In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a potential is considered in order to derive physical implications about the classical limit of a quantum system. The complete set of harmonic potentials is considered, which includes the particle under a uniform force, as well as the harmonic and the inverse harmonic oscillators. In addition, as an example of anharmonic system, the pure quartic oscillator is analyzed. Classical and quantum moments corresponding to stationary states of these systems are analytically obtained without solving any differential equation. Finally, dynamical states are also considered in order to study the differences between their classical and quantum evolution.

By using a model with a spatially global scalar field, we show that the energy density of zero-point modes is exponentially suppressed by an average number of field quanta in a finite volume with respect to the energy density in the stationary state of minimal energy. We describe cosmological implications of the mechanism.

We examine solutions to the classical Ishibashi-Kawai-Kitazawa-Tsuchiya matrix model equations in three space-time dimensions. Closed, open and static two-dimensional universes naturally emerge from such models in the commutative limit. We show that tachyonic modes are a generic feature of these cosmological solutions.

We show that, independently of the scalar field potential and of specific asymptotic properties of the spacetime (asymptotically flat, de Sitter or anti–de Sitter), any static, spherically symmetric or planar, black hole solution of the Einstein theory minimally coupled to a real scalar field with a general potential is mode stable under linear odd-parity perturbations. To this end, we generalize the Regge-Wheeler equation for a generic self-interacting scalar field, and show that the potential of the relevant Schrödinger operator can be mapped, by the so-called S-deformation, to a semipositively defined potential. With these results at hand we study the existence of slowly rotating configurations. The frame dragging effect is compared with the corresponding effect in the case of a Kerr black hole.

We evaluate one-loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared. This complements the minimal-minimal part worked out in the previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007)], and we add the minimal-conformal part in a follow-up paper to complete the full self-mass-squared at one-loop order. The computation is performed using dimensional regularization, and the results are fully renormalized by absorbing divergences with counterterms. The finite results can give rise to quantum corrections to the CC scalar mode functions and therefore to their power spectra.

I propose two scale-dependent measures of the homogeneity of the quantum geometry determined by an ensemble of causal triangulations. The first measure is volumetric, probing the growth of volume with graph geodesic distance. The second measure is spectral, probing the return probability of a random walk with diffusion time. Both of these measures, particularly the first, are closely related to those used to assess the homogeneity of our own universe on the basis of galaxy redshift surveys. I employ these measures to quantify the quantum spacetime homogeneity as well as the temporal evolution of quantum spatial homogeneity of ensembles of causal triangulations in the well-known physical phase. According to these measures, the quantum spacetime geometry exhibits some degree of inhomogeneity on sufficiently small scales and a high degree of homogeneity on sufficiently large scales. This inhomogeneity appears unrelated to the phenomenon of dynamical dimensional reduction. I also uncover evidence for power-law scaling of both the typical scale on which inhomogeneity occurs and the magnitude of inhomogeneity on this scale with the ensemble average spatial volume of the quantum spatial geometries.

We determine the curvature of the pseudocritical line of strong interactions by means of numerical simulations at imaginary chemical potentials. We consider $N_f=2+1$ stout improved staggered fermions with physical quark masses and the tree level Symanzik gauge action, and explore two different sets of lattice spacings, corresponding to temporal extensions $N_t=6$ and $N_t=8$. Both the renormalized chiral condensate and the renormalized chiral susceptibility are used to locate the transition. The determinations obtained from the two quantities are in good agreement, a preliminary continuum extrapolation yields $\kappa =0.013(2)(1)$. We also investigate the impact of a nonzero strange quark chemical potential and compare our results to previous determinations in the literature, discussing the possible sources of systematic errors affecting the various procedures.

In this article we discuss the calculation of single top-quark production in the $t$ channel at two-loop order in QCD. In particular we present the decomposition of the amplitude according to its spin and color structure and present complete results for the two-loop amplitudes in terms of master integrals. For the vertex corrections compact analytic expressions are given. The box contributions are implemented in a publicly available c program.

