In this work we compute the axion mass and, from this (exploiting a well-known relation), we also derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at $T_c$, making use of a chiral effective Lagrangian model which includes the axion, the scalar and pseudoscalar mesons and implements the $U(1)$ axial anomaly of the fundamental theory. We also provide a numerical estimate of the topological susceptibility at $T=0$ (in the physical case of three light quark flavors) and discuss the question of the temperature and quark-mass dependence of the topological susceptibility in the high-temperature regime.

The hadronic form factors of the energy-momentum tensor (EMT) have attracted considerable interest in recent literature. This concerns especially the $D$-term form factor $D(t)$ with its appealing interpretation in terms of internal forces. With their focus on hadron structure, theoretical studies so far have concentrated mainly on strongly interacting systems with short-range forces. Effects on the EMT due to long-range forces like the electromagnetic interaction have not yet been studied. Electromagnetic forces play a small role in the balance of forces inside the proton, but their long-range nature introduces new features which are not present in systems with short-range forces. We use a simple but consistent classical field theoretical model of the proton to show how the presence of long-range forces alters some notions taken for granted in short-range systems. Our results imply that a more careful definition of the $D$-term is required when long-range forces are present.

We describe the $\mathrm{\Lambda }(1405)$ hyperon as a Feshbach resonance of a $\overline{K}N$ quasibound state coupled by a decaying channel of $\pi \mathrm{\Sigma }$ in the Skyrme model. A weakly bound $\overline{K}N$ state is generated in the laboratory frame, while the $\mathrm{\Sigma }$ hyperon as a strongly bound state of $\overline{K}N$ in the intrinsic frame. We obtain a coupling of $\overline{K}N$ and $\pi \mathrm{\Sigma }$ channels by computing a baryon matrix element of the axial current. This coupling enables the decay of the $\overline{K}N$ bound state to $\pi \mathrm{\Sigma }$. It is shown that the Skyrme model supports the $\mathrm{\Lambda }(1405)$ as a narrow Feshbach resonance.

A measurement of the branching fraction of the decay $B_s^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ is performed using proton–proton collision data corresponding to an integrated luminosity of $5{\mathrm{fb}}^{-1}$ collected by the LHCb experiment between 2011 and 2016. The branching fraction is determined to be $\mathcal{B}(B_s^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0)=[8.3\pm 1.6(\mathrm{stat})\pm 0.9(\mathrm{syst})\pm 0.8(\mathrm{norm})\pm 0.3(f_s/f_d)]\times {10}^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third and fourth are due to uncertainties on the branching fraction of the normalization mode $B^0\to \varphi K_{\mathrm{S}}^0$ and the ratio of hadronization fractions $f_s/f_d$. This is the most precise measurement of this branching fraction to date. Furthermore, a measurement of the branching fraction of the decay $B^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ is performed relative to that of the $B_s^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0$ channel, and is found to be $\frac{\mathcal{B}(B^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0)}{\mathcal{B}(B_s^0\to K_{\mathrm{S}}^0{K}_{\mathrm{S}}^0)}=[7.5\pm 3.1(\mathrm{stat})\pm 0.5(\mathrm{syst})\pm 0.3(f_s/f_d)]\times {10}^{-2}$.

It is known that local, Lorentz invariant, unitary theories involving particles with spin 1 demand that the matter sector they couple to are organized by internal physical symmetries and the associated charge conservation, while spin $3/2$ demands supersymmetry. However, the introduction of a spin 2 graviton does not obviously demand new symmetries of the matter sector (although it does demand a universal coupling). In this work we relax the assumption of Lorentz boost symmetry, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. This extends and complements our accompanying work in Part 1 on related issues for spin 1 particles in electromagnetism. In order to avoid potential problems with longitudinal modes of the graviton, we choose to project them out, leaving only two degrees of freedom. We study large classes of theories that a priori may violate Lorentz boost invariance. By requiring the tree-level exchange action be local, we find that consistency demands that the Lorentz boost symmetry must be satisfied by the graviton and the matter sector, and in turn we recover general relativity at this order of analysis.

It is well known that a theory of the (i) Lorentz invariant and (ii) locally interacting (iii) two degrees of freedom of a massless spin 1 particle, the photon, leads uniquely to electromagnetism at large distances. In this work, we remove the assumption of (i) Lorentz boost invariance, but we still demand (ii) and (iii). We consider several broad classes of theories of spin 1, which in general explicitly violate Lorentz symmetry. We restrict to the familiar two degrees of freedom of the photon. We find that most theories lead to nonlocality and instantaneous signaling at a distance. By demanding a mild form of locality (ii), namely that the tree-level exchange action is manifestly local, we find that the photon must still be sourced by a conserved charge with an associated internal symmetry. This recovers the central features of electromagnetism, although it does not by itself impose Lorentz boost symmetry. The case of gravitation dramatically improves the final conclusion and is reported in detail in our accompanying paper Part 2.

