We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have nonzero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function $P_{1,K}(s)$ as $P_1(s)$ which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the x-ray and gamma-ray emission models from various astrophysical objects with nonzero bulk motions such as radio galaxies and astrophysical jets.

We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $⟨A^2⟩$. Including this effect allows to obtain an acceptable fit around 1 to 1.5 GeV, while corroborating the refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\pm 0.5{\mathrm{GeV}}^{-2}$. As a by-product, we can also provide the prediction $⟨g^2{A}^2⟩\approx 3{\mathrm{GeV}}^2$ obtained at the renormalization scale $\mu =10\mathrm{GeV}$.

In this paper we calculate the branching ratios (BRs) of the 32 charmless hadronic $B_c\to AP$ decays $(A=a_1(1260),b_1(1235),K_1(1270),K_1(1400),f_1(1285),f_1(1420),h_1(1170),h_1(1380))$ by employing the perturbative QCD factorization approach. These considered decay channels can only occur via annihilation type diagrams in the standard model. From the numerical calculations and phenomenological analysis, we found the following results: (a) the perturbative QCD predictions for the BRs of the considered $B_c$ decays are in the range of ${10}^{-6}$ to ${10}^{-8}$, while the $CP$-violating asymmetries are absent because only one type tree operator is involved here; (b) the BRs of $\Delta S=0$ processes are generally much larger than those of $\Delta S=1$ ones due to the large Cabibbo-Kobayashi-Maskawa factor of $|V_{ud}/V_{us}{|}^2\sim 19$; (c) since the behavior for the ${}^{1}P_1$ meson is much different from that of the ${}^{3}P_1$ meson, the BRs of $B_c\to A({}^{1}P_1)P$ decays are generally larger than those of $B_c\to A({}^{3}P_1)P$ decays; (d) the perturbative QCD predictions for the BRs of $B_c\to (K_1(1270),K_1(1400)){\eta }^{(\prime )}$ and $(K_1(1270),K_1(1400))K$ decays are rather sensitive to the value of the mixing angle ${\theta }_K$.

In this work, we apply the vector meson dominance model to extract the electromagnetic timelike form factor of the $D^{*}\to D$ transition combining the recent Belle data for $e^{+}{e}^{-}\to D^{*+}{D}^{-}+\mathrm{c}.\mathrm{c}.$ and data for $D^{*}\to D\gamma$. Two solutions are obtained in the interpretation of the cross section lineshape: i) With a relatively large coupling for $\psi D^{*}\overline{D}$ determined by experiment, destructive interferences among those charmonium components are required to bring down the overall cross sections, and then account for the cross section lineshape. ii) With a relatively small value for the $\psi D^{*}\overline{D}$ coupling based on heavy quark theory, an apparent cross section deficit near threshold is observed, and contributions from other mechanisms are needed. It might imply the presence of an additional resonance $X(3900)$. Meanwhile, we also point out that an enhancement like that could be produced by the $D_s^{*}{\overline{D}}_s+\mathrm{c}.\mathrm{c}.$ open channel effects.

We consider the Isgur-Wise function $\xi (\omega )$ within a new modified version of a heavy-light chiral quark model. While early versions of such models gave an absolute value of the slope that was too small, namely ${\xi }^{\prime }(1)\simeq -0.4$ to $-0.3$, we show how extended version(s) may lead to values around $-1$, in better agreement with recent measurements. This is obtained by introducing a new mass parameter in the heavy-quark propagator. We also shortly comment on the consequences for the decay modes $B\to D\overline{D}$.

We calculate the one-loop electroweak corrections to $e^{+}{e}^{-}\to W^{+}{W}^{-}Z$ and $e^{+}{e}^{-}\to ZZZ$ and analyze their impacts on both the total cross section and some key distributions. These processes are important for the measurements of the quartic couplings of the massive gauge bosons which can be a window on the mechanism of spontaneous symmetry breaking. We find that even after subtracting the leading QED corrections, the electroweak corrections can still be large, especially as the energy increases. We compare and implement different methods of dealing with potential instabilities in the routines pertaining to the loop integrals. For the real corrections we apply a dipole subtraction formalism and compare it to a phase-space slicing method.

