We present here a detailed derivation of an explicit spin-dependent expression for the bending angle of light as it traverses in the equatorial plane of a spinning black hole. We show that the deflection produced in the presence of the black hole angular momentum explicitly depends on whether the motion of the light ray is in the direction, or opposite to the spin. Compared to the zero-spin Schwarzschild case, the bending angle is greater for direct orbits, and smaller for retrograde orbits, confirming our physical intuition about the loss of left-right symmetry from a lensing perspective. In addition, we show that for higher spins, the effect is more pronounced resulting in tighter winding of direct orbits with respect to the axis of rotation, and a higher degree of unwinding of retrograde orbits. A direct consequence of this effect is a shift in image positions in strong gravitational lensing.

We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, $\epsilon$, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in $\epsilon$, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in $\epsilon$ follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

Given a scalar field with metastable minima, bubbles nucleate quantum mechanically. When bubbles collide, energy stored in the bubble walls is converted into kinetic energy of the field. This kinetic energy can facilitate the classical nucleation of new bubbles in minima that lie below those of the “parent” bubbles. This process is efficient and classical, and changes the dynamics and statistics of bubble formation in models with multiple vacua, relative to that derived from quantum tunneling.

Multiple lines of evidence indicate an anomalous injection of high-energy $e^{+}{e}^{-}$ in the galactic halo. The recent $e^{+}$ fraction spectrum from the payload for antimatter matter exploration and light-nuclei astrophysics (PAMELA) shows a sharp rise up to 100 GeV. The Fermi gamma-ray space telescope has found a significant hardening of the $e^{+}{e}^{-}$ cosmic-ray spectrum above 100 GeV, with a break, confirmed by HESS at around 1 TeV. The advanced thin ionization calorimeter (ATIC) has also detected a similar excess, falling back to the expected spectrum at 1 TeV and above. Excess microwaves towards the galactic center in the WMAP data are consistent with hard synchrotron radiation from a population of 10–100 GeV $e^{+}{e}^{-}$ (the WMAP “Haze”). We argue that dark matter annihilations can provide a consistent explanation of all of these data, focusing on dominantly leptonic modes, either directly or through a new light boson. Normalizing the signal to the highest energy evidence (Fermi and HESS), we find that similar cross sections provide good fits to PAMELA and the Haze, and that both the required cross section and annihilation modes are achievable in models with Sommerfeld-enhanced annihilation. These models naturally predict significant production of gamma rays in the galactic center via a variety of mechanisms. Most notably, there is a robust inverse-Compton scattered (ICS) gamma-ray signal arising from the energetic electrons and positrons, detectable at Fermi/GLAST energies, which should provide smoking gun evidence for this production.

A rigorous demonstration that given appropriate data on our past light cone leads to the determination of the metric functions and all their time derivatives on our past light cone is presented, thus showing how to evolve the solution we obtain from data on the light cone off it in a well-defined and straightforward way. It also automatically gives a procedure for constructing the solution for all spherically symmetric, inhomogeneous cosmological Lemaître-Tolman-Bondi models in observational coordinates as a Taylor series in time of however many terms we need. Our procedure takes into account the essential data giving the maximum of the observer area (angular-diameter) distance, and the redshift $z_{\max }$ at which that occurs. This enables the determination of the vacuum-energy density ${\mu }_{\Lambda }$, which would otherwise remain undetermined.

Several intriguing phenomena, unlikely within the standard inflationary cosmology, were reported in the cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe and appear to be uncorrelated. Two of these phenomena, termed CMB anomalies, are representative of their disparate nature: the North-South asymmetry in the CMB angular-correlation strength, inconsistent with an isotropic universe, and the cold spot, producing a significant deviation from Gaussianity. We find a correlation between them, at medium angular scales ($\ell =11–20$): we show that a successive diminution of the cold spot (absolute value) temperature implies a monotonic decrease of the North-South asymmetry power, and moreover we find that the cold spot supplies 60% of such power.

The DAMA/LIBRA Collaboration has detected an annual modulation of the recoil rate in NaI crystals with the phase expected for weakly interacting massive particle (WIMP) scattering events. This signal is dramatically inconsistent with upper limits from other experiments for elastically scattering weak-scale WIMPs. However, the results are compatible for the case of inelastic dark matter (iDM). The iDM theory, as implemented by Tucker-Smith and Weiner, constrains the WIMP to a tight contour in ${\sigma }_n-\delta$ space, where $\delta$ is the mass difference between the ground state and excited WIMPs. An urgent priority in direct detection is to test this scenario. The crucial test of the iDM explanation of DAMA—an experimentum crucis—is an experiment with directional sensitivity, which can measure the daily modulation in direction. Because the contrast can be 100%, it is a sharper test than the much smaller annual modulation in the rate. We estimate the significance of such an experiment as a function of the WIMP mass, cross section, background rate, and other parameters. The proposed experiment severely constrains the DAMA/iDM scenario even with modest exposure ($\sim 1000\mathrm{kg}·\mathrm{day}$) on gaseous xenon.

