The Wightman function, the vacuum expectation values (VEVs) of the field squared, and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling in a spherically symmetric static background geometry described by two distinct metric tensors inside and outside a spherical boundary. The exterior and interior geometries can correspond to different vacuum states of the same theory. In the region outside the sphere, the contributions in the VEVs, induced by the interior geometry, are explicitly separated. For the special case of the Minkowskian exterior geometry, the asymptotics of the VEVs near the boundary and at large distances are discussed in detail. In particular, it has been shown that the divergences on the boundary are weaker than in the problem of a spherical boundary in Minkowski spacetime with Dirichlet or Neumann boundary conditions. As an application of general results, de Sitter (dS) and anti–de Sitter (AdS) spaces are considered as examples of the interior geometry. For AdS interiors there are no bound states. In the case of dS geometry and for nonminimally coupled fields, bound states appear for a radius of the separating boundary sufficiently close to the dS horizon. Starting from a critical value of the radius, the Minkowskian vacuum in the exterior region becomes unstable. For small values of the AdS curvature radius, to the leading order, the VEVs in the exterior region coincide with those for a spherical boundary in Minkowski spacetime with a Dirichlet boundary condition. The exceptions are the cases of minimal and conformal couplings: for a minimal coupling, the VEVs are reduced to the case with a Neumann boundary condition, whereas for a conformally coupled field there is no reduction to Dirichlet or Neumann results.

The gradient (Wilson) flow has been introduced recently in order to provide a solid theoretical framework for the smoothing of ultraviolet noise in lattice gauge configurations. It is interesting to ask how it compares with other, more heuristic and numerically cheaper smoothing techniques, such as standard cooling. In this study we perform such a comparison, focusing on observables related to topology. We show that, already for moderately small lattice spacings, standard cooling and the gradient flow lead to equivalent results, both for average quantities and configuration by configuration.

Geodesic equations of the vacuum $C$ metric are derived and solved for various cases. The solutions describe the motion of timelike or null particles with conserved energy and angular momentum. Polar, nearly circular orbits around weakly accelerated black holes may be regarded as a perturbation of circular Schwarzschild geodesics. Results indicate that circular Schwarzschild geodesics of radius $r_0>6m$ are stable under small uniform accelerations along the orbital plane. These stable orbits undergo small oscillations around $r_0$, behaving like a harmonic oscillator driven by a periodic force plus another constant force. Circular orbits with axis parallel to the direction of black hole acceleration are also considered. In this case an algebraic relation expressing the condition of stability is obtained. This refines the stability analysis done in previous literature. We also present an analysis of radial geodesics along the poles. There exist a solution where a particle remains at unstable equilibrium at a fixed distance directly behind the accelerating black hole. Examples of numerical solutions are presented for other more general cases.

We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode, which in perturbation theory has a ghostlike kinetic term, turns into a tachyon when nonlinear interaction is accounted for. The kinetic term and potential for this mode have opposite signs. Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.

We present first a four-dimensional spherical symmetric black hole with small Weyl corrections and find that with increasing Weyl corrections the region of the event horizon existence for the black hole in the parameter space increases for the negative Weyl coupling parameter and decreases for the positive one. Moreover, we also obtain a rotating charged black hole with weak Weyl corrections by the method of complex coordinate transformation. Our results show that the sign of Weyl coupling parameter $\alpha$ yields the different spatial topology of the event horizons for the black hole with its parameters lying in some special regions in the parameter space. We also analyze the dependence of the ergosphere on the Weyl coupling parameter $\alpha$ and find that with the increase of the Weyl corrections the ergosphere in the equatorial plane becomes thick for a black hole with $\alpha >0$, but becomes thin in the case with $\alpha <0$, which means that the energy extraction becomes easier in the background of a black hole with the positive Weyl coupling parameter, but more difficult in the background of a black hole with the negative one.

We present a new approach to discuss two-dimensional chiral and nonchiral hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. For the chiral theory, the constitutive relations may be put in the ideal (chiral) fluid form, whereas the constitutive relations corresponding to nonchiral case do not take the ideal fluid form. The constitutive relations in the presence of both gravity and gauge sectors are new. These expressions, in the absence of the gauge sector, reproduce the results obtained in the gradient expansion approach.

We study the signatures for internal structure of dark matter in direct detection experiments in the context of asymmetric self-interacting dark matter. The self-interaction cross section of two dark matter particles at low energies is assumed to come close to saturating the S-wave unitarity bound, which requires the presence of a resonance near their scattering threshold. The universality of S-wave near-threshold resonances then implies that the low-energy scattering properties of a two-body bound state of dark matter particles are completely determined by its binding energy, irrespective of the underlying microphysics. The form factor for elastic scattering of the bound state from a nucleus and the possibility of break up of the bound state produce new signatures in the nuclear recoil energy spectrum. If these features are observed in experiments, it will give a smoking-gun signature for the internal structure of dark matter.