We have determined the production cross sections of the $X(3872)$ state in the reactions $\overline{D}D\to \pi X$, ${\overline{D}}^{*}D\to \pi X$, and ${\overline{D}}^{*}{D}^{*}\to \pi X$, information which is useful for studies of the $X(3872)$ meson abundance in heavy ion collisions. We construct a formalism considering $X$ as a molecular bound state of ${\overline{D}}^0{D}^{*0}-\mathrm{c}.\mathrm{c}.$, $D^{-}{D}^{*+}-\mathrm{c}.\mathrm{c}.$, and $D_s^{-}{D}_s^{*+}-\mathrm{c}.\mathrm{c}.$ To obtain the amplitudes related to these processes we have made use of effective field Lagrangians. The evaluation of the cross section of the processes involving $D^{*}$ meson(s) requires the calculation of an anomalous vertex, $X{\overline{D}}^{*}{D}^{*}$, which has been obtained by considering triangular loops motivated by the molecular nature of $X(3872)$. Proceeding in this way, we have evaluated the cross section for the reaction ${\overline{D}}^{*}D\to \pi X$, and find that the diagrams involving the $X{\overline{D}}^{*}{D}^{*}$ vertex give a large contribution. Encouraged by this finding we estimate the $X{\overline{D}}^{*}{D}^{*}$ coupling, which turns out to be $1.95\pm 0.22$. We then use it to obtain the cross section for the reaction ${\overline{D}}^{*}{D}^{*}\to \pi X$ and find that, in this case too, the $X{\overline{D}}^{*}{D}^{*}$ vertex is relevant. We also discuss the role of the charged components of $X$ in the determination of the production cross sections.

We present a new general dispersive formalism for evaluating the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. In the suggested approach, this correction is related to the imaginary part of the muon’s electromagnetic vertex function. The latter may be directly related to measurable hadronic processes by means of unitarity and analyticity. As a test we apply the introduced formalism to the case of meson pole exchanges and find agreement with the direct two-loop calculation.

Quantum gravity effects could make a black hole explode in a time shorter than the Hawking radiation time, via local tunneling through a white hole solution. Here we estimate the size of a primordial black hole exploding today via this process, using a simple generic model. Fast radio bursts, strong signals with millisecond duration, which are probably of extragalactic origin and have an unknown source, have wavelengths not far from the expected size of the exploding hole. We also discuss the high-energy component of the signal. These results suggest a new window for quantum gravity phenomenology.

In this paper, we show that positron data from AMS seem to rule out the explanation of the ARCADE isotropic radio background excess in terms of self-annihilating dark matter. In earlier works it was found that leptonic annihilation channels of light dark matter provide a good fit to the excess due to synchrotron emission of the final state particles. However, limits on the self-annihilation cross section derived from the positron data of AMS now severely constrain light self-annihilating dark matter and cross sections below that of a thermal relic are already tested for leptonic annihilation channels. Combining these two results, we conclude that an explanation of the excess in the radio background in terms of self-annihilating dark matter is excluded.

We study the anomalous dimensions for scalar operators in Aharony-Bergman-Jafferis-Maldacena theory in the $SU(2)$ sector. The operators we consider have a classical dimension that grows as $N$ in the large $N$ limit. Consequently, the large $N$ limit is not captured by summing planar diagrams—nonplanar contributions have to be included. We find that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscillators. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the fluctuations of the corresponding giant graviton is dependent on the size of the giant. The first subleading corrections to the large $N$ limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability may not survive beyond the large $N$ limit.

In this paper, we extend our earlier study of the spontaneous $CP$ violating scattering of quarks and antiquarks from QCD $Z(3)$ domain walls for the situation when these walls have asymmetric profiles of the Polyakov loop order parameter $l(x)$. Dynamical quarks lead to the explicit breaking of $Z(3)$ symmetry, which lifts the degeneracy of the $Z(3)$ vacua arising from spontaneous breaking of the $Z(3)$ symmetry in the quark-gluon plasma phase. The resulting domain walls have an asymmetric profile of $l(x)$ (under the reflection $x\to -x$ for a domain wall centered at the origin). We calculate the background gauge field profile $A_0$ associated with this domain wall profile. Interestingly, even with the asymmetric $l(x)$ profile, quark-antiquark scattering from the corresponding gauge field configuration does not reflect this asymmetry. We show that the expected asymmetry in scattering arises when we include the effect of the asymmetric profile of $l(x)$ on the effective mass of quarks and antiquarks and calculate the resultant scattering. We discuss the effects of such asymmetric $Z(3)$ walls in generating quark and antiquark density fluctuations in cosmology, and in relativistic heavy-ion collisions, e.g., event-by-event baryon fluctuations.

