverse) Laplace sum rule within stability criteria. Integrated compact QCD expressions of the leading order spectral functions up to dimension-six condensates are given. Next-to-leading order factorized perturbative contributions are included. We reemphasize the importance to include pertubative radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at leading order in the literature. We also demonstrate that, contrary to a qualitative large $N_c$ counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the Laplace sum rule predictions. Our results are summarized in Tables III to VI. The $Z_c(3900)$ and $Z_{cs}(3983)$ spectra are well reproduced by the ${\mathcal{T}}_c(3900)$ and ${\mathcal{T}}_{cs}(3973)$ tetramoles (superposition of quasidegenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The $Z_c(4025)$ or $Z_c(4040)$ state can be fitted with the $D_0^{*}{D}_1$ molecule having a mass 4023(130) MeV while the $Z_{cs}$ bump around 4.1 GeV can be likely due to the $D_{s0}^{*}{D}_1\oplus D_0^{*}{D}_{s1}$ molecules. The $Z_c(4430)$ could be a radial excitation of the $Z_c(3900)$ weakly coupled to the current, while all strongly coupled ones are in the region $(5634\sim 6527)\mathrm{MeV}$. The double strange tetramole state ${\mathcal{T}}_{css}$, which one may identify with the future $Z_{css}$, is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass splittings of the tetramoles due to $SU(3)$ breakings: $M_{{\mathcal{T}}_{cs}}-M_{{\mathcal{T}}_c}\approx M_{{\mathcal{T}}_{css}}-M_{{\mathcal{T}}_{cs}}\simeq (73\sim 91)\mathrm{MeV}$.

We investigate the transition form factors $f_{+}(q^2)$ and $f_{-}(q^2)$ [or $f_0(q^2)$] for the exclusive semileptonic $B\to D\ell {\nu }_{\ell }$ ($\ell =e$, $\mu$, $\tau$) decays in the standard light-front quark model based on the light-front quantization. The common belief is that while $f_{+}(q^2)$ can be obtained without involving any treacherous contributions such as the zero mode and the instantaneous contribution, $f_{-}(q^2)$ receives those treacherous contributions since it involves at least two components of the current, e.g., $(J^{+},J^{-})$ or $(J^{+},{\mathbf{J}}_{\perp })$. Contrary to the common belief, we show in the Drell-Yan ($q^{+}=0$) frame that $f_{-}(q^2)$ obtained from $(J^{+},J^{-})$ gives identical result to $f_{-}(q^2)$ obtained from $(J^{+},{\mathbf{J}}_{\perp })$ without involving such treacherous contributions in the standard light-front quark model. In our numerical calculations, we obtain the form factors and branching ratios for $B\to D\ell {\nu }_{\ell }$ ($\ell =e$, $\mu$, $\tau$) and compare with the experimental data as well as other theoretical model predictions. Our results for $\mathrm{Br}(B\to D\ell {\nu }_{\ell })$ show reasonable agreement with the experimental data except for the semitauonic $B^0\to D^{-}\tau {\nu }_{\tau }$ decay. The ratio $ℛ(D)=\frac{\mathrm{Br}(B\to D\tau {\nu }_{\tau })}{\mathrm{Br}(B\to D{\ell }^{\prime }{\nu }_{{\ell }^{\prime }})}$ (${\ell }^{\prime }=e$, $\mu$) is also estimated and compared with the experimental data as well as other theoretical predictions.

We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F}=\frac{1}{4}{F}_{\mu \nu }{F}^{\mu \nu }(x)$, $\mathcal{G}=\frac{1}{4}{\tilde{F}}_{\mu \nu }{F}^{\mu \nu }(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity.

The real-time topological susceptibility is studied in $(1+1)$-dimensional massive Schwinger model with a $\theta$-term. We evaluate the real-time correlation function of electric field that represents the topological Chern-Pontryagin number density in ($1+1$) dimensions. Near the parity-breaking critical point located at $\theta =\pi$ and fermion mass $m$ to coupling $g$ ratio of $m/g\approx 0.33$, we observe a sharp maximum in the topological susceptibility. We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point.