Ultracompact objects are self-gravitating systems with a light ring. It was recently suggested that fluctuations in the background of these objects are extremely long lived and might turn unstable at the nonlinear level, if the object is not endowed with a horizon. If correct, this result has important consequences: objects with a light ring are black holes. In other words, the nonlinear instability of ultracompact stars would provide a strong argument in favor of the “black hole hypothesis,” once electromagnetic or gravitational-wave observations confirm the existence of light rings. Here we explore in some depth the mode structure of ultracompact stars, in particular constant-density stars and gravastars. We show that the existence of very long-lived modes—localized near a second, stable null geodesic—is a generic feature of gravitational perturbations of such configurations. Already at the linear level, such modes become unstable if the object rotates sufficiently fast to develop an ergoregion. Finally, we conjecture that the long-lived modes become unstable under fragmentation via a Dyson–Chandrasekhar–Fermi mechanism at the nonlinear level. Depending on the structure of the star, it is also possible that nonlinearities lead to the formation of small black holes close to the stable light ring. Our results suggest that the mere observation of a light ring is a strong evidence for the existence of black holes.

Lovelock theory is a natural extension of the Einstein theory of general relativity to higher dimensions in which the first and second orders correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We present exact black hole solutions of $D\ge 4$-dimensional spacetime for first-, second-, and third-order Lovelock gravities in a string cloud background. Further, we compute the mass, temperature, and entropy of black hole solutions for the higher-dimensional general relativity and Einstein–Gauss–Bonnet theories and also perform thermodynamic stability of black holes. It turns out that the presence of the Gauss–Bonnet term and/or background string cloud completely changes the black hole thermodynamics. Interestingly, the entropy of a black hole is unaffected due to a background string cloud. We rediscover several known spherically symmetric black hole solutions in the appropriate limits.

In real-time lattice simulations of cosmic strings in the Abelian Higgs model, the broken translational invariance introduces lattice artifacts; relativistic strings therefore decelerate and radiate. We introduce two different methods to construct a moving string on the lattice, and study in detail the lattice effects on moving strings. We find that there are two types of lattice artifact: there is an effective maximum speed with which a moving string can be placed on the lattice, and a moving string also slows down, with the deceleration approximately proportional to the exponential of the velocity. To mitigate this, we introduce and study an improved discretization, based on the tree-level Lüscher-Weisz action, which is found to reduce the deceleration by an order of magnitude, and to increase the string speed limit by an amount equivalent to halving the lattice spacing. The improved algorithm is expected to be very useful for 3D simulations of cosmic strings in the early Universe, where one wishes to simulate as large a volume as possible.

The dark sector of the Universe need not be completely separable into distinct dark matter and dark energy components. We consider a model of early dark energy in which the dark energy mimics a dark matter component in both evolution and perturbations at early times. Barotropic aether dark energy scales as a fixed fraction, possibly greater than one, of the dark matter density and has vanishing sound speed at early times before undergoing a transition. This gives signatures not only in cosmic expansion but in sound speed and inhomogeneities, and in number of effective neutrino species. Model parameters describe the timing, sharpness of the transition, and the relative abundance at early times. Upon comparison with current data, we find viable regimes in which the dark energy behaves like dark matter at early times: for transitions well before recombination the dark energy to dark matter fraction can equal or exceed unity, while for transitions near recombination the ratio can only be a few percent. After the transition, dark energy goes its separate way, ultimately driving cosmic acceleration and approaching a cosmological constant in this scenario.

It has been well known since the 1970s that stationary black holes do not generically support scalar hair. Most of the no-hair theorems which support this depend crucially upon the assumption that the scalar field has no time dependence. Here we fill in this omission by ruling out the existence of stationary black hole solutions even when the scalar field may have time dependence. Our proof is fairly general, and in particular applies to noncanonical scalar fields and certain nonasymptotically flat spacetimes. It also does not rely upon the spacetime being a black hole.

In this article we propose a new strategy to address the little hierarchy problem. We show that the addition of a fourth generation with vectorlike quarks to the minimal supersymmetric standard model can raise the predicted value of the physical Higgs mass by mixing with the top sector. The mixing requires a larger top quark Yukawa coupling (by up to $\sim 6\%$) to produce the same top mass. Since loop corrections to $m_h$ go as $y_{\text{top}}^4$, this will in turn increase the predicted value of the physical Higgs mass, a point not previously emphasized in the literature. In the presence of mixing, for A terms and soft masses around 900 GeV, a Higgs mass of 125 GeV can be generated while retaining perturbativity of the gauge couplings, evading constraints from electroweak precision measurements and recent LHC searches, and pushing the Landau pole for the top Yukawa above the GUT scale. Soft masses can be as low as 800 GeV in parts of parameter space with a Landau pole at $\sim {10}^{10}\mathrm{GeV}$. However, the Landau pole can still be pushed above the GUT scale if one sacrifices perturbative unification by adding fields in a $\mathbf{5}+\overline{\mathbf{5}}$ representation. With a ratio of weak-scale vector masses $\ne 1$, soft masses may be slightly below 800 GeV. The model predicts new quarks and squarks with masses $⪆750\mathrm{GeV}$. We briefly discuss potential paths for discovery or exclusion at the LHC.