We consider a general class of scalar tensor theories in three dimensions whose action contains up to second-order derivatives of the scalar field with coupling functions that only depend on the standard kinetic term of the scalar field, thus ensuring the invariance under the constant shift of the scalar field. For this model, we show that the field equations for a stationary metric ansatz together with a purely radial scalar field can be fully integrated. The kinetic term of the scalar field solution is shown to satisfy an algebraic relation depending only on the coupling functions, and hence is constant while the metric solution is nothing but a Bañados-Teitelboim-Zanelli (BTZ)-like metric with an effective cosmological constant fixed in terms of the coupling functions. As a direct consequence the thermodynamics of the solution is shown to be identical to a BTZ-like one with an effective cosmological constant, despite the presence of a scalar field. Finally, the expression of the semiclassical entropy of this solution is also confirmed through a generalized Cardy-like formula involving the mass of the scalar soliton obtained from the black hole by means of a double Wick rotation.

We continue our study of the binary neutron star parameter space by investigating the effect of the spin orientation on the dynamics, gravitational wave emission, and mass ejection during the binary neutron star coalescence. We simulate seven different configurations using multiple resolutions to allow a reasonable error assessment. Due to the particular choice of the setups, five configurations show precession effects, from which two show a precession (“wobbling”) of the orbital plane, while three show a “bobbing” motion; i.e., the orbital angular momentum does not precess, while the orbital plane moves along the orbital angular momentum axis. Considering the ejection of mass, we find that precessing systems can have an anisotropic mass ejection, which could lead to a final remnant kick of $\sim 40\mathrm{km}/\mathrm{s}$ for the studied systems. Furthermore, for the chosen configurations, antialigned spins lead to larger mass ejecta than aligned spins, so that brighter electromagnetic counterparts could be expected for these configurations. Finally, we compare our simulations with the precessing, tidal waveform approximant imrphenompv2_nrtidalv2 and find good agreement between the approximant and our numerical relativity waveforms with phase differences below 1.2 rad accumulated over the last $\sim 16$ gravitational wave cycles.

In the last few decades, lots of universal relations between different global physical quantities of neutron stars have been proposed to constrain the unobservable or hard to be observed properties of neutron stars. But few of them are related to the gravitational redshift or the gravitational binding energy, especially for the fast rotating neutron stars. Here we will focus on the universal relations related to these two quantities. Based on 11 equations of state (EOSs) from the predictions of microscopic nuclear many-body theories for normal or hybrid neutron stars, we proposed a set of new quasiuniversal relations under three rotating cases: static, general rotating and Keplerian rotating. These new quasiuniversal relations provide a potential way to constrain or estimate the unobservable or hard to be observed properties of neutron stars.

We revisit the path integral computation of the Casimir energy between two infinite parallel plates placed in a QED vacuum. We implement perfectly magnetic conductor boundary conditions (as a prelude to the dual superconductor picture of the QCD vacuum) via constraint fields and show how an effective gauge theory can be constructed for the constraint boundary fields, from which the Casimir energy can be simply computed, in perfect agreement with the usual more involved approaches. Gauge invariance is natural in this framework, as well as the generalization of the result to $d$ dimensions. We also pay attention to the case where the outside of the plates is not the vacuum, but a perfect magnetic (super)conductor, disallowing any dynamics outside the plates. We find perfect agreement between both setups.

We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon \mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $\alpha {\alpha }_s$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.

We analyze the $Z$-boson decay $Z\to \gamma X$ into a photon ($\gamma$) plus a hypothetical light boson ($X$) belonging to a dark or secluded sector. Because of its feeble interactions with Standard Model fields, this dark boson behaves as missing energy in the detector. We consider for $X$ the cases of spin-1 (massless dark-photon), spin-0 (axionlike), and spin-2 (gravitonlike) particles and explore the way to untangle its spin origin. All these scenarios predict a universal signature for this decay, characterized by a single monochromatic photon in the $Z$ center of mass, with energy about half of the $Z$ mass, plus a neutrinolike missing energy associated with the $X$ boson. We show that if the $Z\to \gamma X$ signal should be discovered at $e^{+}{e}^{-}$ colliders, the angular distribution of the monochromatic photon in $e^{+}{e}^{-}\to Z\to \gamma X$ can provide a clean probe to discriminate between the $J=1$ and alternative $J=0/2$ spin nature of the dark boson.

