It is shown that for the effective Lagrangian with the factorization ansatz considered here, in the two-body hadronic decay ${\mathcal{B}}_b({\frac{1}{2}}^{+})\to \mathcal{B}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})+V$, with ${\mathcal{B}}_b({\frac{1}{2}}^{+})$ belonging to the representation $\overline{3}$, the only allowed decay channel is ${\mathcal{B}}_b({\frac{1}{2}}^{+})\to \mathcal{B}({\frac{1}{2}}^{+})+V$, where $\mathcal{B}({\frac{1}{2}}^{+})$ belongs to the representation 8 of $SU(3)$. However, for ${\mathcal{B}}_b({\frac{1}{2}}^{+})$ belonging to the sextet representation 6, the allowed decay channels are ${\mathcal{B}}_b({\frac{1}{2}}^{+})\to \mathcal{B}({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})+V$, where $\mathcal{B}({\frac{1}{2}}^{+})$ and $\mathcal{B}({\frac{3}{2}}^{+})$ belong to the octet representation $8^{\prime }$ and the decuplet 10 of $SU(3)$, respectively. The decay channel ${\mathcal{B}}_b({\frac{1}{2}}^{+})\to \mathcal{B}({\frac{1}{2}}^{+})+V$ is analyzed in detail. The decay rate ($\mathrm{\Gamma }$) and the asymmetry parameters $\alpha ,{\alpha }^{\prime },\beta ,\gamma$, and ${\gamma }^{\prime }$ are expressed in terms of four amplitudes. In particular, for the decay ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }+J/\psi$ it is shown that within the factorization framework, using heavy quark spin symmetry, the decay rate and the asymmetry parameters can be expressed in terms of two form factors $F_1$ and $F_2/F_1$, which are to be evaluated in some model. By using the values of these form factors calculated in a quark model, the branching ratio and the asymmetry parameters $\alpha$ and ${\alpha }^{\prime }$ are calculated numerically. For other heavy quarks belonging to the triplet and sextet representations, the results can be easily obtained by using $SU(3)$ symmetry and a phase-space factor. Finally, the decay ${\mathrm{\Omega }}_b^{-}\to {\mathrm{\Omega }}^{-}+J/\psi$ is analyzed within the factorization framework. It is shown that the asymmetry parameter $\alpha$ in this particular decay is zero. The branching ratio obtained in the first approximation is compared with the experimental value.

To a given algebraic curve we assign an infinite family of quantum curves (Schrödinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model we build such quantum curves out of an appropriate representation of the Virasoro algebra, encoded in the structure of the $\alpha /\beta$-deformed matrix integral and its loop equation. We generalize this construction to a large class of algebraic curves by means of a refined topological recursion. We also specialize this construction to various specific matrix models with polynomial and logarithmic potentials, and among other results, show that various ingredients familiar in the study of conformal field theory (Ward identities, correlation functions and a representation of Virasoro operators acting thereon, Belavin-Polyakov-Zamolodchikov equations) arise upon specialization of our formalism to the multi-Penner matrix model.

We review the paradox of low energy excitations of a black hole in anti–de Sitter space (AdS). An appropriately chosen unitary operator in the boundary theory can create a locally strong excitation near the black hole horizon, whose global energy is small as a result of the gravitational redshift. The paradox is that this seems to violate a general rule of statistical mechanics, which states that an operator with energy parametrically smaller than $kT$ cannot create a significant excitation in a thermal system. When we carefully examine the position dependence of the boundary unitary operator that produces the excitation and the bulk observable necessary to detect the anomalously large effect, we find that they do not both fit in a single causal patch. This follows from a remarkable property of position-space AdS correlators that we establish explicitly and resolves the paradox in a generic state of the system, since no combination of observers can both create the excitation and observe its effect. As a special case of our analysis, we show how this resolves the “Born rule” paradox of Marolf and Polchinski [J. High Energy Phys. 01 (2016) 008] and we verify our solution using an independent calculation. We then consider boundary states that are finely tuned to display a spontaneous excitation outside the causal patch of the infalling observer, and we propose a version of causal patch complementarity in AdS/CFT that resolves the paradox for such states as well.

