We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the “master field” the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for a fermion we find a closed expression for the decay rate in ($1+1$) dimensions. It is shown that in the ($1+1$) dimensional case an infrared problem of one-loop correction to the decay rate of a boson is resolved due to a cancellation between soft modes of the field. We also find the boson decay rate in the “sine-Gordon staircase” model in the limits of strong and weak coupling.

We investigate the dynamics of thermalization and the approach to equilibrium in the classical ${\varphi }^4$ theory in $3+1$ spacetime dimensions. The nonequilibrium dynamics is studied by numerically solving the equations of motion in a light-cone-like discretization of the model for a broad range of initial conditions and energy densities. A smooth cascade of energy towards the ultraviolet is found to be the basic mechanism of thermalization. After an initial transient stage, at a time scale of several hundred inverse masses, the squared magnitude of the field spatial gradient becomes larger than the nonlinear term and there emerges a stage of universal cascade, independent of the details of the initial conditions. As the cascade progresses, the modes with higher wave numbers, but well behind the forefront of the cascade, exhibit weaker and weaker nonlinearities well described by the Hartree approximation, while the infrared modes retain strong self-interactions. As a consequence, two time scales for equilibration appear as characteristic of two time-dependent wave number regions. For $k^2\gtrsim \overline{{\varphi }^2}(t)$, we observe an effective equilibration to a time-dependent powerlike spectrum with a time scale in the hundreds of inverse masses; cutoff effects are absent and the Hartree approximation holds for $k^2\gg \overline{{\varphi }^2}(t)$. On the other hand, infrared modes with $k^2\lesssim \overline{{\varphi }^2}(t)$ equilibrate only by time scales in the millions of inverse masses when the cutoff effects become dominant and complete thermalization is setting in. Accordingly, we observe in the field correlator a relatively large and long-lived deviation from the Hartree behavior of a nonperturbative character. There corresponds an effective mass governing the long distance behavior of the correlator which turns out to be significantly smaller than the Hartree mass which is exhibited by the modes with $k^2\gtrsim \overline{{\varphi }^2}(t)$. Virialization and the equation of state start to set in much earlier than thermalization. The applicability of these results in quantum field theory for large occupation numbers and small coupling is analyzed.

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordström (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a $d=5$ Kerr black hole is curved and divergent in the extremal limit. For a $d\ge 6$ Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In $d\ge 5$ the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in $d=5$ with double angular momenta.

We show how a recently discovered black-ring solution with a rotating 2-sphere can be turned into two new solutions of Einstein-Maxwell-dilaton theory. The first is a four-dimensional solution describing a pair of oppositely charged, extremal black holes—known as a black dihole—undergoing uniform acceleration. The second is a five-dimensional solution describing a pair of concentric, static extremal black rings carrying opposite dipole charges—a so-called black diring. The properties of both solutions, which turn out to be formally very similar, are analyzed in detail. We also present, in an appendix, an accelerating version of the Zipoy-Voorhees solution in four-dimensional Einstein gravity.

Modern derivations of the first law of black holes appear to show that the only charges that arise are monopole charges that can be obtained by surface integrals at infinity. However, the recently discovered five dimensional black ring solutions empirically satisfy a first law in which dipole charges appear. We resolve this contradiction and derive a general form of the first law for black rings. Dipole charges do appear together with a corresponding potential. We also include theories with Chern-Simons terms and generalize the first law to other horizon topologies and more generic local charges.

We investigate the properties of a cosmological scenario which undergoes a gravitational phase transition at late times. In this scenario, the Universe evolves according to general relativity in the standard, hot big bang picture until a redshift $z\lesssim 1$. Nonperturbative phenomena associated with a minimally-coupled scalar field catalyzes a transition, whereby an order parameter consisting of curvature quantities such as $R^2$, $R_{ab}{R}^{ab}$, $R_{abcd}{R}^{abcd}$ acquires a constant expectation value. The ensuing cosmic acceleration appears driven by a dark-energy component with an equation-of-state $w<-1$. We evaluate the constraints from type 1a supernovae, the cosmic microwave background, and other cosmological observations. We find that a range of models making a sharp transition to cosmic acceleration are consistent with observations.

