Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly “more correct” to introduce a scheme which actively maintains the constraints by solution (constrained evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations.

We present the four-dimensional equations on a brane with a scalar field nonminimally coupled to the induced Ricci curvature, embedded in a five-dimensional bulk with a cosmological constant. This is a natural extension to a brane-world context of scalar-tensor (Brans-Dicke) gravity. In particular we consider the cosmological evolution of a homogeneous and isotropic (FRW) brane. We identify low-energy and strong-coupling limits in which we recover effectively four-dimensional evolution. We find de Sitter brane solutions with both constant and evolving scalar field. We also consider the special case of a conformally coupled scalar field for which it is possible (when the conformal energy density exactly cancels the effect of the bulk black hole) to recover a conventional four-dimensional Friedmann equation for all energy densities.

A simple model is employed, which allows analytical study of the effects of toroidal currents in accretion discs around Schwarzschild black holes. These toroidal currents generate poloidal magnetic fields which alter the orbital behavior of magnetized particles in the zone between the horizon and the disc. As a consequence, the infall of these particles into the hole can be prevented; analysis based on the appropriate Hamiltonian shows, in particular, the existence of whole sets of stable orbits within the Schwarzschild limit at $r=6M$. These stable structures correspond to potential wells, which can accommodate particles with arbitrary high energy; hence, a considerable amount of energy can be stored quite near the hole, and possibly released in due turn, via perturbations in the internal dynamics of the accretion disc.

We consider the ${\Theta }^{+}(1540)$ pentaquark in the string model that correctly reproduces the linear Regge trajectories for the case of orbtal excitations of light $q\overline{q}$ mesons and $qqq$ baryons. Assuming (and arguing in favor of) the diquark-antiquark-diquark ($[ud]\overline{s}[ud]$) clustering of this orbitally excited object we found its mass about 290 MeV above the experimental value 1540 MeV. In the model considered this discrepancy could be attributed to the change of the constituent mass of $\overline{s}$ antiquark as compared to that of $s$ quark localized at the string end.

We present a class of supersymmetric models in which the lightest Higgs boson mass can be as large as a few hundred GeV ($200\sim 300\mathrm{G}\mathrm{e}\mathrm{V}$) while the successful minimal supersymmetric standard model prediction for gauge coupling unification is preserved. The theories are formulated on a 5D warped space truncated by two branes, and a part of the Higgs sector is localized on the infrared brane. The structure of the Higgs sector in the four-dimensional effective theory below the Kaluza-Klein mass scale is essentially that of the next-to-minimal supersymmetric standard model, or related theories. However, large values of the next-to-minimal supersymmetric standard model couplings at the weak scale are now possible as these couplings are required to be perturbative only up to the infrared cutoff scale, which in general can be much lower than the unification scale. This allows the possibility of generating a large quartic coupling in the Higgs potential thereby significantly raising the Higgs boson mass bound. We present two particularly simple models. In the first model, the quark and lepton fields are localized on the ultraviolet brane, where the grand unified symmetry is broken. In the second model, the quark and lepton fields are localized on the infrared brane, and the unified symmetry is broken both on the ultraviolet and infrared branes. Our theories potentially allow the possibility of a significant reduction in the fine-tuning needed for correct electroweak symmetry breaking, although this is somewhat model dependent.

In this paper we explore the possibility that (a) fermion masses, (b) neutrino oscillations, (c) $CP$ nonconservation, and (d) flavor violations get intimately linked to each other within supersymmetric grand unification based on SO(10) or an effective $\mathrm{G}(224)=\mathrm{S}\mathrm{U}(2{)}_L\times \mathrm{S}\mathrm{U}(2{)}_R\times \mathrm{S}\mathrm{U}(4{)}^c$ symmetry. We extend the framework proposed previously by Babu, Pati, and Wilczek which successfully described fermion masses and neutrino oscillations, to include $CP$ violation. Assuming flavor universal SUSY-breaking parameters at $M^{*}\gtrsim M_{\mathrm{G}\mathrm{U}\mathrm{T}}$, and that $CP$ violation arises through phases in the fermion mass matrices, we show how the presence of a grand unified theory threshold induces new and calculable $CP$ and flavor violations. Including standard model (SM) and SUSY contributions, we find that the Babu, Pati, and Wilczek framework can correctly account for the observed flavor and/or $CP$ violations in $\Delta m_K$, $\Delta m_{B_d}$, $S(B_d\to J/\psi K_S)$, and ${ϵ}_K$. While SUSY contribution is small ($\lesssim$ a few percent) for the first three quantities, for ${ϵ}_K$ it is sizable ($\sim 20\%–25\%$) and negative (as desired) compared to that of the SM. The model predicts $S(B_d\to \varphi K_S)$ to be in the range $+(0.65–0.73)$, close to the SM prediction. The model yields $Re({ϵ}^{\prime }/ϵ{)}_{\mathrm{S}\mathrm{U}\mathrm{S}\mathrm{Y}}\approx +(4–14)\times {10}^{-4}$; the relevance of this contribution can be assessed only when the associated matrix elements are known reliably. The model also predicts that the electric dipole moments of the neutron and the electron should be discovered with improvements in current limits by factors of 10 to 100.