The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on ${\mathrm{AdS}}_{d+1}$. This was established in the sense that at large $N$ the generating functional of correlation functions of single-trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the $O(N)$ vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared recently in holographic contexts. In particular, the ERG tensor network appears to share the general structure of cMERA but differs in important ways. We comment on possible holographic implications.

It has recently been found that quasinormal modes of asymptotically anti-de Sitter (AdS) black holes in theories with higher curvature corrections may help to describe the regime of intermediate ’t Hooft coupling in the dual field theory. Here, we consider quasinormal modes of a scalar field in the background of spherical Gauss–Bonnet–anti-de Sitter (AdS) black holes. In general, the eigenvalues of wave equations are found here numerically, but at a fixed Gauss-Bonnet constant $\alpha =R^2/2$ (where $R$ is the AdS radius), an exact solution of the scalar field equation has been obtained. Remarkably, the purely imaginary modes, which are usually appropriate only to some gravitational perturbations, were found here even for a test scalar field. These purely imaginary modes of the Einstein-Gauss-Bonnet theory do not have the Einsteinian limits, because their damping rates grow, when $\alpha$ is decreasing. Thus, these modes are nonperturbative in $\alpha$. The real oscillation frequencies of the perturbative branch are linearly related to their Schwarzschild-AdS limits $\mathrm{Re}({\omega }_{\mathrm{G}\mathrm{B}})=\mathrm{Re}({\omega }_{\mathrm{SAdS}})(1+K(D)(\alpha /R^2))$, where $D$ is the number of spacetime dimensions. Comparison of the analytical formula with the frequencies found by the shooting method allows us to test the latter. In addition, we found exact solutions to the master equations for gravitational perturbations at $\alpha =R^2/2$ and observed that for the scalar type of gravitational perturbations an eikonal instability develops.

We propose a unique stellar model under the $f(R,\mathcal{T})$ gravity by using the conjecture of Mazur-Mottola [P. Mazur and E. Mottola, Report No. LA-UR-01-5067, P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004)] which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides a repulsive force over the thin spherical shell. This thin shell is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel’dovich’s conjecture of stiff fluid [Y. B. Zel’dovich, Mon. Not. R. Astron. Soc. 160, 1 (1972)], does counterbalance the repulsive force exerted by the interior core region. The exterior spherical region is completely vacuum and assumed to be de Sitter spacetime which can be described by the Schwarzschild solution. Under this specification we find out a set of exact and singularity-free solution of the gravastar which presents several other physically valid features within the framework of alternative gravity.

Thermodynamical properties of black holes in gravitational theories without local Lorentz invariance have been subject to intense investigation in past years due to the presence of universal horizons, which are strong causal barriers even for superluminal signals. Here we present a novel general method for deriving the Smarr formula for this class of theories: in particular we show that the Smarr formulas for Einstein-Æther theory and infrared Hořava gravity follow from scale invariance. We not only reproduce straightforwardly previous findings for static black hole solutions, but we are also able to generalize them to the case of stationary rotating black holes. Finally, we apply our results to the rotating black holes with universal horizon as found in three dimensions, from which we shall draw some lessons on the viability of black hole thermodynamics for black hole solutions endowed with universal horizons.

Cosmic backreaction refers to the general question of whether a homogeneous and isotropic cosmological model is able to predict the correct expansion dynamics of our inhomogeneous Universe. One aspect of this issue concerns the validity of the continuous approximation: does a system of point masses expand the same way as a fluid does? This article shows that it is not exactly the case in Newtonian gravity, although the associated corrections vanish in an infinite Universe. It turns out that Gauss’s law is a key ingredient for such corrections to vanish. Backreaction, therefore, generically arises in alternative theories of gravitation, which threatens the trustworthiness of their cosmological tests. This phenomenon is illustrated with a toy model of massive gravity.

