We develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a kinklike soliton built from two real scalar fields with different mass parameters.

Stimulated by the recent observation of ${\mathrm{\Omega }}_c$ as well as past observations of $P_c(4380)$ and $P_c(4450)$, we perform a coupled-channel analysis of ${\mathrm{\Xi }}_c^{*}\overline{K}/{\mathrm{\Omega }}_c\eta /{\mathrm{\Omega }}_c^{*}\eta /{\mathrm{\Xi }}_c{\overline{K}}^{*}/{\mathrm{\Xi }}_c^{\prime }{\overline{K}}^{*}/{\mathrm{\Omega }}_c\omega$ systems to search for possible ${\mathrm{\Omega }}_c$-like molecular states by using a one-boson-exchange potential. Our results suggest that there exists a loosely bound molecular state—a ${\mathrm{\Xi }}_c^{*}\overline{K}/{\mathrm{\Omega }}_c\eta /{\mathrm{\Omega }}_c^{*}\eta /{\mathrm{\Xi }}_c{\overline{K}}^{*}/{\mathrm{\Xi }}_c^{\prime }{\overline{K}}^{*}/{\mathrm{\Omega }}_c\omega$ with $I(J^P)=0(3/2^{-})$—that is mainly composed of the ${\mathrm{\Xi }}_c^{*}\overline{K}$ system. The two-body strong decay width is also studied, where we find that ${\mathrm{\Xi }}_c^{\prime }\overline{K}$ is the dominant decay channel.

It is shown that the recent data on the $K_S^0{K}^{+}$ correlation in Pb-Pb interactions agree with the data on the $\gamma \gamma \to \eta {\pi }^0$ and $\varphi \to \eta {\pi }^0\gamma$ reactions and support the four-quark model of the $a_0(980)$ meson. It is shown that the data does not contradict the validity of the Gaussian assumption. The study of two-kaon correlations could provide more information about light scalar mesons after increasing the accuracy of the experimental and theoretical descriptions.

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.

The predictions of a model which was tuned in 2013 to describe the elastic and diffractive $pp$- and/or $p\overline{p}$-data at collider energies up to 7 TeV are compared with the new 13 TeV TOTEM results. The possibility of the presence of an odd-signature Odderon exchange contribution is discussed.

Investigations of the existence of pentaquark states containing a single $b$ (anti)quark decaying weakly into four specific final states $J/\psi K^{+}{\pi }^{-}p$, $J/\psi K^{-}{\pi }^{-}p$, $J/\psi K^{-}{\pi }^{+}p$, and $J/\psi \varphi (1020)p$ are reported. The data sample corresponds to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$ in 7 and 8 TeV $pp$ collisions acquired with the LHCb detector. Signals are not observed and upper limits are set on the product of the production cross section times branching fraction with respect to that of the ${\mathrm{\Lambda }}_b^0$.

This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski space. This construction is in contrast to the often used, nonsmooth BMS transformations that appear in a gauge-fixed description of the theory.

Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by comparing the distance between pairs of spheres with that of their centers. The quantum Ricci curvature is designed for use on non-smooth and discrete metric spaces, and to satisfy the key criteria of scalability and computability. We test the prescription on a variety of regular and random piecewise flat spaces, mostly in two dimensions. This enables us to quantify its behavior for short lattices distances and compare its large-scale behavior with that of constantly curved model spaces. On the triangulated spaces considered, the quantum Ricci curvature has good averaging properties and reproduces classical characteristics on scales large compared to the discretization scale.

We investigate the phase diagram of quantum gravity with a vertex expansion about constantly-curved backgrounds. The graviton two- and three-point function are evaluated with a spectral sum on a sphere. We obtain, for the first time, curvature-dependent UV fixed point functions of the dynamical fluctuation couplings $g^{*}(R)$, ${\mu }^{*}(R)$, and ${\lambda }_3^{*}(R)$, and the background $f(R)$-potential. Based on these fixed point functions we compute solutions to the quantum and the background equation of motion with and without standard model matter. We have checked that the solutions are robust against changes of the truncation.

For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.

We compute the scaling dimensions of operators with large global charge and spin in $2+1$ dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (i) a single phonon, (ii) two vortices, and (iii) multiple vortices. We also compute correlation functions with two such operators and the Noether current.

In the present paper, perturbations against a Q-ball solution are considered. It is shown that if we calculate the U(1) charge and the energy of the modes, which are solutions to linearized equations of motion, up to the second order in perturbations, we will get incorrect results. In particular, for the time-dependent modes we will obtain nonzero terms, which explicitly depend on time, indicating the nonconservation over time of the charge and the energy. It is shown that, as expected, this problem can be resolved by considering nonlinear equations of motion for the perturbations, providing second-order corrections to the solutions of linearized equations of motion. It turns out that contributions of these corrections to the charge and the energy can be taken into account without solving explicitly the nonlinear equations of motion for the perturbations. It is also shown that the use of such nonlinear equations not only recovers the conservation over time of the charge and the energy but also results in the additivity of the charge and the energy of different modes forming the perturbation.