An approach, recently proposed to calculate the nucleon generalized parton distributions (GPDs) in a constituent quark model (CQM) scenario, in which the constituent quarks are taken as complex systems, is used to obtain helicity-dependent GPDs. They are obtained from the wave functions of the nonrelativistic CQM of Isgur and Karl, convoluted with the helicity-dependent GPDs of the constituent quarks themselves. The latter are modeled by using the polarized structure functions of the constituent quark, the double distribution representation of GPDs, and a phenomenological constituent quark form factor. The present approach permits us to access a kinematical range corresponding to both the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and the Efremov-Radyushkin-Brodsky-Lepage regions, for small values of the momentum transfer and of the skewedness parameter. In this kinematical region, the present calculation represents a prerequisite for the evaluation of cross sections relevant to deeply virtual Compton scattering. In particular, we have calculated the leading twist helicity-dependent GPD $\tilde{H}$ and, from our expressions, its general relations with the nonrelativistic definition of the axial form factor and with the leading twist polarized quark density are consistently recovered.

We study a class of nonperturbative corrections to single-inclusive photon cross sections at measured transverse momentum $p_T$, in the large-$x_T$ limit. We develop an extension of the joint (threshold and transverse momentum) resummation formalism, appropriate for large $x_T$, in which there are no kinematic singularities associated with recoil, and for which matching to fixed-order and to threshold resummation at next-to-leading logarithm (NLL) is straightforward. Beyond NLL, we find contributions that can be attributed to recoil from initial-state radiation. Associated power corrections occur as inverse powers of $p_T^2$ and are identified from the infrared structure of integrals over the running coupling. They have significant energy-dependence and decrease from typical fixed-target to collider energies. Energy conservation, which is incorporated into joint resummation, moderates the effects of perturbative recoil and power corrections for large $x_T$.

The presence of the triplet ${\Delta }_L$ in left-right symmetric theories leads to type-II seesaw mechanism for the neutrino masses. In these models, assuming a normal mass hierarchy for the heavy Majorana neutrinos, we derive a lower bound on the mass of the lightest of heavy Majorana neutrinos from the leptogenesis constraint. From this bound we establish a consistent picture for the hierarchy of heavy Majorana neutrinos in a class of left-right symmetric models in which we identify the neutrino Dirac mass matrix with that of Fritzsch type charged lepton mass matrix. It is shown that these values are compatible with the current neutrino oscillation data.

Unstable D-particles in type-IIB string theory correspond to sphaleron solutions in the dual gauge theory. We construct an explicit time-dependent solution for the sphaleron decay on $S^3\times \mathbb{R}$, as well as the coherent state corresponding to the decay product. We develop a method to count the number of bulk particles in the AdS/CFT setup. When applied to our coherent state, the naive number operator ${\widehat{O}}_J^{†}{\widehat{O}}_J$ is shown to be inappropriate, even in the large-$N$ limit. The reason is that the final state consists of a large number of particles. By computing all probabilities for finding multiparticle states in the coherent state, we deduce the bulk particle content of the final state of the sphaleron decay. The qualitative features of this spectrum are compared with the results expected from the gravity side, and agreement is found.

The recent progress in embedding inflation in string theory has made it clear that the problem of moduli stabilization cannot be ignored in this context. In many models a special role is played by the volume modulus, which is modified in the presence of mobile branes. The challenge is to stabilize this modified volume while keeping the inflaton mass small compared to the Hubble parameter. It is then crucial to know not only how the volume modulus is modified, but also to have control over the dependence of the potential on the inflaton field. We address these questions within a simple setting: toroidal $\mathcal{N}=1$ type IIB orientifolds. We calculate corrections to the superpotential and show how the holomorphic dependence on the properly modified volume modulus arises. The potential then explicitly involves the inflaton, leaving room for lowering the inflaton mass through moderate fine-tuning of flux quantum numbers.

We reconsider cosmological constraints on extra dimension theories from the excess production of Kaluza-Klein gravitons. We point out that, if the normalcy temperature is above 1 GeV, then graviton states produced at this temperature will decay early enough that they do not affect the present day dark matter density, or the diffuse gamma ray background. We rederive the relevant cosmological constraints for this scenario.

