In this paper we consider compactifications of massive type IIA supergravity on manifolds with $SU(3)$ structure. We derive the gravitino mass matrix of the effective four-dimensional $\mathcal{N}=2$ theory and show that vacuum expectation values of the scalar fields naturally induce spontaneous partial supersymmetry breaking. We go on to derive the superpotential and the Kähler potential for the resulting $\mathcal{N}=1$ theories. As an example we consider the $SU(3)$ structure manifold $SU(3)/U(1)\times U(1)$ and explicitly find $\mathcal{N}=1$ supersymmetric minima where all the moduli are stabilized at nontrivial values without the use of nonperturbative effects.

We present a computation of the coherent state path integral for a generic linear system using “functional methods” (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built from a first-order differential operator with coherent state boundary conditions. We show how this determinant can be expressed in terms of the symplectic transformation generated by the (in general, time-dependent) quadratic Hamiltonian for the system. We briefly discuss the conditions under which the coherent state path integral for a linear system actually exists. A necessary—but not sufficient—condition for existence of the path integral is that the symplectic transformation generated by the Hamiltonian is (unitarily) implementable on the Fock space for the system.

We construct two distinct classes of exact type III solutions of the $D=4$ Einstein-Yang-Mills system. The solutions are embeddings of the non-Abelian plane waves in spacetimes in Kundt’s class. Reduction of the solutions to type N leads to generalized $pp$ and Kundt waves. The geodesic equations are briefly discussed.

The attractor mechanism is usually thought of as the fixing of the near-horizon moduli of a Bogomol’nyi-Prasad-Sommerfield (BPS) black hole in terms of conserved charges measured at infinity. Recent progress in understanding BPS solutions in five dimensions indicates that this is an incomplete story. Moduli can instead be fixed in terms of dipole charges, and their corresponding values can be found by extremizing a certain attractor function built out of these charges. BPS black rings provide an example of this phenomenon. We give a general derivation of the attractor mechanism in five dimensions based on the recently developed classification of BPS solutions. This analysis shows when it is the dipole charges versus the conserved charges that fix the moduli. It also yields explicit expressions for the fixed moduli.

Through a principal component analysis, we study how accurately cosmic microwave background observables can constrain inflaton potentials in a model-independent manner. We apply the general slow-roll approximation in our analysis where we allow, in contrast to the standard slow-roll approximation, the possibility of variations in $V^{\prime \prime }(\varphi )$ and take into account the fact that horizon crossing is not an instantaneous event. Our analysis provides a set of modes to be used in fitting observables. We find that of order five of these modes will be constrained by future observations, so a fully general data analysis package could use the amplitudes of just a handful of modes as free parameters and retain all relevant information in the data.

This article presents an original code for big bang nucleosynthesis in a baryon inhomogeneous model of the Universe. In this code neutron diffusion between high and low baryon density regions is calculated simultaneously with the nuclear reactions and weak decays that compose the nucleosynthesis process. The size of the model determines the time when neutron diffusion becomes significant. This article describes in detail how the time of neutron diffusion relative to the time of nucleosynthesis affects the final abundances of ${}^4\mathrm{He}$, deuterium and ${}^7\mathrm{Li}$. These results will be compared with the most recent observational constraints of ${}^4\mathrm{He}$, deuterium and ${}^7\mathrm{Li}$. This inhomogeneous model has ${}^4\mathrm{He}$ and deuterium constraints in concordance for baryon-to-photon ratio $\eta =(4.3-12.3)\times {10}^{-10}$ ${}^7\mathrm{Li}$ constraints are brought into concordance with the other isotope constraints by including a depletion factor as high as 5.9. These ranges for the baryon-to-photon ratio and for the depletion factor are larger than the ranges from a standard big bang nucleosynthesis model.

