While the expansion rate of a homogeneous isotropic universe is simply proportional to the square-root of the energy density, the expansion rate of an inhomogeneous universe also depends on the nature of the density inhomogeneities. In this paper we calculate to second order in perturbation variables the expansion rate of an inhomogeneous universe and demonstrate corrections to the evolution of the expansion rate. While we find that the mean correction is small, the variance of the correction on the scale of the Hubble radius is sensitive to the physical significance of the unknown spectrum of density perturbations beyond the Hubble radius.

I present results for the two-loop self-energy functions for neutral and charged Higgs scalar bosons in minimal supersymmetry. The contributions given here include all terms involving the QCD coupling, and those following from Feynman diagrams involving Yukawa couplings and scalar interactions that do not vanish as the electroweak gauge couplings are turned off. The impact of these contributions on the computation of pole masses of the neutral and charged Higgs scalar bosons is studied in a few examples.

Although supersymmetry has not been seen directly by experiment, there are powerful physics reasons to suspect that it should be an ingredient of nature and that superpartner masses should be somewhat near the weak scale. I present an argument that if we dismiss our ordinary intuition of fine-tuning, and focus entirely on more concrete physics issues, the PeV scale might be the best place for supersymmetry. PeV-scale supersymmetry admits gauge coupling unification, predicts a Higgs mass between 125 GeV and 155 GeV, and generally disallows flavor changing neutral currents and CP-violating effects in conflict with current experiment. The PeV scale is motivated independently by dark matter and neutrino mass considerations.

We consider various possibilities for generating neutrino masses in supersymmetric models with an additional $\mathrm{U}(1{)}^{\prime }$ gauge symmetry. One class of models involves two extra $\mathrm{U}(1{)}^{\prime }\times \mathrm{U}(1{)}^{\prime \prime }$ gauge symmetries, with $\mathrm{U}(1{)}^{\prime \prime }$ breaking at an intermediate scale and yielding small Dirac masses through high-dimensional operators. The right-handed neutrinos $N_i^c$ can naturally decouple from the low energy $\mathrm{U}(1{)}^{\prime }$, avoiding cosmological constraints. A variant version can generate large Majorana masses for $N_i^c$ and an ordinary seesaw. We secondly consider models with a pair of heavy triplets which couple to left-handed neutrinos. After integrating out the heavy triplets, a small neutrino Majorana mass matrix can be generated by the induced nonrenormalizable terms. We also study models involving the double-seesaw mechanism, in which heavy Majorana masses for $N_i^c$ are associated with the TeV-scale of $\mathrm{U}(1{)}^{\prime }$ breaking. We give the conditions to avoid runaway directions in such models and discuss simple patterns for neutrino masses.

The photon-meson transition form factors of light pseudoscalar mesons ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$ are systematically calculated in a light-cone framework, which is applicable as a light-cone quark model at low $Q^2$ and is also physically in accordance with the light-cone perturbative quantum chromodynamics approach at large $Q^2$. The calculated results agree with the available experimental data at high-energy scale. We also predict the low $Q^2$ behaviors of the photon-meson transition form factors of ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$, which are measurable in the $e+A(\mathrm{N}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{u}\mathrm{s})\to e+A+M$ process via the Primakoff effect at JLab and DESY.

The physics of pions within a finite volume is explored using lattice regularized chiral perturbation theory. This regularization scheme permits a straightforward computational approach to be used in place of analytical continuum techniques. Using the pion mass, decay constant, form factor and charge radius as examples, it is shown how numerical results for volume dependences are obtained at the one-loop level from simple summations.

We consider the quark-meson-model in a finite three-dimensional volume using the Schwinger proper-time renormalization group. We derive and solve the flow equations for finite volume in local potential approximation. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. The corresponding effective meson potential breaks chiral O(4) symmetry explicitly, depending on $\sigma$ and $\overrightarrow{\pi }$ fields separately. We calculate the volume dependence of the pion mass and of the pion decay constant with the renormalization group flow equations and compare with recent results from chiral perturbation theory in a finite volume.