The effective equation of motion is derived for a scalar field interacting with other fields in a Friedmann-Robertson-Walker background space-time. The dissipative behavior reflected in this effective evolution equation is studied both in simplified approximations as well as numerically. The relevance of our results to inflation are considered both in terms of the evolution of the inflaton field as well as its fluctuation spectrum. A brief examination also is made of supersymmetric models that yield dissipative effects during inflation.

The behavior of the action of the instantons describing vacuum decay in a de Sitter is investigated. For a near-to-limit instanton (a Coleman-de Luccia instanton close to some Hawking-Moss instanton) we find approximate formulas for the Euclidean action by expanding the scalar field and the metric of the instanton in the powers of the scalar field amplitude. The order of the magnitude of the correction to the Hawking-Moss action depends on the order of the instanton (the number of crossings of the barrier by the scalar field): for instantons of odd and even orders the correction is of the fourth and third order in the scalar field amplitude, respectively. If a near-to-limit instanton of the first order exists in a potential with the curvature at the top of the barrier greater than $4\times (\mathrm{\text{Hubble constant}}{)}^2$, which is the case if the fourth derivative of the potential at the top of the barrier is greater than some negative limit value, the action of the instanton is less than the Hawking-Moss action and, consequently, the instanton determines the outcome of the vacuum decay if no other Coleman-de Luccia instanton is admitted by the potential. A numerical study shows that for the quartic potential the physical mode of the vacuum decay is given by the Coleman-de Luccia instanton of the first order also in the region of parameters in which the potential admits two instantons of the second order.

The measured densities of dark and baryonic matter are surprisingly close to each other, even though the baryon asymmetry and the dark matter are usually explained by unrelated mechanisms. We consider a scenario where the dark matter $S$ is produced nonthermally from the decay of a messenger particle $X$, which carries the baryon number and compensates for the baryon asymmetry in the Universe, thereby establishing a connection between the baryonic and dark matter densities. We propose a simple model to realize this scenario, adding only a light singlet fermion $S$ and a colored particle $X$ which could have a mass in the $\mathcal{O}$(TeV) range and a lifetime to appear long-lived in collider detector. Therefore in hadron colliders the signal is similar to that of a stable or long-lived gluino in supersymmetric models.

Particle decay during inflation is studied by implementing a dynamical renormalization group resummation combined with a small $\Delta$ expansion. $\Delta$ measures the deviation from the scale invariant power spectrum and regulates the infrared. In slow-roll inflation, $\Delta$ is a simple function of the slow-roll parameters ${ϵ}_V,{\eta }_V$. We find that quantum fluctuations can self-decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-decay of the inflaton quantum fluctuations during slow-roll inflation. For wavelengths deep inside the Hubble radius the decay is enhanced by the emission of ultrasoft collinear quanta, i.e., bremsstrahlung radiation of superhorizon quanta which becomes the leading decay channel for physical wavelengths $H\ll k_{\mathrm{p}\mathrm{h}}(\eta )\ll H/({\eta }_V-{ϵ}_V)$. The decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations decay with a power law ${\eta }^{\Gamma }$ in conformal time where in terms of the amplitude of curvature perturbations ${△}_{\mathcal{R}}^2$, the scalar spectral index $n_s$, the tensor to scalar ratio $r$ and slow-roll parameters: $\Gamma \simeq [32{\xi }_V^2{△}_{\mathcal{R}}^2/(n_s-1+\frac{r}{4}{)}^2][1+\mathcal{O}({ϵ}_V,{\eta }_V)]$. The behavior of the growing mode ${\eta }^{{\eta }_V-{ϵ}_V+\Gamma }/\eta$ features an anomalous scaling dimension $\Gamma$. We discuss the implications of these results for scalar and tensor perturbations as well as for non-Gaussianities in the power spectrum. The recent Wilkinson Map Anisotropy Probe data suggests $\Gamma \gtrsim 3.6\times {10}^{-9}$.

A simple derivation of the low-energy effective action for brane worlds is given, highlighting the role of conformal invariance. We show how to improve the effective action for a positive- and negative-tension brane pair using the AdS/CFT correspondence.

High statistics Dalitz-plot distribution of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay obtained recently by KLOE collaboration is fitted to the results of corresponding theoretical calculations in Chiral Perturbation Theory (ChPT) with unitarity corrections taken into account. The quark mass ratio $Q=\sqrt{[m_s^2-(m_d+m_u{)}^2/4]/(m_d^2-m_u^2)}$ can be obtained from this analysis. We get $Q=22.8\pm 0.4$ which differs from the value $Q_{DT}=24.2$ that follows from Dashen’s theorem and agrees with recently calculated electromagnetic kaon mass difference.