Dark matter (DM) annihilation during hydrogen recombination ($z\sim 1000$) will alter the recombination history of the Universe, and affect the observed CMB temperature and polarization fluctuations. Unlike other astrophysical probes of DM, this is free of the significant uncertainties in modelling galactic physics, and provides a method to detect and constrain the cosmological abundances of these particles. We parametrize the effect of DM annihilation as an injection of ionizing energy at a rate ${ϵ}_{\mathrm{DM}}$, and argue that this simple “on the spot” modification is a good approximation to the complicated interaction of the annihilation products with the photon-electron plasma. Generic models of DM do not change the redshift of recombination, but change the residual ionization after recombination. This broadens the surface of last scattering, suppressing the temperature fluctuations and enhancing the polarization fluctuations. We use the temperature and polarization angular power spectra to measure these deviations from the standard recombination history, and therefore, indirectly probe DM annihilation. The modifications to the temperature power spectrum are nearly degenerate with the primordial scalar spectral index and amplitude; current CMB data are therefore unable to put any constraints on the annihilation power. This degeneracy is broken by polarization; Planck will have the sensitivity to measure annihilation power ${ϵ}_{\mathrm{DM}}(z=1000)>{10}^{-15}\mathrm{eV}/\mathrm{s}/\mathrm{\text{proton}}$, while high sensitivity experiments (e.g. NASA’s CMBpol) could improve that constraint to ${ϵ}_{\mathrm{DM}}(z=1000)>4\times {10}^{-16}\mathrm{eV}/\mathrm{s}/\mathrm{\text{proton}}$, assuming a fractional detector sensitivity of $\Delta T/T\sim 1\mu \mathrm{K}$ and a beam of $3^{\prime }$. These limits translate into a lower bound on the mass of the DM particle, $M_{\mathrm{DM}}>10-100\mathrm{GeV}$, assuming a single species with a cross section of $⟨{\sigma }_{A}v⟩\sim 2\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$, and a fraction $f\sim 0.1-1$ of the rest mass energy used for ionization. The bounds for the Wilkinson microwave anisotropy probe (WMAP) 4y data are significantly lower, because of its lack of high $S/N$ polarization measurements, but it can strongly constrain $\mathcal{O}(\mathrm{MeV})$ particles such as those proposed by Boehm et al. (2004).

In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are “real.” On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as $\alpha$, the fine structure constant, goes to zero, and the standard result, which appears to be independent of $\alpha$, corresponds to the $\alpha \to \infty$ limit.

We discuss the possibility of formation and subsequent detection of a supersymmetric bound state composed of a slepton-antislepton pair at the next linear collider. The Green function method is used within a nonrelativistic approximation to estimate the threshold production cross section of the $2P$ bound state. The parameter space of gauge mediated symmetry breaking (GMSB) models allow a particular scenario in which a charged slepton (${\tilde{e}}_R,{\tilde{\mu }}_R$ or ${\tilde{\tau }}_1$) is the next-to-lightest supersymmetric particle (NLSP). Within this scenario the produced $2P$ bound-state decays, through a dipole transition, into the $1S$ ground-state with branching ratio $\approx 100\%$ emitting a very soft ($\approx 1\mathrm{MeV}$) photon which goes undetected. The spectroscopy of the $1S$-state shows that it decays into two photons with $\mathrm{Br}\approx 0.5$ up to $m_{\mathrm{NLSP}}\approx 1\mathrm{TeV}$. Thus NLSP sleptonium threshold production gives rise to the signal $e^{+}{e}^{-}\to 2P\to 1S+“\mathrm{soft}\gamma ”\to \gamma \gamma$ which when compared with the standard model two-photon process ($e^{+}{e}^{-}\to \gamma \gamma$ ) has a statistical significance ($SS=$signal/noise) which, at an energy offset from threshold of $E=20\mathrm{GeV}$, goes from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval $[100,200]\mathrm{GeV}$.

We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the $SU(2{)}_L\times SU(2{)}_R$ chiral theory with nondegenerate quarks and the $SU(3{)}_L\times SU(3{)}_R$ chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.

We present a systematic analysis at the leading log order of the influence of combination of bilinear and trilinear $R$ parity violating couplings on the decay $b\to s+\gamma$. Such contributions have never been explored in the context of $b\to s+\gamma$ decay. We show that influence of charged-slepton-Higgs mixing mediated loops can dominate the SM and MSSM contributions and hence can provide strong bounds on the combination of bilinear-trilinear $R$ parity violating couplings. Such contributions also are enhanced by large $\tan \beta$. With substantially extended basis of operators (28 operators), we provide illustrative analytical formulas of the major contributions to complement our complete numerical results which demonstrate the importance of QCD running effects.