$D_s$ mesons are studied in three quantum channels ($J^P=0^{+}$, $1^{+}$ and $2^{+}$), where experiments have identified the very narrow $D_{s0}^{*}(2317)$, $D_{s1}(2460)$ and narrow $D_{s1}(2536)$, $D_{s2}^{*}(2573)$. We explore the effect of nearby $DK$ and $D^{*}K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or $2+1$ dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $16^3\times 32$ or $32^3\times 64$). In addition to $\overline{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with $m_{\pi }\simeq 156\mathrm{MeV}$ renders the $D_{s1}(2460)$ as a strong interaction bound state 44(10) MeV below $D^{*}K$ threshold, which is in agreement with the experiment. The $D_{s0}^{*}(2317)$ is found 37(17) MeV below $DK$ threshold, close to the experiment value of 45 MeV. The narrow resonances $D_{s1}(2536)$ and $D_{s2}^{*}(2573)$ are also found close to the experimental masses.

We present a detailed analysis on the $B_c$ meson semileptonic decays, $B_c\to {\eta }_c(J/\psi )\ell \nu$, up to next-to-leading order (NLO) QCD correction. We adopt the principle of maximum conformality (PMC) to set the renormalization scales for those decays. After applying the PMC scale setting, we determine the optimal renormalization scales for the $B_c\to {\eta }_c(J/\psi )$ transition form factors (TFFs). Because of the same ${\beta }_0$-terms, the optimal PMC scales at the NLO level are the same for all those TFFs, i.e., ${\mu }_r^{\mathrm{PMC}}\approx 0.8\mathrm{GeV}$. We adopt a strong coupling model from the massive perturbation theory to achieve a reliable pQCD estimation in this low energy region. Furthermore, we adopt a monopole form as an extrapolation for the $B_c\to {\eta }_c(J/\psi )$ TFFs to all their allowable $q^2$ region. Then, we predict ${\mathrm{\Gamma }}_{B_c\to {\eta }_c\ell \nu }(\ell =e,\mu )=(71.53_{-8.90}^{+11.27})\times 10^{-15}\mathrm{GeV}$, ${\mathrm{\Gamma }}_{B_c\to {\eta }_c\tau \nu }=(27.14_{-4.33}^{+5.93})\times 10^{-15}\mathrm{GeV}$, ${\mathrm{\Gamma }}_{B_c\to J/\psi \ell \nu }(\ell =e,\mu )=(106.31_{-14.01}^{+18.59})\times 10^{-15}\mathrm{GeV}$, ${\mathrm{\Gamma }}_{B_c\to J/\psi \tau \nu }=(28.25_{-4.35}^{+6.02})\times 10^{-15}\mathrm{GeV}$, where the uncertainties are squared averages of all the mentioned error sources. We show that the present prediction of the production cross section times branching ratio for $B_c^{+}\to J/\psi {\ell }^{+}v$ relative to that for $B^{+}\to J/\psi K^{+}$, i.e., $\Re (J/\psi {\ell }^{+}\nu )$, is in a better agreement with CDF measurements than the previous predictions.

We investigate how local parity breaking due to large topological fluctuations may affect hadron physics. A modified dispersion relation is derived for the lightest vector mesons $\rho$ and $\omega$. They exhibit a mass splitting depending on their polarization. We present a detailed analysis of the angular distribution associated to the lepton pairs created from these mesons searching for polarization dependencies. We propose two angular variables that carry information related to the parity breaking effect. Possible signatures for experimental detection of local parity breaking that could potentially be seen by the PHENIX and STAR collaborations are discussed.

The mixing of new vectorlike leptons with leptons in the standard model can generate flavor violating couplings of $h$, $W$ and $Z$ between heavy and light leptons. Focusing on the couplings of the muon, the partial decay width of $h\to e_4^{\pm }{\mu }^{\mp }$, where $e_4$ is the new lepton, can be significant when this process is kinematically allowed. Subsequent decays $e_4^{\pm }\to Z{\mu }^{\pm }$ and $e_4^{\pm }\to W^{\pm }\nu$ lead to the same final states as $h\to Z{Z}^{*}\to Z{\mu }^{+}{\mu }^{-}$ and $h\to W{W}^{*}\to W\mu \nu$, thus possibly affecting measurements of these processes. We calculate $h\to e_4{\ell }_i\to Z{\ell }_i{\ell }_j$, where ${\ell }_{i,j}$ are standard model leptons, including the possibility of off-shell decays, interference with $h\to Z{Z}^{*}\to Z{\ell }_i{\ell }_i$, and the mass effect of ${\ell }_{i,j}$ which are important when the mass of $e_4$ is close to the mass of the Higgs boson. We derive constraints on masses and couplings of the heavy lepton from the measurement of $h\to 4\ell$. We focus on the couplings of the muon and discuss possible effects on $h\to Z{Z}^{*}$ from the region of parameters that can explain the anomaly in the measurement of the muon $g-2$.