The so-called “hyperon puzzle” in the theory of neutron stars is considered in the framework of modified $f(R)$ gravity. We show that for simple hyperon equations of state, it is possible to obtain the maximal neutron star mass which satisfies the recent observational data for PSR J1614-2230, in higher-derivative models with power-law terms as $f(R)=R+\gamma R^2+\beta R^3$. The soft hyperon equation of state under consideration is usually treated as unrealistic in the standard general relativity. The numerical analysis of the mass-radius relation for massive neutron stars with a hyperon equation of state in modified gravity turns out to be consistent with observations. Thus, we show that the same modified gravity can solve at once three problems: a consistent description of the maximal mass of a neutron star, a realistic mass-radius relation, and a method to account for hyperons in the equation of state.

A novel cooling mechanism is proposed for neutron stars, based on the recent development in the studies of the QCD phase diagram. A possible appearance of the inhomogeneous chiral phase makes the quark beta decay without gluonic interaction. An estimate of the neutrino emissivity shows the order of ${10}^{24–26}(T/{10}^9{)}^6(\mathrm{erg}{\mathrm{cm}}^{-3}{\mathrm{s}}^{-1})$ near the phase boundaries, whose efficiency is comparable with the usual quark cooling or pion cooling, but it works only in the limited density region. These features may give another cooling scenario of neutron stars.

We prove that there are energetically stable bimetric theories. These theories satisfy a positive energy theorem. We construct a model example.

We present an operator definition of the collisional energy and momentum loss suffered by an energetic charged particle in the presence of a medium. Our approach uses the energy-momentum tensor of the medium to evaluate the energy and momentum transfer rates. We apply this formalism to an energetic lepton or quark propagating in thermal electron-positron or quark-gluon plasmas, respectively. By using two different approaches to describe the energetic charged particle, an external current approach and a diagrammatic approach, we show explicitly that the operator method reproduces the known results for collisional energy loss from the scattering rate formalism. We further use our results to evaluate the collisional energy and momentum loss for the cases of heavy quark propagation through a quark-gluon plasma and energetic muon propagation in an electron-positron plasma produced in a high-intensity laser field.

We use the recently developed kinetic theory with Berry curvature to describe the fermions and antifermions of a chiral relativistic plasma. We check that this transport approach allows us to reproduce the chiral anomaly equation of relativistic quantum field theory at finite temperature. We also check that it allows us to describe the anomalous gauge polarization tensor that appears in the hard thermal (and/or dense) effective field theory. We also construct an energy density associated to the gauge collective modes of the chiral relativistic plasma, valid in the case of small couplings or weak fields, which can be the basis for the study of their dynamical evolution.

Unlike the Standard Model (SM), supersymmetric models stabilize the electroweak (EW) scale $v$ at the quantum level and predict that $v$ is a function of the TeV-valued SUSY parameters (${\gamma }_{\alpha }$) of the UV Lagrangian. We show that the (inverse of the) covariance matrix of the model in the basis of these parameters and the usual deviation $\delta {\chi }^2$ (from ${\chi }_{\min }^2$ of a model) automatically encode information about the “traditional” EW fine-tuning measuring this stability, provided that the EW scale $v\sim m_Z$ is indeed regarded as a function $v=v(\gamma )$. It is known that large EW fine-tuning may signal an incomplete theory of soft terms and can be reduced when relations among ${\gamma }_{\alpha }$ exist (due to GUT symmetries, etc.). The global correlation coefficient of this matrix can help one investigate if such relations are present. An upper bound on the usual EW fine-tuning measure (“in quadrature”) emerges from the analysis of the $\delta {\chi }^2$ and the $s$-standard deviation confidence interval by using $v=v(\gamma )$ and the theoretical approximation (loop order) considered for the calculation of the observables. This upper bound avoids subjective criteria for the “acceptable” level of EW fine-tuning for which the model is still “natural.”

The muon $g_{\mu }-2$ discrepancy between theory and experiment may be explained by a light vector boson $Z_d$ that couples to the electromagnetic current via kinetic mixing with the photon. We illustrate how the existing electron $g_e-2$, pion Dalitz decay, and other direct production data disfavor that explanation if the $Z_d$ mainly decays into $e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}$. Implications of a dominant invisible $Z_d$ decay channel, such as light dark matter, along with the resulting strong bounds from the rare $K\to \pi$ + missing energy decay are examined. The $K$ decay constraints may be relaxed if destructive interference effects due to $Z-Z_d$ mass mixing are included. In that scenario, we show that accommodating the $g_{\mu }-2$ data through relaxation of $K$ decay constraints leads to interesting signals for dark parity violation. As an illustration, we examine the alteration of the weak mixing angle running at low $Q^2$, which can be potentially observable in polarized electron scattering or atomic physics experiments.