We study the threshold enhancement effects of baryon–antibaryon systems in $J/\psi$ decays at BES using parity $P$, charge conjugation $C$, and flavor $\mathrm{S}\mathrm{U}(3)$ symmetries. The $P$ and $C$ symmetries restrict the $p\overline{p}$ in $J/\psi \to \gamma p\overline{p}$ to be in a state with $C=+1$, while the $p\overline{p}$ in $J/\psi \to {\pi }^{0}p\overline{p}$ to be with $C=-1$. Combining the $C$ and $P$ symmetries with flavor $\mathrm{S}\mathrm{U}(3)$ symmetry, i.e., the CPS symmetry, we find that the $\Lambda \overline{p}$ system cannot be in $0^{+}$ and $0^{-}$ states in $J/\psi \to K^{+}\Lambda \overline{p}$. We provide a consistent explanation of observation and nonobservation of near threshold enhancements in $J/\psi \to K^{+}\Lambda \overline{p}$ and $J/\psi \to {\pi }^{0}p\overline{p}$, respectively. We also find that near baryon pair threshold enhancement can happen in several channels for $J/\psi$ decays and can be several times larger than that observed in $J/\psi \to K^{+}\Lambda \overline{p}$ in some channels.

There exist many experimental indications that final-state interactions (FSIs) may play a prominent role not only in charmful $B$ decays but also in charmless $B$ ones. We examine the final-state rescattering effects on the hadronic $B$ decay rates and their impact on direct CP violation. The color-suppressed neutral modes such as $B^0\to D^0{\pi }^0,{\pi }^0{\pi }^0,{\rho }^0{\pi }^0,K^0{\pi }^0$ can be substantially enhanced by long-distance rescattering effects. The direct CP-violating partial rate asymmetries in charmless $B$ decays to $\pi \pi /\pi K$ and $\rho \pi$ are significantly affected by final-state rescattering, and their signs are generally different from that predicted by the short-distance (SD) approach. For example, direct CP asymmetry in $B^0\to {\rho }^0{\pi }^0$ is increased to around 60% due to final-state rescattering effects whereas the short-distance picture gives about 1%. Evidence of direct CP violation in the decay ${\overline{B}}^0\to K^{-}{\pi }^{+}$ is now established, while the combined BABAR and Belle measurements of ${\overline{B}}^0\to {\rho }^{\pm }{\pi }^{\mp }$ imply a $3.6\sigma$ direct CP asymmetry in the ${\rho }^{+}{\pi }^{-}$ mode. Our predictions for CP violation agree with experiment in both magnitude and sign, whereas the QCD factorization predictions (especially for ${\rho }^{+}{\pi }^{-}$) seem to have some difficulty with the data. Direct CP violation in the decay $B^{-}\to {\pi }^{-}{\pi }^0$ is very small ($\lesssim 1\%$) in the standard model even after the inclusion of FSIs. Its measurement will provide a nice way to search for new physics as in the standard model QCD penguins cannot contribute (except by isospin violation). Current data on $\pi K$ modes seem to violate the isospin sum-rule relation, suggesting the presence of electroweak penguin contributions. We have also investigated whether a large transverse polarization in $B\to \varphi K^{*}$ can arise from the final-state rescattering of $D^{(*)}{\overline{D}}_s^{(*)}$ into $\varphi K^{*}$. While the longitudinal polarization fraction can be reduced significantly from short-distance predictions due to such FSI effects, no sizable perpendicular polarization is found owing mainly to the large cancellations occurring in the processes $\overline{B}\to D_s^{*}\overline{D}\to \varphi {\overline{K}}^{*}$ and $\overline{B}\to D_s{\overline{D}}^{*}\to \varphi {\overline{K}}^{*}$, and this can be understood as a consequence of CP and SU(3) [CPS] symmetry. To fully account for the polarization anomaly (especially the perpendicular polarization) observed in $B\to \varphi K^{*}$, FSI from other states or other mechanism, e.g., the penguin-induced annihilation, may have to be invoked. Our conclusion is that the small value of the longitudinal polarization in $VV$ modes cannot be regarded as a clean signal for new physics.

