We study the physical process version and the equilibrium state version of the first law of thermodynamics for a charged $p$-brane. The general setting for our investigations is ($n+p+1$)-dimensional Einstein dilaton gravity with ($p+2$) strength form fields.

Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form ${\mathcal{C}}^2=C_{\alpha \beta \gamma \delta }{C}^{\alpha \beta \gamma \delta }$. The Gauss-Bonnet equation in four-dimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar ${\mathcal{C}}^2$ correction. An important new feature of the spaces with dimension $D>4$ is that in the presence of the Weyl curvature-squared term a necessary solution differs from the corresponding “classical” vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by “quantum corrections,” assuming that the gravitational radius $r_0$ is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).

Recently, a number of analytic prescriptions for computing the nonlinear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus they must be compared with numerical simulations to assess their range of validity. We present a direct side-by-side comparison of several of these analytic approaches, using a suite of high-resolution N-body simulations as a reference, and discuss some general trends. All of the analytic results correctly predict the behavior of the power spectrum at the onset of nonlinearity, and improve upon a pure linear theory description at very large scales. All of these theories fail at sufficiently small scales. At low redshift the dynamic range in scale where perturbation theory is both relevant and reliable can be quite small. We also compute for the first time the two-loop contribution to standard perturbation theory for cold dark matter models, finding improved agreement with simulations at large redshift. At low redshifts however the two-loop term is larger than the one-loop term on quasilinear scales, indicating a breakdown of the perturbation expansion. Finally, we comment on possible implications of our results for future studies. A software package implementing the methods presented here is available at http://mwhite.berkeley.edu/Copter.

We calculate pion vector and scalar form factors in two-flavor lattice QCD and study the chiral behavior of the vector and scalar radii $⟨r^2{⟩}_{V,S}$. Numerical simulations are carried out on a ${16}^3\times 32$ lattice at a lattice spacing of 0.12 fm with quark masses down to $\sim m_s/6$, where $m_s$ is the physical strange quark mass. Chiral symmetry, which is essential for a direct comparison with chiral perturbation theory (ChPT), is exactly preserved in our calculation at finite lattice spacing by employing the overlap quark action. We utilize the so-called all-to-all quark propagator in order to calculate the scalar form factor including the contributions of disconnected diagrams and to improve statistical accuracy of the form factors. A detailed comparison with ChPT reveals that the next-to-next-to-leading-order contributions to the radii are essential to describe their chiral behavior in the region of quark mass from $m_s/6$ to $m_s/2$. Chiral extrapolation based on two-loop ChPT yields $⟨r^2{⟩}_V=0.409(23)(37){\mathrm{fm}}^2$ and $⟨r^2{⟩}_S=0.617(79)(66){\mathrm{fm}}^2$, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants.

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with a relatively small number of gauge configurations.

A combined analysis of the electromagnetic pion and kaon form factors in the neighborhood of $J/\psi$ and $\psi (2S)$ and of the strong decay amplitude of these resonances into kaons is presented. In the presence of a large relative phase between strong and electromagnetic resonance amplitudes the branching ratio, as measured in electron-positron annihilation, receives an additional contribution from the interference between resonance and continuum amplitude neglected in earlier papers. We note that the large relative phase between strong and electromagnetic amplitudes observed in earlier phenomenological analyses relies critically on the specific assumptions on $SU(3)$ symmetry and breaking. Without these assumptions this phase remains effectively undetermined. Also, the modulus of their ratio depends critically on the details of the theory input.

In this article, spherically symmetric thin-shell wormholes supported by a generalized Chaplygin gas are constructed and their stability under perturbations preserving the symmetry is studied. Wormholes with charge and with a cosmological constant are analyzed and the results are compared with those obtained for the original Chaplygin gas, which was considered in a previous work. For some values of the parameters, one stable configuration is also present and a new extra unstable solution is found.

The tensor-vector-scalar theory of gravity, which was designed as a relativistic implementation to the modified dynamics paradigm, has fared quite well as an alternative to dark matter, on both galactic and cosmological scales. However, its performance in the Solar System, as embodied in the post-Newtonian formalism, has not yet been fully investigated. We calculate the post-Newtonian parameters for TeVeS with the cosmological value of the scalar field taken into account, and show that in this situation the cosmological value of the scalar field is tightly linked to the vector field coupling constant $K$, preventing the former from evolving as predicted by its equation of motion. We show that generalizing TeVeS to have an Æther-type vector action, as suggested by Skordis, removes the aforesaid link, and this generalized version of TeVes has its $\beta$, $\gamma$, and $\xi$ parameterized post-Newtonian parameters identical to those in GR, while solar system constraints on the preferred frame parameters ${\alpha }_1$ and ${\alpha }_2$ can be satisfied within a modest range of small values of the scalar and vector fields coupling parameters, and for cosmological values of the scalar field consistent with evolution within the framework of existing cosmological models.