We reexamine the possibility of employing the viscosity over entropy density ratio as a diagnostic tool to identify a phase transition in hadron physics to the strongly coupled quark-gluon plasma and other circumstances where direct measurement of the order parameter or the free energy may be difficult. It has been conjectured that the minimum of $\eta /s$ does indeed occur at the phase transition. We now make a careful assessment in a controlled theoretical framework, the linear sigma model at large $N$, and indeed find that the minimum of $\eta /s$ occurs near the second-order phase transition of the model due to the rapid variation of the order parameter (here the $\sigma$ vacuum expectation value) at a temperature slightly smaller than the critical one.

We study the production of $C=+$ charmonium states $X$ in $e^{+}{e}^{-}\to \gamma +X$ at $B$ factories with $X={\eta }_c(nS)$ ($n=1$, 2, 3), ${\chi }_{cJ}(mP)$ ($m=1$, 2), and ${}^{1}D_2(1D)$. In the $S$- and $P$-wave case, contributions of QED with one-loop QCD corrections are calculated within the framework of nonrelativistic QCD (NRQCD), and in the $D$-wave case only the QED contribution is considered. We find that in most cases the one-loop QCD corrections are negative and moderate, in contrast to the case of double charmonium production $e^{+}{e}^{-}\to J/\psi +X$, where one-loop QCD corrections are positive and large in most cases. We also find that the production cross sections of some of these states in $e^{+}{e}^{-}\to \gamma +X$ are larger than that in $e^{+}{e}^{-}\to J/\psi +X$ by an order of magnitude even after the negative one-loop QCD corrections are included. We then argue that search for the $X(3872)$, $X(3940)$, $Y(3940)$, and $X(4160)$ in $e^{+}{e}^{-}\to \gamma +X$ at $B$ factories may be helpful to clarify the nature of these states. For completeness, the production of bottomonium states in $e^{+}{e}^{-}$ annihilation is also discussed.

We study the vector-vector interaction within the framework of the hidden gauge formalism for the channels with quantum numbers charm $C=0$ and strangeness $S=0$ in the energy region around 4000 MeV. By looking for poles in the complex plane we find three resonances that could be identified by the mass, width, and quantum numbers with the $Y\left(3940\right)$, $Z\left(3940\right)$, and $X\left(4160\right)$, these poles appear with isospin $I=0$ and $J^{\mathrm{PC}}=0^{++}$, $2^{++}$ and $2^{++}$, respectively. Whereas the $Y\left(3940\right)$ and $Z\left(3940\right)$ are coupled more strongly to $D^{*}{\overline{D}}^{*}$, the $X\left(4160\right)$ is basically a $D_s^{*}{\overline{D}}_s^{*}$ molecular state. Another two extra resonances appear in our approach with $I=0$, 1 and $J^{\mathrm{PC}}=1^{+-}$, $2^{++}$ which are not found in the PDG with masses $M=3945$, 3912 MeV and widths $\Gamma =0$, 120 MeV, respectively.

We construct domain-wall brane models based on the grand-unification group SO(10), generalizing the SU(5) model of Davies, George, and Volkas. Motivated by the Dvali-Shifman proposal for the dynamical localization of gauge bosons, the SO(10) symmetry is spontaneously broken inside the wall. We present two scenarios: in the first, the unbroken subgroup inside the wall is $\mathrm{SU}(5)\times \mathrm{U}(1{)}_X$, and in the second it is the left-right symmetry group $\mathrm{SU}(3)\times \mathrm{SU}(2{)}_L\times \mathrm{SU}(2{)}_R\times U(1{)}_{B-L}$. In both cases we demonstrate that the phenomenologically-correct fermion zero modes can be localized to the wall, and we briefly discuss how the symmetry-breaking dynamics may be extended to induce breaking to the standard model group with subsequent electroweak breaking. Dynamically localized gravity is realized through the type 2 Randall-Sundrum mechanism.

To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003); Prog. Theor. Phys. 113, 481 (2005)] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007). We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.

A one-loop effective potential of the Higgs field on the Schwarzschild background is derived in the framework of a toy model: a $SO(N)$ scalar multiplet interacting with the gauge fields, the $SO(N)$ gauge symmetry being broken by the Higgs mechanism. As expected, the potential depends on the space point and results in a mass shift of all massive particles near a black hole. It is shown that the obtained potential is generally covariant, depends on the space point through the metric component $g_{00}$ in the adapted coordinates, and has the same form for an arbitrary static, spherically symmetric background. Some properties of this potential are investigated. In particular, if the conformal symmetry holds valid for massless particles on the given background, there exist only two possible scenarios depending on the sign of an arbitrary constant arising from the regularization procedure: the masses of all massive particles grow infinitely, when they approach the black hole horizon, or the gauge symmetry is restored at a finite distance from the horizon and all particles become massless. If the conformal symmetry is spoiled, an additional term in the effective potential appears and the intermediate regime arises. Several normalization conditions fixing the undefined constants are proposed, and estimations for the mass shifts are given in these cases. It should be mentioned that the use of the one-loop approximation becomes questionable in the region where the one-loop effective potential acquires large values. So, in that region, we can believe in the obtained results only to a certain extent.

We treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity. We find that the flight times of pulses can fluctuate due to modification of the graviton vacuum by the compactification. In the case of a five-dimensional Kaluza-Klein theory, the mean variation in flight time can grow logarithmically with the flight distance. This effect is in principle observable, but too small to serve as a realistic probe of the existence of extra dimensions. This differs from the conclusion reached in an earlier work. We also examine the effect of the compactification on the widths of spectral lines, and find that there is a small line narrowing effect. This effect is also small for compactification well above the Planck scale, but might serve as a test of the existence of extra dimensions.

We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested sampling with flat and, for the first time, curved spatial geometries of the Universe, using data from the CMB anisotropies, the Union supernovae (SN) sample, and a combined measurement of the integrated Sachs-Wolfe effect. The CMB alone favors a 3% (positively correlated) isocurvature contribution in both the flat and curved cases. The nonadiabatic contribution to the observed CMB temperature variance is $0<{\alpha }_T<7\%$ at 98% C.L. in the curved case. In the flat case, combining the CMB with SN data artificially biases the result towards the pure adiabatic $\Lambda \mathrm{CDM}$ concordance model, whereas in the curved case the favored level of nonadiabaticity stays at the 3% level with all combinations of data. However, the ratio of Bayes factors, or $\Delta \ln $ (evidence), is more than 5 points in favor of the flat adiabatic $\Lambda \mathrm{CDM}$ model, which suggests that the inclusion of the 5 extra parameters of the curved isocurvature model is not supported by the current data. The results are very sensitive to the second and third acoustic peak regions in the CMB temperature angular power: therefore a careful calibration of these data will be required before drawing decisive conclusions on the nature of primordial perturbations. Finally, we point out that the odds for the flat nonadiabatic model are 1:3 compared to the curved adiabatic model. This may suggest that it is not much less motivated to extend the concordance model with 4 isocurvature degrees of freedom than it is to study the spatially curved adiabatic model, though at the moment the model selection disfavors both of these models.

We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the Universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parametrized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parametrized post-Einsteinian templates for the binary coalescence of equal-mass, nonspinning compact objects in a quasicircular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.

In a previous paper [S. Iso, N. Okada, and Y. Orikasa, Phys. Lett. B 676, 81 (2009).], we have proposed the minimal $B-L$ extended standard model as a phenomenologically viable model that realizes the Coleman-Weinberg-type breaking of the electroweak symmetry. Assuming the classical conformal invariance and stability up to the Planck scale, we will show in this paper that the model naturally predicts TeV scale $B-L$ breaking as well as a light standard-model singlet Higgs boson and light right-handed neutrinos around the same energy scale. We also study phenomenology and detectability of the model at the Large Hadron Collider and the International Linear Collider.

Thermal properties of glueballs in $SU(3)$ Yang-Mills theory are investigated in a large temperature range from $0.3T_c$ to $1.9T_c$ on anisotropic lattices. The glueball operators are optimized for the projection of the ground states by the variational method with a smearing scheme. Their thermal correlators are calculated in all 20 symmetry channels. It is found in all channels that the pole masses $M_G$ of glueballs remain almost constant when the temperature is approaching the critical temperature $T_c$ from below, and start to reduce gradually with the temperature going above $T_c$. The correlators in the $0^{++}$, $0^{-+}$, and $2^{++}$ channels are also analyzed based on the Breit-Wigner Ansatz by assuming a thermal width $\Gamma$ to the pole mass ${\omega }_0$ of each thermal glueball ground state. While the values of ${\omega }_0$ are insensitive to $T$ in the whole temperature range, the thermal widths $\Gamma$ exhibit distinct behaviors at temperatures below and above $T_c$. The widths are very small (approximately a few percent of ${\omega }_0$ or even smaller) when $T<T_c$, but grow abruptly when $T>T_c$ and reach values of roughly $\Gamma \sim {\omega }_0/2$ at $T\approx 1.9T_c$.

Partial Split Supersymmetry with violation of $R$-parity as a model for neutrino masses is explored. It is shown that at the one-loop level the model can give predictions that are in agreement with all present experimental values for the neutrino sector. An analytical result is that the small solar neutrino mass difference can be naturally explained in the decoupling limit for the heavy Higgs mass eigenstates.

We report a measurement of the $CP$-odd fraction and the time-dependent $CP$ violation in $B^0\to D^{*+}{D}^{*-}$ decays, using $657\times {10}^6$ $B\overline{B}$ events collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We measure a $CP$-odd fraction of $R_{\perp }=0.125\pm 0.043(\mathrm{stat})\pm 0.023(\mathrm{syst})$. From the distributions of the proper-time intervals between a $B^0\to D^{*+}{D}^{*-}$ decay and the other $B$ meson in the event, we obtain evidence of $CP$ violation with measured parameters ${\mathcal{A}}_{D^{*+}{D}^{*-}}=0.15\pm 0.13(\mathrm{stat})\pm 0.04(\mathrm{syst})$ and ${\mathcal{S}}_{D^{*+}{D}^{*-}}=-0.96\pm 0.25(\mathrm{stat}{)}_{-0.16}^{+0.13}(\mathrm{syst})$.