Gravitational radiation is an excellent field for testing theories of gravity in strong gravitational fields. The current observations on the gravitational-wave (GW) bursts by LIGO have already placed various constraints on the alternative theories of gravity. In this paper, we investigate the possible bounds which could be placed on the Brans-Dicke gravity using GW detection from inspiraling compact binaries with the proposed Einstein Telescope, a third-generation GW detector. We first calculate in detail the waveforms of gravitational radiation in the lowest post-Newtonian approximation, including the tensor and scalar fields, which can be divided into the three polarization modes, i.e., “plus mode,” “cross mode,” and “breathing mode.” Applying the stationary phase approximation, we obtain their Fourier transforms, and derive the correction terms in amplitude, phase, and polarization of GWs, relative to the corresponding results in general relativity. Imposing the noise level of the Einstein Telescope, we find that the GW detection from inspiraling compact binaries, composed of a neutron star and a black hole, can place stringent constraints on the Brans-Dicke gravity. The bound on the coupling constant ${\omega }_{\mathrm{BD}}$ depends on the mass, sky position, inclination angle, polarization angle, luminosity distance, redshift distribution, and total observed number $N_{\mathrm{GW}}$ of the binary systems. Taking into account all the burst events up to redshift $z=5$, we find that the bound could be ${\omega }_{\mathrm{BD}}\gtrsim 10^6\times (N_{\mathrm{GW}}/10^4{)}^{1/2}$. Even for the conservative estimation with $10^4$ observed events, the bound is still more than one order tighter than the current limit from Solar System experiments. So, we conclude that the Einstein Telescope will provide a powerful platform to test alternative theories of gravity.

Affine gravity, a gravity theory based on affine connection with no notion of metric, supports scalar field dynamics only if scalar fields have nonvanishing potential. The nonvanishing vacuum energy ensures that the cosmological constant is nonvanishing. It also ensures that the energy-momentum tensor of vacuum gives the dynamically generated metric tensor. We construct this affine setup and study primordial inflation in it. We study inflationary dynamics in affine gravity and general relativity, comparatively. We show that nonminimally coupled inflaton dynamics can be transformed into minimally coupled ones with a modified potential. We also show that there is one unique frame in affine gravity, as opposed to the Einstein and Jordan frames in general relativity. Future observations with higher accuracy may be able to test affine gravity.

We present a detailed comparison between tidal effective-one-body (EOB) models and new state-of-the-art numerical relativity simulations for nonspinning binary neutron star systems. This comparison is the most extensive one to date, covering a wide range in the parameter space and encompassing the energetics of the binary, the periastron advance, the time and frequency evolution of the gravitational wave phase for the dominant mode, and several subdominant modes. We consider different EOB models with tidal effects that have been proposed, including the model with dynamical tides of Hinderer et al. [Phys. Rev. Lett. 116, 181101 (2016)] and the gravitational self-force (GSF) inspired tidal EOB model of Bernuzzi et al. [Phys. Rev. Lett. 114, 161103 (2015)]. The EOB model with dynamical tides leads to the best representation of the systems considered here; however, the differences to the GSF-inspired model are small. A common feature is that for systems where matter effects are large, i.e., stiff equations of state or small total masses, all EOB models underestimate the tidal effects and differences to the results from numerical relativity simulations become noticeable near the merger. We analyze this regime to diagnose the shortcomings of the models in the late inspiral, where the two neutron stars are no longer isolated bodies moving in vacuum. Our work will serve to guide further advances in modeling these systems.

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of $N$-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial $O({\mathrm{\Phi }}^3)$ post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger $O({\mathrm{\Phi }}^4)$ (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the $\kappa$ skewness and kurtosis, however, we find significant bias of up to $2.5\sigma$. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

We introduce a new local symmetry into the fermion sector of a gauge invariant Lagrangian which may or may not contain a scalar or spontaneous symmetry breaking. The standard model in the unitary gauge and QCD are particular cases where this symmetry may apply. We determine the associated vector and axial vector currents and their conservation laws. We show that a single current conservation law may lead to multiple Ward-Takahashi identities. Our results can potentially have important consequences for effective models of low-energy QCD and hadron structure. As a specific example, we discuss the construction of tetraquark states within a generalized linear sigma model and show that this new symmetry probes the tetraquarks in a manner that is consistent with the large $N_c$ limit of QCD.

We use effective field theory and thermal field theory to study the dynamical screening effect in the QED plasma on the $\alpha \text{−}\alpha$ scattering at the ${}^8\mathrm{Be}$ resonance. Dynamical screening leads to an imaginary part of the potential which results in a thermal width for the resonance and dominates over the previously considered static screening effect. As a result, both the resonance energy and width increase with the plasma temperature. Furthermore, dynamical screening can have a huge impact on the $\alpha \text{−}\alpha$ thermal nuclear scattering rate. For example, when the temperature is around 10 keV, the rate is suppressed by a factor of about 900. We expect similar thermal suppressions of nuclear reaction rates to occur in those reactions dominated by an above threshold resonance with a thermal energy. Dynamical screening effects on nuclear reactions can be relevant to cosmology and astrophysics.