We find the solution for the scale factor in a flat universe driven by dust plus a component characterized by a constant parameter of state which dominates in the asymptotic future. We also present an analytic formula (in terms of hypergeometric functions) for the past light cone in such a universe. As applications of this result, we give analytic expressions for the luminosity distance and for the acoustic scale, where the latter determines the peaks positions in the pattern of cosmic microwave background (CMB) anisotropies.

We consider several ways to test for topology directly in harmonic space by comparing the measured $a_{\ell m}$ with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test. Using correlation matrices for cubic and slab-space tori, we study how these tests behave as a function of the minimal scale probed and as a function of the size of the Universe. We also apply them to different first-year Wilkinson microwave anisotropy probe CMB maps and confirm that the Universe is compatible with being infinitely big for the cases considered. We argue that there is an information theoretical limit (given by the Kullback-Leibler divergence) on the size of the topologies that can be detected.

We prove that a flow of cold collisionless particles from all directions in and out of a region necessarily forms a caustic. A corollary is that, in cold dark matter cosmology, galactic halos have inner caustics in addition to the more obvious outer caustics. The outer caustics are fold catastrophes located on topological spheres surrounding the galaxy. To obtain the catastrophe structure of the inner caustics, we simulate the infall of cold collisionless particles in a fixed gravitational potential. The structure of inner caustics depends on the angular momentum distribution of the infalling particles. We confirm a previous result that the inner caustic is a “tricusp ring” when the initial velocity field is dominated by net overall rotation. A tricusp ring is a closed tube whose cross section is a section of an elliptic umbilic catastrophe. However, tidal torque theory predicts that the initial velocity field is irrotational. For irrotational initial velocity fields, we find the inner caustic to have a tentlike structure which we describe in detail in terms of the known catastrophes. We also show how the tent caustic transforms into a tricusp ring when a rotational component is added to the initial velocity field.

In astrophysical environments with intense neutrino fluxes, neutrino-neutrino forward scattering contributes both diagonal and off-diagonal potentials to the flavor-basis Hamiltonian that governs neutrino flavor evolution. We examine a special case where adiabatic flavor evolution can produce an off-diagonal potential from neutrino-neutrino forward scattering that dominates over both the corresponding diagonal term and the potential from neutrino-matter forward scattering. In this case, we find a solution that, unlike the ordinary Mikeyhev-Smirnov-Wolfenstein scenario, has both neutrinos and antineutrinos maximally mixed in medium over appreciable ranges of neutrino and antineutrino energy. Employing the measured solar and atmospheric neutrino mass-squared differences, we identify the conditions on neutrino fluxes that are required for this solution to exist deep in the supernova environment, where it could affect the neutrino signal, heavy-element nucleosynthesis, and even the revival of the supernova shock. We speculate on how this solution might or might not be attained in realistic supernova evolution. Though this solution is ephemeral in time and/or space in supernovae, it may signal the onset of subsequent appreciable flavor mixing for both neutrinos and antineutrinos.

The quantum nondemolition (QND) intracavity topologies of gravitational-wave detectors proposed several years ago allow us, in principle, to obtain sensitivity significantly better than the standard quantum limit using relatively small amount of optical pumping power. In this article we consider an improved more practical version of the optical lever intracavity scheme. It differs from the original version by the symmetry which allows to suppress influence of the input light amplitude fluctuation. In addition, it provides the means to inject optical pumping inside the scheme without increase of optical losses. We consider also sensitivity limitations imposed by the local meter which is the key element of the intracavity topologies. Two variants of the local meter are analyzed, which are based on the spectral variation measurement and on the discrete sampling variation measurement, correspondingly. The former one, while can not be considered as a candidate for a practical implementation, allows, in principle, to obtain the best sensitivity and thus can be considered as an ideal “asymptotic case” for all other schemes. The DSVM-based local meter can be considered as a realistic scheme but its sensitivity, unfortunately, is by far not so good just due to a couple of peculiar numeric factors specific for this scheme. From our point of view search of new methods of mechanical QND measurements probably based on improved DSVM scheme or which combine the local meter with the pondermotive squeezing technique, is necessary.