We consider two different effective polymerization schemes applied to $D$-dimensional, spherically symmetric black hole interiors. It is shown that polymerization of the generalized area variable alone leads to a complete, regular, single-horizon spacetime in which the classical singularity is replaced by a bounce. The bounce radius is independent of rescalings of the homogeneous internal coordinate, but does depend on the arbitrary fiducial cell size. The model is therefore necessarily incomplete. It nonetheless has many interesting features: After the bounce, the interior region asymptotes to an infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically continued across the horizon, the black hole exterior exhibits asymptotically vanishing quantum corrections due to the polymerization. In all spacetime dimensions except four, the falloff is too slow to guarantee invariance under Poincaré transformations in the exterior asymptotic region. Hence, the four-dimensional solution stands out as the only example which satisfies the criteria for asymptotic flatness. In this case it is possible to calculate the quantum-corrected temperature and entropy. We also show that polymerization of both phase space variables, the area and the conformal mode of the metric, generically leads to a multiple horizon solution which is reminiscent of polymerized minisuperspace models of spherically symmetric black holes in loop quantum gravity.

The behavior of cosmological evolution is studied in the case when a phantom fluid that contributes to the accelerated expansion of the Universe is introduced in an $F(R)$ model. At the early stages of the history of the Universe, the dark fluid is seen to give rise to a deceleration of its expansion. For $t$ close to present time it works as an additional contribution to the effective cosmological constant and, later, it produces the transition to a phantom era, which could actually be taking place right now in some regions of the cosmos, and might have observable consequences. For $t$ close to the rip time, the Universe becomes completely dominated by the dark fluid, whose equation of state is phantomlike at that time. Our model, which is able to reproduce the dark energy period quite precisely, may still be modified in such a way that the epoch dominated by an effective cosmological constant—produced by the $F(R)$ term and by the dark fluid contribution—becomes significantly shorter, which is what happens when a matter term is included. The dark fluid with phantom behavior gives rise to a superaccelerated phase, as compared with the case where just the viable $F(R)$ term contributes. It is also seen explicitly that an $F(R)$ theory can be constructed from a phantom model in a scalar-tensor theory, in which the scalar field does not behave as phantom (in the latter case the action for $F(R)$ would be complex). Promising $F(R)$ models that are able to cross the phantom divide in a convenient way are constructed explicitly.

It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, general relativity is recovered within a certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to at least 7. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in higher dimensions, but are shifted with respect to their standard values. This effect opens up new scenarios where a maximally symmetric solution in higher dimensions could decay into the compactified spacetime either by tunneling or through a gravitational analog of ghost condensation. Indeed, this is what occurs requiring both the extra dimensions and the four-dimensional cosmological constant to be small.

In this paper we construct, and investigate some thermal properties of, the noncommutative counterpart of Rindler space, which we call $\kappa$-Rindler space. This space is obtained by changing variables in the defining commutators of $\kappa$-Minkowski space. We then rederive the commutator structure of $\kappa$-Rindler space with the help of an appropriate star product, obtained from the $\kappa$-Minkowski one. Using this star product, following the idea of Padmanabhan, we find the leading order, $1/\kappa$ correction to the Hawking thermal spectrum.

We lay out the frameworks to numerically study the structure formation in both linear and nonlinear regimes in general dark-matter-coupled scalar field models, and give an explicit example where the scalar field serves as a dynamical dark energy. Adopting parameters of the scalar field which yield a realistic cosmic microwave background (CMB) spectrum, we generate the initial conditions for our $N$-body simulations, which follow the spatial distributions of the dark matter and the scalar field by solving their equations of motion using the multilevel adaptive grid technique. We show that the spatial configuration of the scalar field tracks well the voids and clusters of dark matter. Indeed, the propagation of scalar degree of freedom effectively acts as a fifth force on dark matter particles, whose range and magnitude are determined by the two model parameters $(\mu ,\gamma )$, local dark matter density as well as the background value for the scalar field. The model behaves like the $\Lambda \mathrm{CDM}$ paradigm on scales relevant to the CMB spectrum, which are well beyond the probe of the local fifth force and thus not significantly affected by the matter-scalar coupling. On scales comparable or shorter than the range of the local fifth force, the fifth force is perfectly parallel to gravity and their strengths have a fixed ratio $2{\gamma }^2$ determined by the matter-scalar coupling, provided that the chameleon effect is weak; if on the other hand there is a strong chameleon effect (i.e., the scalar field almost resides at its effective potential minimum everywhere in the space), the fifth force indeed has suppressed effects in high density regions and shows no obvious correlation with gravity, which means that the dark-matter–scalar-field coupling is not simply equivalent to a rescaling of the gravitational constant or the mass of the dark matter particles. We show these spatial distributions and (lack of) correlations at typical redshifts $(z=0,1,5.5)$ in our multigrid million-particle simulations. The viable parameters for the scalar field can be inferred on intermediate or small scales at late times from, e.g., weak lensing and phase space properties, while the predicted Hubble expansion and linearly simulated CMB spectrum are virtually indistinguishable from the standard $\Lambda \mathrm{CDM}$ predictions.