The inclusion of the unstable features of a spin-1 particle, without breaking the electromagnetic gauge invariance, can be properly accomplished by including higher order contributions as done in the so-called fermion loop scheme (for the $W$ gauge boson) and the boson loop scheme (for vector mesons). This induces a nontrivial modification to the electromagnetic vertex of the particle, which must be considered in addition to any other contribution computed as stable particles. Considering the modified electromagnetic vertex, we obtain general expressions for the corresponding corrections to the multipoles as a function of the mass of the particles in the loop. For the $W$ gauge boson no substantial deviations from the stable case are observed. For the $\rho$ and $K^{*}$ mesons the mass of the particles in the loop has a significant effect, and can be comparable with corrections of a different nature.

A universal description of the hyperfine splittings (HFS) in bottomonium and the $B_q$ ($q=n$, $s$, $c$) mesons is obtained with a universal strong coupling constant ${\alpha }_s(\mu )=0.310$ in a spin-spin potential. Other characteristics are calculated within the field correlator method, taking the freezing value of the strong coupling independent of $n_f$. The HFS $M(B^{*})-M(B)=45.5(1)\mathrm{MeV}$, $M(B_s^{*})-M(B_s)=46.2(1)\mathrm{MeV}$ are obtained in full agreement with experiment both for $n_f=3$ and $n_f=4$. In bottomonium, $M({\rm Y}(9460))-M({\eta }_b)=71.1\mathrm{MeV}$ for $n_f=5$ agrees with the BABAR data, while a smaller HFS, equal to 63.4(5) MeV, is obtained for $n_f=4$. We predict HFS $M({\rm Y}(2S))-M({\eta }_b(2S))=36(1)\mathrm{MeV}$, $M({\rm Y}(3S))-M(\eta (3S))=28(1)\mathrm{MeV}$, and the mass difference $M(B_c^{*})-M(B_c)=58(1)\mathrm{MeV}$, which gives $M(B_c^{*})=6334(1)\mathrm{MeV}$. If a coupling with open channels is neglected, for higher states the masses $M(B_c(2{}^{1}S_0))=6865(5)\mathrm{MeV}$ and $M(B_c^{*}(2S{}^{3}S_1))=6901(5)\mathrm{MeV}$ are calculated.

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein’s equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large $N$. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

As an extension of our previous work concerning the large $N$ reduction on group manifolds, we study the large $N$ reduction on coset spaces. We show that large $N$ field theories on coset spaces are described by certain corresponding matrix models. We also construct Chern-Simons–like theories on group manifolds and coset spaces, and give their reduced models.

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in Dvali-Gabadadze-Porrati type scale parameter $m$, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk $M$ and $m$. This cutoff $M_{\mathrm{cutoff}}=\sqrt{Mm}$ is much higher than the analogous strong coupling scale of the Dvali-Gabadadze-Porrati model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the ($d+1$)-dimensional bulk with the brane carrying the $d$-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of $d=4$.

In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.

We construct new seven-dimensional gravity by adding two topological terms to the Einstein-Hilbert action. For a certain choice of the coupling constants, these terms exist naturally in seven-dimensional gauged supergravity from the $S^4$ reduction of eleven-dimensional supergravity with the $R^4$ corrections. We derive the full set of the equations of motion. We find that the static spherically-symmetric black holes are unmodified by the topological terms. We obtain squashed ${\mathrm{AdS}}_7$, and also squashed seven spheres and $Q^{111}$ spaces in Euclidean signature.

Future ground-based and space-borne interferometric gravitational-wave detectors may capture between tens and thousands of binary coalescence events per year. There is a significant and growing body of work on the estimation of astrophysically relevant parameters, such as masses and spins, from the gravitational-wave signature of a single event. This paper introduces a robust Bayesian framework for combining the parameter estimates for multiple events into a parameter distribution of the underlying event population. The framework can be readily deployed as a rapid post-processing tool.

We develop a new covariant formalism to treat spherically symmetric spacetimes in metric $f(R)$ theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general $f(R)$ gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only vacuum solution with vanishing Ricci scalar. We also show that our general framework provides a clear way of showing that the Schwarzschild solution is not a unique static spherically symmetric solution, providing some insight into how the current form of Birkhoff’s theorem breaks down for these theories.

The global dynamics of a homogeneous Universe in loop quantum cosmology is viewed as a scattering process of its geometrodynamical equivalent. This picture is applied to build a flexible (easy to generalize) and not restricted just to exactly solvable models method of verifying the preservation of the semiclassicality through the bounce. The devised method is next applied to two simple examples: (i) the isotropic Friedmann-Robertson-Walker universe, and (ii) the isotropic sector of the Bianchi I model. For both of them we show that the dispersions in the logarithm of the volume $\ln (v)$ and scalar field momentum $\ln (p_{\varphi })$ in the distant future and past are related via strong triangle inequalities. This implies, in particular, a strict preservation of the semiclassicality (in considered degrees of freedom) in both the cases (i) and (ii). Derived inequalities are general: valid for all the physical states within the considered models.