The process $e^{+}{e}^{-}\to t\overline{t}H$ is considered in the kinematic end point region where the Higgs energy is close to its maximal energy. In perturbative QCD, using the loop expansion, the amplitudes are plagued by Coulomb singularities that need to be resummed. We show that the QCD dynamics in this end point region is governed by nonrelativistic heavy quarkonium dynamics, and we use a nonrelativistic effective theory to compute the Higgs energy distribution at leading and next-to-leading-logarithmic approximation in the nonrelativistic expansion. Updated numbers for the total cross section including the summations in the Higgs energy end point region are presented.

Motivated by the recent indications of the possibility of sizable deviations of the mixing-induced $CP$ violation parameter, $S_f$, in the penguin-dominated $b\to sq\overline{q}$ transition decays such as $B^0\to (\varphi ,\omega ,{\rho }^0,{\eta }^{\prime },\eta ,{\pi }^0,f_0)K_S$ from $\sin 2\beta$ determined from $B\to J/\psi K_S$, we study final-state rescattering effects on their decay rates and $CP$ violation. Recent observations of large direct $CP$ asymmetry in modes such as $B^0\to K^{+}{\pi }^{-},{\rho }^{-}{\pi }^{+}$ suggest that final-state phases in two-body $B$ decays may not be small. It is therefore important to examine these long-distance effects on penguin-dominated decays. Such long-distance effects on $S_f$ are found to be generally small [i.e. $\mathcal{O}(1-2\%)$] or negligible except for the $\omega K_S$ and ${\rho }^0{K}_S$ modes where $S_f$ is lowered by around 15% for the former and increased by the same percentage for the latter. However, final-state rescattering can enhance the $\omega K_S$, $\varphi K_S$, ${\eta }^{\prime }{K}_S$, ${\rho }^0{K}_S$, and ${\pi }^0{K}_S$ rates significantly and flip the signs of direct $CP$ asymmetries of the last two modes. Direct $CP$ asymmetries in $\omega K_S$ and ${\rho }^0{K}_S$ channels are predicted to be ${\mathcal{A}}_{\omega K_S}\approx -0.13$ and ${\mathcal{A}}_{{\rho }^0{K}_S}\approx 0.47$, respectively. However, direct $CP$ asymmetry in all the other $b\to s$ penguin-dominated modes that we study is found to be rather small ($\lesssim$ a few percent), rendering these modes a viable place to search for the $CP$-odd phases beyond the standard model. Since $\Delta S_f$ ($\equiv -{\eta }_f{S}_f-S_{J/\psi K_S}$, with ${\eta }_f$ being the $CP$ eigenvalue of the final state $f$) and ${\mathcal{A}}_f$ are closely related, the theoretical uncertainties in the mixing-induced parameter $S_f$ and the direct $CP$ asymmetry parameter ${\mathcal{A}}_f$ are also coupled. Based on this work, it seems difficult to accommodate $|\Delta S_f|>0.10$ within the standard model for $B^0\to (\varphi ,\omega ,{\rho }^0,{\eta }^{\prime },\eta ,{\pi }^0)K_S$; in particular, ${\eta }^{\prime }{K}_S$ is especially clean in our picture. For $f_0{K}_S$, at present we cannot make reliable estimates. The sign of the central value of $\Delta S_f$ for all the modes we study is positive but quite small, compared to the theoretical uncertainties, so that at present conclusive statements on the sign are difficult to make.

We consider neutrino mixing and oscillations in quantum field theory and compute the neutrino lepton charge in decay processes where neutrinos are generated. We also discuss the proper definitions of flavor charge and states and clarify the issues of the possibility of different mass parameters in field mixing.