We derive precise standard model predictions for the dilepton invariant mass and the $\tau$ energy distributions in inclusive $B\to X_c\tau \overline{\nu }$ decay. We include ${\mathrm{\Lambda }}_{\mathrm{QCD}}^2/m_b^2$ and ${\alpha }_s$ corrections using the $1S$ short-distance mass scheme, and estimate shape function effects near maximal $\tau$ energy. These results can improve the sensitivity of $b\to c\tau \overline{\nu }$ related observables to beyond standard model physics.

In this work, we carry out the study on $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ ($J=0,1,2$) by considering the hadronic loop mechanism. Our results show that Belle’s preliminary data of the branching ratios for $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ can be well reproduced in our calculation with a common parameter range, which reflects the similarity among these $\mathrm{\Upsilon }(5S)\to {\chi }_{bJ}\omega$ decays of concern.

$\mathrm{SU}(N_c)$ gauge theories containing matter fields may be invariant under transformations of some subgroup of the ${\mathbb{Z}}_{N_c}$ center; the maximum such subgroup is ${\mathbb{Z}}_p$, with $p$ depending on $N_c$ and the representations of the various matter fields in the theory. Confining $\mathrm{SU}(N_c)$ gauge theories in either $3+1$ or $2+1$ space-time dimensions and with matter fields in any representation have string tensions for representation $R$ given by ${\sigma }_R={\sigma }_f\frac{p_R(p-p_R)g(p_R(p-p_R))}{(p-1)g(p-1)}$ with $p_R=n_R\mathrm{mod}(p)$, where ${\sigma }_f$ is the string tension for the fundamental representation, $g$ is a positive finite function and $n_R$ is the n-ality of $R$. This implies that a necessary condition for a theory in this class to have an area law is invariance of the theory under a nontrivial subgroup of the center. Significantly, these results depend on $p$ regardless of the value of $N_c$.

We investigate the consequences of space-time being curved on space-based quantum communication protocols. We analyze tasks that require either the exchange of single photons in a certain entanglement distribution protocol or beams of light in a continuous-variable quantum key distribution scheme. We find that gravity affects the propagation of photons, therefore adding additional noise to the channel for the transmission of information. The effects could be measured with current technology.

We analyze the nonrelativistic approximation of the Dirac equation for slow fermions, having small kinetic energies compared to their rest energy $m$ and moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential to order $1/m$, induced by a static metric of spacetime excluding possible rotations of the coordinate frame. The derivation of the nonrelativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy–Wouthuysen transformation. We discuss the chameleon field as source of a torsion field and torsion–matter interactions.

The sign problem in QCD at finite temperature and density leads naturally to the consideration of complex saddle points of the action or effective action. The global symmetry $\mathcal{CK}$ of the finite-density action, where $\mathcal{C}$ is charge conjugation and $\mathcal{K}$ is complex conjugation, constrains the eigenvalues of the Polyakov loop operator $P$ at a saddle point in such a way that the action is real at a saddle point, and net color charge is zero. The values of ${\mathrm{Tr}}_{F}P$ and ${\mathrm{Tr}}_F{P}^{†}$ at the saddle point are real but not identical, indicating the different free energy cost associated with inserting a heavy quark versus an antiquark into the system. At such complex saddle points, the mass matrix associated with Polyakov loops may have complex eigenvalues, reflecting oscillatory behavior in color-charge densities. We illustrate these properties with a simple model which includes the one-loop contribution of gluons and two flavors of massless quarks moving in a constant Polyakov loop background. Confinement-deconfinement effects are modeled phenomenologically via an added potential term depending on the Polyakov loop eigenvalues. For sufficiently large temperature $T$ and quark chemical potential $\mu$, the results obtained reduce to those of perturbation theory at the complex saddle point. These results may be experimentally relevant for the compressed baryonic matter experiment at FAIR.

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background. In addition to a dark energy field $\chi$ associated with the gravitational sector, we take into account multiple scalar fields ${\varphi }_I$ ($I=1,2,\dots ,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I={\partial }_{\mu }{\varphi }_I{\partial }^{\mu }{\varphi }_I$. These additional scalar fields can model the perfect fluids of radiation and nonrelativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce nontrivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields ${\varphi }_I$ are generally suppressed relative to that for the dark energy field $\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

The local momentum space expansion for the real vector field is considered. Using Riemann normal coordinates we obtain an expansion of the Feynman Green function up to and including terms that are quadratic in the curvature. The results are valid for a nonminimal operator such as that arising from a general Feynman-type gauge fixing condition. The result is used to derive the first three terms in the asymptotic expansion for the coincidence limit of the heat kernel without taking the trace, thus obtaining the untraced heat kernel coefficients. The spacetime dimension is kept general before specializing to four dimensions for comparison with previously known results. As a further application we reexamine the anomalous trace of the stress-energy-momentum tensor for the Maxwell field and comment on the gauge dependence.