The natural Next-to-Minimal Supersymmetric Standard Model (nNMSSM) is featured by predicting one $CP$-even Higgs boson satisfying $m_{h_1}\lesssim 120\mathrm{GeV}$ and Higgsinos lighter than about 300 GeV, and consequently, the cross section for dark matter (DM)-nucleon scattering in this scenario is usually quite large. We study the diphoton signal of the light Higgs boson in nNMSSM by considering the tight constraints from the latest LUX and PandaX-II experiments, and we conclude that the optimal value of the signal rate at 8 TeV LHC is greatly reduced in comparison with earlier predictions. For example, previous studies indicated that the rate may exceed 120 fb for $m_{h_1}\simeq 80\mathrm{GeV}$, while it is at most 25 fb if the lightest neutralino in the scenario is fully responsible for the measured DM relic density. We also investigate the case of $m_{h_1}\simeq 98\mathrm{GeV}$, which is hinted by the excesses of the large electron proton collider analysis on $Z\overline{b}b$ signal and the compact muon solenoid analysis on the diphoton signal. We conclude that nNMSSM can simultaneously explain the excesses at the $1\sigma$ level without violating any known constraints.

A persistence of several anomalies in muon physics, such as the muon anomalous magnetic moment and the muonic hydrogen Lamb shift, hints at new light particles beyond the Standard Model. We address a subset of these models that have a new light scalar state with sizable couplings to muons and suppressed couplings to electrons. A novel way to search for such particles would be through muon beam-dump experiments by (1) missing momentum searches; (2) searches for decays with displaced vertices. The muon beams available at CERN and Fermilab present attractive opportunities for exploring the new scalar with a mass below the dimuon threshold, and potentially covering a range of relevant candidate models. For the models considered in this paper, both types of signals, muon missing momentum and anomalous energy deposition at a distance, can probe a substantial fraction of the unexplored parameter space of the new light scalar, including a region that can explain the muon anomalous magnetic moment discrepancy.

A new algorithm is developed allowing the Monte Carlo study of a $1+1$-dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from $\mathcal{O}(N^3)$ to less than $\mathcal{O}(N^2)$. As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real-time dynamics of a scalar ${\varphi }^4$ theory with weak and strong couplings.

Investigation of the resonances $X(4140)$ and $X(4274)$, which were recently confirmed by the LHCb Collaboration [1], is carried out by treating them as the color triplet and sextet $[cs][\overline{c}\overline{s}]$ diquark-antidiquark states with the spin-parity $J^P=1^{+}$, respectively. We calculate the masses and meson-current couplings of these tetraquarks in the context of the QCD two-point sum rule method by taking into account the quark, gluon, and mixed vacuum condensates up to eight dimensions. We also study the vertices $X(4140)J/\psi \varphi$ and $X(4274)J/\psi \varphi$ and evaluate corresponding strong couplings $g_{X(4140)J/\psi \varphi }$ and $g_{X(4274)J/\psi \varphi }$ by means of the QCD light-cone sum rule method and a technique of the soft-meson approximation. In turn, these couplings contain required information to determine the width of the $X(4140)\to J/\psi \varphi$ and $X(4274)\to J/\psi \varphi$ decay channels. We compare our results for the masses and decay widths of the $X(4140)$ and $X(4274)$ resonances with the LHCb data and alternative theoretical predictions.

In this work we study the decay constants of $B$ and $B_s$ mesons based on the wave function obtained in the relativistic potential model. Our results are in good agreement with experimental data which enables us to apply this method to the investigation of $B$-meson distribution amplitudes. A very compact form of the distribution amplitude is obtained. We also investigate the one-loop QCD corrections to the pure leptonic decays of $B$ mesons. We find that, after subtracting the infrared divergence in the one-loop corrections using the factorization method, the QCD one-loop corrections to the hard amplitude of leptonic decay will be zero.