We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by an additional term $\lambda (u·\partial \varphi {)}^2$ in the scalar field Lagrangian, where the parameter $\lambda$ and the background vector $u^{\mu }$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D>2$, the Casimir stress by using Green’s function techniques for two specific choices of the vector $u^{\mu }$. In the timelike case, $u^{\mu }=(1,0,\dots ,0)$, the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor $(1+\lambda {)}^{-1/2}$. For the radial spacelike case, $u^{\mu }=(0,1,0,\dots ,0)$, we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value ${\lambda }_c={\lambda }_c(D)$ at which the Casimir stress transits from a repulsive behavior to an attractive one for any $D>2$. The physically relevant case $D=3$ is analyzed in detail where the critical value ${\lambda }_c{|}_{D=3}=0.0025$ was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of $D$.

We construct solutions of four-dimensional $N=2$ gauged supergravity coupled to vector multiplets which are holographically dual to superconformal line defects. For the gauged STU and the $\mathrm{SU}(1,n)/\mathrm{U}(1)\times \mathrm{SU}(n)$ coset models, we use the solutions to calculate holographic observables such as the expectation value of the defect and one-point functions in the presence of the defect.

We construct a static and spherical excited state without singularities in renormalizable quantum gravity with background-free nature asymptotically. Its diameter is given by a correlation length of the quantum gravity, longer than the Planck length by 2 orders of magnitude, and it has a Schwarzschild tail outside. The quantum gravity dynamics inside is described by employing a nonperturbative expression of higher-order corrections assumed from a physical requirement that the dynamics disappear at the edge where it is in strong coupling. A running coupling constant that is a manifestation of nonlinearity and nonlocality is managed by approximating it as a mean field that depends on the radial coordinate. If the mass is several times the Planck mass, we can set up a system of linearized equations of motion for the gravitational potentials incorporating the running effect and obtain the excited state as its solution. It may be a candidate for dark matter and will give a new perspective on black hole physics.

We study the polar quasinormal modes of spontaneously scalarized black holes in Einstein-Gauss-Bonnet theory. In previous works we showed that a set of nodeless solutions of the fundamental branch of the model studied in [D. D. Doneva and S. S. Yazadjiev, Phys. Rev. Lett. 120, 131103 (2018)] are stable under both radial [J. L. Blazquez-Salcedo et al., Phys. Rev. D 98, 084011 (2018)] and axial perturbations [J. L. Blazquez-Salcedo et al., Phys. Rev. D 101, 104006 (2020)]. Here we calculate the polar quasinormal modes and show that this set of solutions is stable against the polar perturbations as well. Thus for a certain region of the parameter space the scalarized black holes are potentially stable physically interesting objects. The spectrum of the polar quasinormal modes differs both quantitatively and qualitatively from the Schwarzschild one which offers the possibility to test the Gauss-Bonnet theory via the future gravitational wave observations.

We study the thermodynamics and the kinetics of the Hawking-Page phase transition in Einstein gravity and in massive gravity based on the underlying free energy landscape. For Einstein gravity, Schwarzschild–anti-de Sitter (AdS) black holes as well as thermal AdS space can be considered as macroscopic emergent states or phases. The stability and phase transition of these states can be determined by free energy landscape topography quantified by the barrier height between the state basins. Due to the thermal fluctuations, a black hole or AdS space has the chance to escape from one phase to another phase. The first passage process describes a system that undergoes such a kinetic process for the first time, and the mean first passage time can typically be used to quantify the kinetic speed. The probabilistic evolution of such a stochastic process can be described by the corresponding Fokker-Planck equation. We derive analytical integral expressions for the mean first passage time and its fluctuations. The results show that the mean first passage time and its fluctuations are closely related to free energy landscape topography through barrier heights and the temperature. The conclusions for the Hawking-Page phase transition in massive gravity are qualitatively similar to those in Einstein gravity. This study provides a systematic way of studying black hole thermodynamics and kinetics of the black holes from free energy landscape topography.

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell =L\exp ({\gamma }_0)$, where $L$ is the coordinate length of the strut, and ${\gamma }_0$ is the value of the metric function $\gamma$ on the strut.

In the present paper, we use the holographic approach to describe the early-time acceleration and the late-time acceleration eras of our Universe in a unified manner. Such “holographic unification” is found to have a correspondence with various higher curvature cosmological models with or without matter fields. The corresponding holographic cutoffs are determined in terms of the particle horizon and its derivatives, or the future horizon and its derivatives. As a result, the holographic energy density we propose is able to merge various cosmological epochs of the Universe from a holographic point of view. We find the holographic correspondence of several $F(R)$ gravity models, including axion-$F(R)$ gravity models, of several Gauss-Bonnet $F(G)$ models and finally of $F(T)$ models, and in each case we demonstrate that it is possible to describe in a unified way inflation and late-time acceleration in the context of the same holographic model.