We present an improved calculation of $B\to$ light vector form factors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is typically 10% and can be improved, at least in part, by reducing the uncertainty of hadronic input parameters. We present our results in a way which details the dependence of the form factors on these parameters and facilitates the incorporation of future updates of their values from, e.g., lattice calculations. We also give simple and easy-to-implement parametrizations of the $q^2$ dependence of the form factors which are valid in the full kinematical regime of $q^2$.

The standard model prediction for the ${\overline{B}}^0\to X_{s,d}\gamma$ decay amplitude with a right-handed photon is believed to be tiny, suppressed by $m_{s,d}/m_b$, compared to the amplitude with a left-handed photon. We show that this suppression is fictitious: In inclusive decays, the ratio of these two amplitudes is only suppressed by $g_s/(4\pi )$, and in exclusive decays by ${\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}/m_b$. The suppression is not stronger in ${\overline{B}}^0\to X_d\gamma$ decays than it is in ${\overline{B}}^0\to X_s\gamma$. We estimate that the time dependent $CP$ asymmetries in $B\to K^{*}\gamma$, $\rho \gamma$, $K_S{\pi }^0\gamma$, and ${\pi }^{+}{\pi }^{-}\gamma$ are of order 0.1 and that they have significant uncertainties.

We consider the dimensional reduction of 11D supergravity to type IIA in ten dimensions, and study the conditions for supersymmetry in terms of $p$-form spinor bilinears of the supersymmetry parameter. For a bosonic solution to be supersymmetric these $p$ forms must satisfy a set of differential relations, which we derive in full; the supersymmetry variations of the dilatino give a set of algebraic relations which are also derived. These results are then used to provide the generalized calibration conditions for some of the basic brane solutions, we also follow up a suggestion of Hackett-Jones and Smith and present a calibration condition for IIA supertubes. We find that a probe supertube satisfies this bound but does not saturate it, with the bound successfully accounting for the D0 charge of the supertube but not the string charge; we speculate that there should be a stronger calibration inequality than the one given.

The Noether currents associated with the nonlinearly realized super-Poincaré symmetries of the Green-Schwarz (Nambu-Goto-Akulov-Volkov) action for a non-Bogomol'nyi-Prasad-Sommerfield (non-BPS) $p=2$ brane embedded in a $N=1$, $D=4$ target superspace are constructed. The $R$ symmetry current, the supersymmetry currents, the energy-momentum tensor and the scalar central charge current are shown to be components of a world-volume supercurrent. The centrally extended superconformal transformations are realized on the Nambu-Goldstone boson and fermion fields of the non-BPS brane. The superconformal currents form supersymmetry multiplets with the world-volume conformal central charge current and special conformal current being the primary components of the supersymmetry multiplets containing all the currents. Correspondingly the superconformal symmetry breaking terms form supersymmetry multiplets the components of which are obtainable as supersymmetry transformations of the primary currents' symmetry breaking terms.

The Randall-Sundrum scenario, with a $1+3$-dimensional brane in a five-dimensional bulk spacetime, can be generalized in various ways. We consider the case where the $Z_2$ symmetry at the brane is relaxed, and in addition the gravitational action is generalized to include an induced gravity term on the brane. We derive the complete set of equations governing the gravitational dynamics for a general brane and bulk, and identify how the asymmetry and the induced gravity act as effective source terms in the projected field equations on the brane. For a Friedmann brane in an anti-de Sitter bulk, the solution of the Friedmann equation is given by the solution of a quartic equation. We find the perturbative solutions for small asymmetry, which has an effect at late times.

I derive formulas for variations of mass, angular momentum, and canonical energy in Einstein $(n-2)$-gauge form field theory by means of the Arnowitt-Deser-Misner formalism. Considering the initial data for the manifold with an interior boundary which has the topology of $(n-2)$ sphere, I obtained the generalized first law of black hole thermodynamics. Supposing that a black hole event horizon comprises a bifurcation Killing horizon with a bifurcate surface, I find that the solution is static in the exterior world, when the Killing timelike vector field is normal to the horizon and has vanishing electric or magnetic fields on static slices.