We study the possibility of using matter-wave interferometry techniques to build a gravitational wave detector. We derive the response function and find that it contains a term proportional to the derivative of the gravitational wave, a point which has been disputed recently. We then study in detail the sensitivity that can be reached by such a detector and find that, if it is operated near resonance, it can reach potentially interesting values in the high frequency regime. The correlation between two or more of such devices can further improve the sensitivity for a stochastic signal.

Marginally trapped surfaces (MTSs) are commonly used in numerical relativity to locate black holes. For dynamical black holes, it is not known generally if this procedure is sufficiently reliable. Even for Schwarzschild black holes, Wald and Iyer constructed foliations which come arbitrarily close to the singularity but do not contain any MTSs. In this paper, we review the Wald-Iyer construction, discuss some implications for numerical relativity, and generalize to the well-known Vaidya spacetime describing spherically symmetric collapse of null dust. In the Vaidya spacetime, we numerically locate non spherically symmetric trapped surfaces which extend outside the standard spherically symmetric trapping horizon. This shows that MTSs are common in this spacetime and that the event horizon is the most likely candidate for the boundary of the trapped region.

The new $f_0(1790)$ meson recently observed by BES Collaboration in $J/\Psi$ decay, is seen only in the Okubo-Zweig-Iizuka (OZI)-forbidden channel. It is shown that chiral symmetry restoration in excited hadrons implies a new selection rule of dynamical origin that forbids some of the OZI-favored mechanisms of decays. Hence decays into channels that are suppressed by OZI can become dominant.

Neutralino dark matter is generally assumed to be relatively heavy, with a mass near the electroweak scale. This does not necessarily need to be the case, however. In the next-to-minimal supersymmetric standard model (NMSSM) and other supersymmetric models with an extended Higgs sector, a very light $CP$-odd Higgs boson can naturally arise making it possible for a very light neutralino to annihilate efficiently enough to avoid being overproduced in the early Universe. In this article, we explore the characteristics of a supersymmetric model needed to include a very light neutralino, $100\mathrm{MeV}<m_{{\tilde{\chi }}_1^0}<20\mathrm{GeV}$, using the NMSSM as a prototype. We discuss the most important constraints from Upsilon decays, $b\to s\gamma$, $B_s\to {\mu }^{+}{\mu }^{-}$ and the magnetic moment of the muon, and find that a light bino or singlino neutralino is allowed, and can be generated with the appropriate relic density. It has previously been shown that the positive detection of dark matter claimed by the DAMA collaboration can be reconciled with other direct dark matter experiments such as CDMS II if the dark matter particle is rather light, between about 6 and 9 GeV. A singlino or binolike neutralino could easily fall within this range of masses within the NMSSM. Additionally, models with sub-GeV neutralinos may be capable of generating the 511 keV gamma-ray emission observed from the galactic bulge by the INTEGRAL/SPI experiment. We also point out measurements which can be performed immediately at CLEO, BABAR, and Belle using existing data to discover or significantly constrain this scenario.

We consider $\mathrm{SU}(3{)}_C\times \mathrm{SU}(2{)}_{AL}\times \mathrm{SU}(2{)}_{BL}\times \mathrm{U}(1{)}_Y$ as the low-energy subgroup of supersymmetric $\mathrm{SU}(3{)}^6$ unification. This may imply small deviations from quark-lepton universality at the TeV scale, as allowed by neutron-decay data. New particles are predicted with specific properties. We discuss, in particular, the new heavy gauge bosons corresponding to $\mathrm{SU}(2{)}_{AL}\times \mathrm{SU}(2{)}_{BL}\to \mathrm{SU}(2{)}_L$.