We generalize the small scale dynamics of the Universe by taking into account models with an equation of state which evolves with time, and provide a complete formulation of the cluster virialization attempting to address the nonlinear regime of structure formation. In the context of the current dark energy models, we find that galaxy clusters appear to form at $z\sim 1-2$, in agreement with previous studies. Also, we investigate thoroughly the evolution of spherical matter perturbations, as the latter decouple from the background expansion and start to “turn around” and finally collapse. Within this framework, we find that the concentration parameter depends on the choice of the considered dark energy (homogeneous or clustered). In particular, if the distribution of the dark energy is clustered then we produce more concentrated structures with respect to the homogeneous dark energy. Finally, comparing the predicted concentration parameter with the observed concentration parameter, measured for four massive galaxy clusters, we find that the scenario which contains a pure homogeneous dark energy is unable to reproduce the data. The situation becomes somewhat better in the case of an inhomogeneous (clustered) dark energy.

We explore the potential of the CERN Large Hadron Collider to access a strongly interacting electroweak symmetry breaking sector via weak boson scattering with $W^{+}{W}^{-}jj$, $ZZjj$, and $W^{\pm }Zjj$ final states. As examples of models with scalar or vector resonances we concentrate on a scenario with a heavy Higgs boson and on a warped Higgsless Kaluza-Klein model of narrow spin-one resonances. The signal and the most prominent background processes are evaluated using exact tree-level matrix elements including full off-shell and finite width effects for final states with two tagging jets and four leptons. Using double forward jet-tagging techniques, we derive dedicated cuts on the observable jets and charged leptons to suppress standard model backgrounds. We demonstrate that the LHC has substantial sensitivity to strong interactions in the electroweak symmetry breaking sector.

An accurate low-energy dispersive parametrization of the scalar $K\pi$ form factor was constructed some time ago in terms of a single parameter guided by the Callan-Treiman low-energy theorem. A similar twice-subtracted dispersive parametrization for the vector $K\pi$ form factor will be investigated here. The robustness of the parametrization of these two form factors will be studied in great detail. In particular the cutoff dependence, the isospin breaking effects, and the possible, though not highly probable, presence of zeros in the form factors will be discussed. Interesting constraints in the latter case will be obtained from the soft-kaon analog of the Callan-Treiman theorem and a comparison with the recent $\tau \to K\pi {\nu }_{\tau }$ data.

We calculate, with several corrections, the nonrelativistic binding by Higgs exchange and gluon exchange between six top and six antitop quarks (actually replaced by left-handed $b$ quarks from time to time). The remarkable result is that, within our calculational accuracy of the order of 14% in the top-quark Yukawa coupling $g_t$, the experimental running top-quark Yukawa coupling $g_t=0.935$ happens to have just that value which gives a perfect cancellation of the unbound $\mathrm{\text{mass}}=12$ top-quark masses by this binding energy. In other words the bound state is massless to the accuracy of our calculation. Our calculation is in disagreement with a similar calculation by Kuchiev et al., but this deviation may be explained by a phase transition. We and Kuchiev et al. compute on different sides of this phase transition.

In the $J/\psi$ radiative decay channels $J/\psi \to \gamma V\overline{V}$, the result of partial wave analysis indicates that the $V\overline{V}$ systems are predominately pseudoscalar component, and most of these channels have relatively large branching ratios at an order of ${10}^{-3}$. Meanwhile, vector mesons, such as $\rho$, $\omega$, and $K^{*}$, have strong couplings with nucleons and/or hyperons. This suggests a dynamical mechanism describing the $\eta p\overline{p}$ form factors for higher $\eta$ mesons, such as $\eta (1405/1475)$ and $\eta (1760)$. It is thus natural to expect that rescatterings of these vector meson pairs into $p\overline{p}$ of $0^{-}$ partial wave could be an important source contributing to $J/\psi \to \gamma p\overline{p}$ of which the branching ratio is at the order of ${10}^{-4}$. Our calculation justifies this point. In particular, we find that interferences between different rescattering amplitudes can produce a significant threshold enhancement in the invariant mass spectrum of $p\overline{p}$. Without introducing dramatic ingredients, our model provides a natural explanation for the peculiar threshold enhancement observed by BES-II in $J/\psi \to \gamma p\overline{p}$. Additional experimental constraints on the $V\overline{V}\to p\overline{p}$ transitions are examined. This mechanism in $J/\psi \to \omega p\overline{p}$ is also discussed.

We calculate the expected branching fraction of the second-class-current decay $\tau \to \pi {\eta }^{\prime }{\nu }_{\tau }$, motivated by a recent experimental upper-limit determination of this quantity. The largest contribution to the branching fraction is due to the intermediate $a_0(980)$ scalar meson, assuming it is a $\overline{u}d$ state. Smaller contributions arise from $a_0(1450)$, $\rho (770)$, and $\rho (1450)$. Our calculated values are substantially below the experimental upper limit, and are smaller still if the $a_0(980)$ is a four-quark state, as often suggested. Thus, a precise measurement or tight upper limit has the potential to determine the nature of the $a_0(980)$, as well as provide information about new scalar interactions.