We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard $R^2$, $(\mathrm{\text{Ricci}}{)}^2$ terms, and in the next order contain $(\mathrm{\text{Riemann}}{)}^3$ as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the $(\mathrm{\text{Riemann}}{)}^3$ term.

Gamma-ray bursts (GRBs) have been regarded as standard candles at very high redshift for cosmology research. We have proposed a new method to calibrate GRB distance indicators with Type Ia supernova (SNe Ia) data in a completely cosmology-independent way to avoid the circularity problem that had limited the direct use of GRBs to probe cosmology [N. Liang, W. K. Xiao, Y. Liu, and S. N. Zhang, Astrophys. J. 685, 354 (2008).]. In this paper, a simple method is provided to combine GRB data into the joint observational data analysis to constrain cosmological models; in this method those SNe Ia data points used for calibrating the GRB data are not used to avoid any correlation between them. We find that the $\Lambda \mathrm{CDM}$ model is consistent with the joint data in the $1\mathrm{\text{−}}\sigma$ confidence region, using the GRB data at high redshift calibrated with the interpolating method, the Constitution set of SNe Ia, the cosmic microwave background radiation from Wilkinson Microwave Anisotropy Probe five year observation, the baryonic acoustic oscillation from the spectroscopic Sloan Digital Sky Survey Data Release 7 galaxy sample, the x-ray baryon mass fraction in clusters of galaxies, and the observational Hubble parameter versus redshift data. Comparing to the joint constraints with GRBs and without GRBs, we find that the contribution of GRBs to the joint cosmological constraints is a slight shift in the confidence regions of cosmological parameters to better enclose the $\Lambda \mathrm{CDM}$ model. Finally, we reconstruct the acceleration history of the Universe up to $z>6$ with the distance moduli of SNe Ia and GRBs and find some features that deviate from the $\Lambda \mathrm{CDM}$ model and seem to favor oscillatory cosmology models; however, further investigations are needed to better understand the situation.

We discuss the primordial spectrum of a massless and minimally coupled scalar field, produced during the initial anisotropic epoch before the onset of inflation. We consider two models of the anisotropic cosmology, the (planar) Kasner-de Sitter solution (Bianchi I) and the Taub-NUT-de Sitter solution (Bianchi IX), where the 3-space geometry is initially anisotropic, followed by the de Sitter phase due to the presence of a positive cosmological constant. We discuss the behavior of a quantized, massless and minimally coupled scalar field in the anisotropic stage. This scalar field is not the inflaton and hence does not contribute to the background dynamics. We focus on the quantization procedure and evolution in the preinflationary anisotropic background. Also, in this paper for simplicity the metric perturbations are not taken into account. The initial condition is set by the requirement that the scalar field is initially in an adiabatic state. Usually, in a quantum harmonic oscillator system, an adiabatic process implies the one where the potential changes slowly enough compared to its size, and the time evolution can be obtained from the zeroth order WKB approximation. In our case, such a vacuum state exists only for limited solutions of the anisotropic universe, whose spacetime structure is regular in the initial times. In this paper, we call our adiabatic vacuum state the anisotropic vacuum. In the Kasner-de Sitter model, for one branch of planar solutions there is an anisotropic vacuum unless $k_3\ne 0$, where $k_3$ is the comoving momentum along the third direction, while in the other branch there is no anisotropic vacuum state. In the first branch, for the moderate modes, $k_3\sim k$, where $k$ is the total comoving momentum, the scalar power spectrum has an oscillatory behavior and its direction dependence is suppressed. For the planar modes, $k_3\ll k$, in contrast, the direction dependence becomes more important, because of the amplification of the scalar amplitude during this interval of the violation of WKB approximation in the initial anisotropic stage. The qualitative behaviors in the Taub-NUT-de Sitter models are very similar to the case of the first branch of the planar Kasner-de Sitter model.

We study the first law of thermodynamics in IR modified Hořava-Lifshitz spacetime. Based on the Bekenstein-Hawking entropy, we obtain the integral formula and the differential formula of the first law of thermodynamics for the Kehagias-Sfetsos black hole by treating $\omega$ as a new state parameter and redefining a mass that is just equal to $M_{\mathrm{ADM}}$ obtained by Myung [32] if we take $\alpha =3\pi /8$.