Because of the nonlinearity of the Einstein equations, the cosmological fluctuations which are generated during inflation on a wide range of wavelengths do not evolve independently. In particular, to second order in perturbation theory, the first order fluctuations back-react both on the background geometry and on the perturbations themselves. In this paper, the gravitational backreaction of long-wavelength (super-Hubble) scalar metric fluctuations on the perturbations themselves is investigated for a large class of inflationary models. Specifically, the equations describing the evolution of long-wavelength cosmological metric and matter perturbations in an inflationary universe are solved to second order in both the amplitude of the perturbations and in the slow-roll expansion parameter. Assuming that the linear fluctuations have random phases, we show that the fractional correction to the power spectrum due to the leading infrared backreaction terms does not change the shape of the spectrum. The amplitude of the effect is suppressed by the product of the inflationary slow-roll parameter and the amplitude of the linear power spectrum. The nongaussianity of the spectrum induced by backreaction is commented upon.

An algebraic method for evaluating bare nucleon matrix elements of quark operators is proposed. Thereby, bare nucleon matrix elements are traced back to vacuum matrix elements. The method is similar to the soft pion theorem. Matrix elements of two-quark, four-quark and six-quark operators inside the bare nucleon are considered.

Radiative corrections to neutrino mixings in seesaw models depend on the nature of new physics between the weak and the grand unified theory (GUT)-seesaw scales and can be taken into account using the renormalization group equations. This new physics effect becomes particularly important for models with quasidegenerate neutrino masses where small neutrino mixings at the seesaw scale can get magnified by radiative renormalization effects alone to match observations. This mechanism of radiative magnification which provides a simple understanding of why lepton mixings are so different from quark mixings was demonstrated by us for the standard supersymmetry (SUSY) scenario where the particle spectrum becomes supersymmetric above the weak scale. In this paper, we examine this phenomenon in split supersymmetry scenarios and find that the mechanism works also for this scenario provided the SUSY scale is at least 2–3 orders below the GUT-seesaw scale and one has larger values of $\tan \beta$.

We report the results of a search for the flavor-changing neutral current process $b\to d\gamma$ using a sample of $275\times {10}^6$ $B$ meson pairs accumulated by the Belle detector at KEKB. We find no significant signal for the exclusive decays $B^{-}\to {\rho }^{-}\gamma$, ${\overline{B}}^0\to {\rho }^0\gamma$, or ${\overline{B}}^0\to \omega \gamma$. Assuming an isospin relation between the three modes, we set an upper limit for the combined branching fraction $\mathcal{B}(B\to (\rho ,\omega )\gamma )$, of $1.4\times {10}^{-6}$ at the 90% confidence level. This limit can be used to constrain the ratio of CKM matrix elements $|V_{td}/V_{ts}|$.

We consider the Darboux transformation as a method of construction of exact nonsingular solutions describing the three-dimensional brane that interacts with five-dimensional gravity and the bulk scalar field. To make it work, the five-dimensional Einstein’s equations and the Israel’s conditions are being reduced to the Schrödinger equation with the jump-like potential and the wave functions sewing conditions in jump point correspondingly. We show further that it is always possible to choose the functions in Crum’s determinants in such way that the five-dimensional Ricci scalar $R$ will always be finite both on brane and in bulk. The new exact solutions being the generalizations of the model with the odd superpotential are presented. Described formalism is also appliable to the cases of more realistic branes with cosmological expansion. As an example, via the usage of the simple orbifold model ($S_1/{\mathbb{Z}}_2$) and one-time Darboux transformation we construct the models where the cosmological constant on the visible brane is exponentially small.

As a supersymmetric extension of the Randall-Sundrum model, we consider a 5-dimensional Hořava-Witten type theory and derive its low energy effective action. The model we consider is a two-brane system with a bulk scalar field satisfying the Bogomol’nyi-Prasad-Sommerfield (BPS) condition. We solve the bulk equations of motion using a gradient expansion method, and substitute the solution into the original action to get the 4-dimensional effective action. The resultant effective theory can be cast into the form of Einstein gravity coupled with two scalar fields, one arising from the radion, the degree of freedom of the interbrane distance, and the other from the bulk scalar field. We also clarify the relation between our analysis and the moduli approximation.