We perform a detailed renormalization group analysis to study a ($2+1$)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort of field theory can describe the competition and coexistence between distinct long-range orders, and therefore plays a vital role in statistical physics and condensed matter physics. We first derive and solve the renormalization group equations of all the relevant physical parameters, and then show that the system does not have any stable fixed point in the lowest energy limit. Interestingly, this conclusion holds in both the ordered and disordered phases, and also at the quantum critical point. Therefore, the originally continuous transitions are unavoidably turned to first order due to ordering competition. Moreover, we examine the impacts of massless Goldstone boson generated by continuous symmetry breaking on ordering competition, and briefly discuss the physical implications of our results.

In the present paper, we have investigated the role of the cosmic string on spin current and Hall electric field. Due to the background cosmic string, the modified electric field of the system generates renormalized spin-orbit coupling, which induces a modified non-Abelian gauge field. The defect causes a change in the Aharonov-Bohm and Aharonov-Casher phases appearing due to the modified electromagnetic field. In addition, for a time varying electric field we perform explicit analytic calculations to derive the exact form of spin electric field and spin current, which is defect parameter dependent and of oscillating type. Furthermore, in an asymmetric crystal within the Drude model approach we investigate the dependence of the cosmic string parameters on cosmic string induced Hall electric field.

It is a well-known result that any formulation of unimodular gravity is classically equivalent to general relativity (GR); however, a debate exists in the literature about this equivalence at the quantum level. In this work, we investigate the UV quantum structure of a diffeomorphism-invariant formulation of unimodular gravity using functional renormalization group methods in a Wilsonian context. We show that the effective action of the unimodular theory acquires essentially the same form as that of GR in the UV, and that both theories share similar UV completions within the framework of the asymptotic safety scenario for quantum gravity. Furthermore, we find that in this context the unimodular theory can appear to be nonpredictive due to an increasing number of relevant couplings at high energies, and we explain how this unwanted feature is in the end avoided.

In the three-dimensional pure Einstein gravity, the geometries of the vacuum space-times are always trivial, and gravitational waves (gravitons) are strictly forbidden. For the first time, we find a vacuum circularly symmetric black hole with nontrivial geometries in $f(R)$ gravity theory, in which a true singularity appears. In this frame with nontrivial geometry, a perturbative gravitational wave does exist. Beyond the perturbative level, we make a constructive proof of the existence of a gravitational wave in $f(R)$ gravity, where the Birkhoff-like theorem becomes invalid. We find two classes of exact solutions of circularly symmetric pure gravitational wave radiation and absorption.

We analyze different claims on the role of the coupling constant $\lambda$ in so-called $\lambda$-$R$ models, a minimal generalization of general relativity inspired by Hořava-Lifshitz gravity. The dimensionless parameter $\lambda$ appears in the kinetic term of the Einstein-Hilbert action, leading to a one-parameter family of classical theories. Performing a canonical constraint analysis for closed spatial hypersurfaces, we obtain a result analogous to that of Bellorín and Restuccia, who showed that all nonprojectable $\lambda$-$R$ models are equivalent to general relativity in the asymptotically flat case. However, the tertiary constraint present for closed boundary conditions assumes a more general form. We juxtapose this with an earlier finding by Giulini and Kiefer, who ruled out a range of $\lambda$-$R$ models by a physical, cosmological argument. We show that their analysis can be interpreted consistently within the projectable sector of Hořava-Lifshitz gravity, thus resolving the apparent contradiction.

Placing signal templates (grid points) as efficiently as possible to cover a multidimensional parameter space is crucial in computing-intensive matched-filtering searches for gravitational waves, but also in similar searches in other fields of astronomy. To generate efficient coverings of arbitrary parameter spaces, stochastic template banks have been advocated, where templates are placed at random while rejecting those too close to others. However, in this simple scheme, for each new random point its distance to every template in the existing bank is computed. This rapidly increasing number of distance computations can render the acceptance of new templates computationally prohibitive, particularly for wide parameter spaces or in large dimensions. This paper presents a neighboring cell algorithm that can dramatically improve the efficiency of constructing a stochastic template bank. By dividing the parameter space into subvolumes (cells), for an arbitrary point an efficient hashing technique is exploited to obtain the index of its enclosing cell along with the parameters of its neighboring templates. Hence only distances to these neighboring templates in the bank are computed, massively lowering the overall computing cost, as demonstrated in simple examples. Furthermore, we propose a novel method based on this technique to increase the fraction of covered parameter space solely by directed template shifts, without adding any templates. As is demonstrated in examples, this method can be highly effective.