In our previous paper, based on the Carter & Quintana framework and the Damour-Soffel-Xu scheme, we deduced a complete and closed set of post-Newtonian dynamical equations for elastically deformable astronomical bodies. In this paper, we expand the general-relativistic perturbation equations of elastic deformable bodies (field equations, stress-strain relation, Euler equation) in terms of Generalized Spherical Harmonics. This turns the set of complicated partial differential equations into a set of ordinary differential equations. This will be useful for numerical applications that mainly deal with the global dynamics of the Earth.

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we “quantize” the classical random walk by finding, subject to a certain condition of “strong positivity”, the most general Markovian, translationally invariant “decoherence functional” with nearest neighbor transitions.

We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the nonequilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation emerges naturally. We consider a particle species that is stable in the vacuum and interacts with heavier particles that constitute a thermal bath in equilibrium. Asymptotic theory suggests a definition of a fully renormalized single particle distribution function. Its real time dynamics is completely determined by the nonequilibrium effective action which furnishes a Dyson-like resummation of the perturbative expansion. The distribution function reaches thermal equilibrium on a time scale $\sim 1/2{\Gamma }_k(T)$ with ${\Gamma }_k(T)$ being the quasiparticle relaxation rate. The equilibrium distribution function depends on the full spectral density as a consequence the fluctuation-dissipation relation. Such dependence leads to off shell contributions to the particle abundance. A specific model of a bosonic field $\Phi$ in interaction with two heavier bosonic fields ${\chi }_{1,2}$ is studied. The decay of the heaviest particle and its recombination lead to a width of the spectral function for the particle $\Phi$ and to off shell corrections to the abundance. We find substantial departures from the Bose-Einstein result both in the high temperature and the low temperature but high momentum region. In the latter the abundance is exponentially suppressed but larger than the Bose-Einstein result. We obtain the Boltzmann equation in renormalized perturbation theory and highlight the origin of the differences. Cosmological consequences are discussed: we argue that the corrections to the abundance of cold dark matter candidates are observationally negligible and that recombination erases any possible spectral distortions of the cosmic microwave background (CMB). However we expect that the enhancement at high temperature may be important for baryogenesis.

Vacuum alignment in technicolor models provides an attractive origin for the quarks' $CP$ violation and, possibly, a natural solution for the strong-$CP$ problem of QCD. We discuss these topics in this paper. Then we apply them to determine plausible mixing matrices for left and right-handed quarks. These matrices determine the Cabibbo-Kobayashi-Maskawa matrix as well as new mixing angles and phases that are observable in extended technicolor (ETC) and topcolor (TC2) interactions. We determine the contributions of these new interactions to $CP$-violating and mixing observables in the $K^0$, $B_d$ and $B_s$ systems. Consistency with mixing and $CP$ violation in the $K^0$ system requires assuming that ETC interactions are electroweak generation-conserving even if technicolor has a walking gauge coupling. Large ETC gauge boson masses and small intergenerational mixing then result in negligibly small ETC contributions to $B$-meson mixing and $CP$ violation and to $\mathrm{R}\mathrm{e}({ϵ}^{\prime }/ϵ)$. We confirm our earlier strong lower bounds on TC2 gauge boson masses from $B_d$–${\overline{B}}_d$ mixing. We then pay special attention to the possibility that current experiments indicate a deviation from standard model expectations of the values of $\sin 2\beta$ measured in $B_d\to J/\psi K_S$, $\varphi K_S$, ${\eta }^{\prime }{K}_S$, and $\pi K_S$, studying the ability of TC2 to account for these. We also determine the TC2 contribution to $\Delta M_{B_s}$ and to $\mathrm{R}\mathrm{e}({ϵ}^{\prime }/ϵ)$, and find them to be appreciable.

We investigate the decays $\eta ,{\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ up to next-to-leading order in the framework of the combined $1/N_c$ and chiral expansions. Counter terms of unnatural parity at next-to-leading order with unknown couplings are important to acommodate the results both to the experimental decay width and the photon spectrum. The presence of these coefficients does not allow for a determination of the number of colors from these decays.