Present experimental data shows a $3.8\sigma$-level discrepancy with the standard model in $\overline{B}\to D^{(*)}\tau {\overline{\nu }}_{\tau }$. Some new physics models have been considered to explain this discrepancy that propose a possible new source of $CP$ violation. In this paper, we construct $CP$-violating observables by using multipion decays in $B\to D\tau {\nu }_{\tau }$, and estimate the sensitivity of these observables to generic $CP$-violating operators. We also discuss the possibilities of $CP$ violation in leptoquark models and in the type-III two-Higgs-doublet model.

Large azimuthal quadrupole and octupole asymmetries have recently been found in $p+\mathrm{Pb}$ collisions at the LHC. We argue that these might arise from a projectile dipole scattering off fluctuations in the target with a size on the order of the dipole. In a holographic scenario, parity-even angular moments $v_{2n}$ are generated by the real part of the light-like Wilson loop due to the contribution from the background metric to the Nambu-Goto action. On the other hand, parity-odd moments $v_{2n+1}$ must arise from the imaginary part of the light-like Wilson loop, which is naturally induced by a fluctuating Neveu-Schwarz 2-form.

Using the factorization approach, we investigate the ${\overline{B}}^0\to {\overline{K}}^0{K}^{+}{\pi }^{-}$ and ${\overline{B}}^0\to K^0{K}^{-}{\pi }^{+}$ decays individually including the resonant and nonresonant contributions. Under the flavor SU(3) symmetry, we obtain the total branching fraction $BR[{\overline{B}}^0\to ({\overline{K}}^0{K}^{+}{\pi }^{-}+K^0{K}^{-}{\pi }^{+})]=(7.17_{-0.53-1.42-0.07}^{+0.50+1.97+0.08})\times {10}^{-6}$, which is in agreement with the recent measurements of BABAR and LHCb within errors. For the decay ${\overline{B}}^0\to {\overline{K}}^0{K}^{+}{\pi }^{-}$, the nonresonant background and $a_0^{+}(1450)$ pole in the current-induced process provide a large contribution, the latter of which has not been included in previous studies. On the contrary, the decay ${\overline{B}}^0\to K^0{K}^{-}{\pi }^{+}$ is dominated by the nonresonant background and the off-shell ${\rho }^{-}$ pole. When the flavor SU(3) symmetry breaking and the final-state rescattering are considered under two different scenarios, the results can also accommodate the experimental data with large uncertainties. Moreover, the direct $CP$ asymmetry of ${\overline{B}}^0\to {\overline{K}}^0{K}^{+}{\pi }^{-}$ is found to be sensitive to the matrix element of scalar density. These predictions could be further tested in the LHCb experiment or Super-b factory in the future.

The doubly charmed hadron production at $B$ factories is of special importance for the study of the hadron structure and the color connections before hadronization. To suppress the combination background fluctuations of the reconstructed hadron mass spectra, we suggest a three-jet event shape trigger. After these three jets are identified by their energy and angular distributions, it is found that (1) the background process $e^{+}{e}^{-}\to c\overline{c}\to h^{\prime }s$ in consideration of the final hadron system ${\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+}+X$ is significantly suppressed, and (2) for the selected events, about half of the particles, ${\mathrm{\Lambda }}_c^{+}$, $K^{-}$, ${\pi }^{+}$, which obviously cannot belong to the decay products of the doubly charmed hadron, can be vetoed. The relevant hadronization is investigated.

We develop a matrix element based reconstruction method called event deconstruction. The method uses information from the hard matrix element and a parton shower to assign probabilities to whether a final state was initiated by a signal or background process. We apply this method in the signal process of a ${\mathit{Z}}^{\prime }$ decaying to boosted top quarks in an all hadronic final state and discuss envisioned improvements of the method. We find that event deconstruction can considerably improve on existing reconstruction techniques.

We investigate the impact of the latest data on Higgs boson branching ratios on the minimal model with a universal extra dimension. Combining constraints from vacuum stability requirements with these branching ratio measurements we are able to make realistic predictions for the signal strengths in this model. We use these to find a lower bound of 1.3 TeV on the size parameter $R^{-1}$ of the model at 95% confidence level, which is far more stringent than any other terrestrial bound obtained till now and is compatible with the dark matter constraints from the Wilkinson Microwave Anisotropy Probe data.