The hadronic charmless $B$ decays into a scalar meson and a pseudoscalar meson are studied within the framework of QCD factorization. Based on the QCD sum rule method, we have derived the leading-twist light-cone distribution amplitudes of scalar mesons and their decay constants. Although the light scalar mesons $f_0(980)$ and $a_0(980)$ are widely perceived as primarily the four-quark bound states, in practice it is difficult to make quantitative predictions based on the four-quark picture for light scalars. Hence, predictions are made in the 2-quark model for the scalar mesons. The short-distance approach suffices to explain the observed large rates of $f_0(980)K^{-}$ and $f_0(980){\overline{K}}^0$ that receive major penguin contributions from the $b\to ss\overline{s}$ process. When $f_0(980)$ is assigned as a four-quark bound state, there exist extra diagrams contributing to $B\to f_0(980)K$. Therefore, a priori the $f_0(980)K$ rate is not necessarily suppressed for a four-quark state $f_0(980)$. The predicted ${\overline{B}}^0\to a_0^{\pm }(980){\pi }^{\mp }$ and $a_0^{+}(980)K^{-}$ rates exceed the current experimental limits, favoring a four-quark nature for $a_0(980)$. The penguin-dominated modes $a_0(980)K$ and $a_0(1450)K$ receive predominant weak annihilation contributions. There exists a twofold experimental ambiguity in extracting the branching ratio of $B^{-}\to {\overline{K}}_0^{*0}(1430){\pi }^{-}$, which can be resolved by measuring other $K_0^{*}(1430)\pi$ modes in conjunction with the isospin symmetry consideration. Large weak annihilation contributions are needed to explain the $K_0^{*}(1430)\pi$ data. The decay ${\overline{B}}^0\to {\kappa }^{+}{K}^{-}$ provides a nice ground for testing the 4-quark and 2-quark nature of the $\kappa$ meson. It can proceed through $W$-exchange and hence is quite suppressed if $\kappa$ is made of two quarks, while it receives a tree contribution if $\kappa$ is predominately a four-quark state. Hence, an observation of this channel at the level of $\gtrsim {10}^{-7}$ may imply a four-quark assignment for the $\kappa$. Mixing-induced $CP$ asymmetries in penguin-dominated modes are studied and their deviations from $\sin 2\beta$ are found to be tiny.

The analysis of $B\to J/\psi K_2^{\star }(1430)$ decay mode is complicated by the fact that close to the $J^{PC}=2^{++}$ meson $K_2^{*}(1430)$, there lie other $J^{PC}=1^{--}$ and $J^{PC}=0^{++}$ resonances, $K^{\star }(1410)$ and $K_0^{\star }(1430)$ respectively. We show how an angular analysis can be used to isolate the contributions from the different resonances and partial waves contributing to the final state $B\to J/\psi K_X$, where $K_X$ could be any of the resonance $K_2^{\star }(1430)$, $K^{\star }(1410)$ or $K_0^{\star }(1430)$. For this purpose we study the time integrated differential decay rate. We also construct a time-dependent angular asymmetry that enables a clean measurement of the mixing phase $\beta$ in the mode $B\to J/\psi K_2^{*}(1430)$ alone, without contributions from the decay modes $B\to J/\psi K_0^{*}(1430)$ or $B\to J/\psi K^{*}(1410)$. Throughout this work we do not make theoretical assumptions on the hadronic form factors involved in these processes.

The velocity nonrelativistic QCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.

We revise and extend expectations for the properties of charmonium states that lie above charm threshold, in light of new experimental information. We refine the Cornell coupled-channel model for the coupling of $c\overline{c}$ levels to two-meson states, defining resonance masses and widths by pole positions in the complex energy plane, and suggest new targets for experiment.