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [Phys. Rev. D 67, 104015 (2003)]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

We consider quasinormal modes of the massive Dirac field in the background of a Schwarzschild-Tangherlini black hole. Different dimensions of the spacetime are considered, from $d=4$ to $d=9$. The quasinormal modes are calculated using two independent methods: WKB and continued fraction. We obtain the spectrum of quasinormal modes for different values of the overtone number and angular quantum number. An analytical approximation of the spectrum valid in the case of large values of the angular quantum number and mass is calculated. Although we do not find unstable modes in the spectrum, we show that for large values of the mass, the quasinormal modes can become very slowly damped, giving rise to quasistationary perturbations.

We show how supersymmetric hybrid inflation with scalar spectral index $n_{\mathrm{s}}\simeq 0.96–0.97$ is realized in the context of quasiminimal supergravity if we insist that the inflationary potential not exhibit any local extrema. We also address the problem of the initial conditions for both monotonic and nonmonotonic inflationary potentials.

The decay of gravitational potentials in the presence of dark energy leads to an additional, late-time contribution to anisotropies in the cosmic microwave background (CMB) at large angular scales. The imprint of this so-called integrated Sachs-Wolfe (ISW) effect to the CMB angular power spectrum has been detected and studied in detail, but reconstructing its spatial contributions to the CMB map, which would offer the tantalizing possibility of separating the early- from the late-time contributions to CMB temperature fluctuations, is more challenging. Here, we study the technique for reconstructing the ISW map based on information from galaxy surveys and focus in particular on how its accuracy is impacted by the presence of photometric calibration errors in input galaxy maps, which were previously found to be a dominant contaminant for ISW signal estimation. We find that both including tomographic information from a single survey and using data from multiple, complementary galaxy surveys improve the reconstruction by mitigating the impact of spurious power contributions from calibration errors. A high-fidelity reconstruction further requires one to account for the contribution of calibration errors to the observed galaxy power spectrum in the model used to construct the ISW estimator. We find that if the photometric calibration errors in galaxy surveys can be independently controlled at the level required to obtain unbiased dark energy constraints, then it is possible to reconstruct ISW maps with excellent accuracy using a combination of maps from two galaxy surveys with properties similar to Euclid and SPHEREx.

We study phase transitions in $SU(\infty )$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia. Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. We speculate that in the pure gauge theory, although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infinite $N$.

The inert two-Higgs-doublet model (i2HDM) is a theoretically well-motivated example of a minimal consistent dark matter (DM) model which provides monojet, mono-$Z$, mono-Higgs, and vector-boson-$\mathrm{fusion}+{\mathit{E}}_{\mathrm{T}}^{\mathrm{miss}}$ signatures at the LHC, complemented by signals in direct and indirect DM search experiments. In this paper we have performed a detailed analysis of the constraints in the full five-dimensional parameter space of the i2HDM, coming from perturbativity, unitarity, electroweak precision data, Higgs data from the LHC, DM relic density, direct/indirect DM detection, and LHC monojet analysis, as well as implications of experimental LHC studies on disappearing charged tracks relevant to a high DM mass region. We demonstrate the complementarity of the above constraints and present projections for future LHC data and direct DM detection experiments to probe further i2HDM parameter space. The model is implemented into the CalcHEP and micrOMEGAs packages, which are publicly available at the HEPMDB database, and it is ready for a further exploration in the context of the LHC, relic density, and DM direct detection.

It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the three-point function and the calculation of the neutron electric dipole moment with the $\theta$ term suffer from a noise problem due to the $\sqrt{V}$ fluctuation. We identify these problems to have the same origin and the $\sqrt{V}$ problem can be overcome by utilizing the cluster decomposition principle. We demonstrate this by considering the calculations of the glueball mass, the strangeness content in the nucleon, and the $CP$ violation angle in the nucleon due to the $\theta$ term. It is found that for lattices with physical sizes of 4.5–5.5 fm, the statistical errors of these quantities can be reduced by a factor of 3 to 4. The systematic errors can be estimated from the Akaike information criterion. For the strangeness content, we find that the systematic error is of the same size as that of the statistical one when the cluster decomposition principle is utilized. This results in a 2 to 3 times reduction in the overall error.

We use the method of light-cone sum rules to study the electromagnetic transition of the ${\mathrm{\Xi }}_{cc}^{*++}$ into ${\mathrm{\Xi }}_{cc}^{++}\gamma$, whose decay width is estimated to be ${13.7}_{-7.9}^{+17.7}\mathrm{keV}$. This value is large enough for the ${\mathrm{\Xi }}_{cc}^{*++}$ to be observed in the ${\mathrm{\Xi }}_{cc}^{++}\gamma$ channel, and we propose to continually search for it in future LHCb and BelleII experiments.