In some previous treatments of multiple scattering in hadron-hadron collisions a sharp distinction was introduced between a soft part of the interaction, which generates the parton population and the hard part which produces the scattering between forward and backward partons, this last being followed by other soft processes that give rise to the hadronization. So at the elementary partonic level the interaction is elastic. An attempt to complete this description is now presented; it introduces into the dynamics the possibility of hard production. The topic is developed at the level in which in an elementary partonic collision at most one secondary particle is produced but this production can happen any number of times and may be followed by the reabsorption of the produced partons and by their elastic scattering. Some possible consequences of these basically inelastic processes are outlined.

Baryon magnetic moments and beta decay ratios ${(G}_A{/G}_V)$ are calculated in a phenomenological quark model. Nonstatic effects of pion exchange and orbital excitation are included. Good agreement with experiment is found for a combined fit to all measured baryon magnetic moments and beta decay ratios. The model predicts an antiquark content for the proton that is consistent with the Gottfried sum rule.

We present an extension of boundary string field theory on disc and ${\mathrm{RP}}^2$ worldsheet geometries. Finding an appropriate Becchi-Rouet-Stora (BRS) operator in the case of the ${\mathrm{RP}}^2$ geometry, we generalize the background independent open string field theory (or boundary string field theory) of Witten on a unit disc. The space of two-dimensional field theories on ${\mathrm{RP}}^2$ is spanned by the scalar operator inserted at the nontrivial loop of ${\mathrm{RP}}^2.$ We discuss the off-shell extension of the crosscap states, which provides an interpolation of orientifold planes of various dimensions.

We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a “bounce” to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we reobtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation amplitude is typically small, as desired to match observation.

We explicitly construct Green’s functions for a field in an arbitrary representation of a gauge group propagating in noncommutative instanton backgrounds based on the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in a noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as in the commutative case.

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.

A new viewpoint for the gauge hierarchy problem is proposed: compactification at a large scale, $1/R,$ leads to a low energy effective theory with supersymmetry softly broken at a much lower scale, $\alpha /R.\mathrm{}$ The hierarchy is induced by an extremely small angle $\alpha$ which appears in the orbifold compactification boundary conditions. The same orbifold boundary conditions break Peccei-Quinn symmetry, leading to a new solution to the $\mu$ problem. Explicit 5D theories are constructed with gauge groups $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ and $\mathrm{SU}\left(5\right),$ with matter in the bulk or on the brane, which lead to the (next-to) minimal supersymmetric standard model below the compactification scale. In all cases the soft supersymmetry-breaking and $\mu$ parameters originate from bulk kinetic energy terms, and are highly constrained. The supersymmetric flavor and $\mathrm{CP}$ problems are solved.

In this paper we address the question of the phenomena of Andreev reflection between the cold quark-gluon plasma phase and the color-flavor-locking (CFL) color superconductor. We show that there are two different types of reflections connected with the structure of the CFL phase. We also calculate the probability current at the interface and we show that it vanishes for an energy of scattering quarks below the superconducting gap.

A regularized model of a noncommutative formulation of the double compactified $D=11\mathrm{}$ supermembrane with nontrivial winding in terms of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ valued maps is obtained. The condition of nontrivial winding is described in terms of a nontrivial line bundle introduced in the formulation of the compactified supermembrane. The multivalued geometrical objects of the model related to the nontrivial wrapping are described in terms of a $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ geometrical object, which in the $\overrightarrow{N}\infty$ limit converges to the symplectic connection related to the area-preserving diffeomorphisms of the recently obtained noncommutative description of the compactified $D=11\mathrm{}$ supermembrane [I. Martín, J. Ovalle, and A. Restuccia, Phys. Rev. D 64, 096001 (2001)]. The $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ regularized canonical Lagrangian is explicitly obtained. The spectrum of the Hamiltonian of the double compactified $D=11\mathrm{}$ supermembrane is discussed. Generically, it contains local string such as spikes with zero energy. However, the sector of the theory corresponding to a principle bundle characterized by the winding number $n\ne 0,$ described by the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ model we propose, is shown to have no local stringlike spikes and hence the spectrum of this sector should be discrete.

We study thermodynamic evaporation of Schwarzschild–de Sitter black holes in terms of a low energy perturbation theory. A small black hole which is far from the cosmological horizon and observers at the spacelike hypersurface where black hole attraction and expansion of cosmological horizon balance exactly are considered. In the low energy perturbation, scalar field equations are solved in both regions of the hypersurface and scattering amplitudes are derived. Then the desired thermal temperatures from the two horizons are obtained as a “minimal” value of the statistical thermal temperature, and the fine tuning between amplitudes gives a relation between the two temperatures.

The vector and tensor fluctuations of vortices localizing gravity in the context of the six-dimensional Abelian Higgs model are studied. These stringlike solutions break spontaneously six-dimensional Poincaré invariance leading to a finite four-dimensional Planck mass and to a regular geometry both in the bulk and on the core of the vortex. While the tensor modes of the metric are decoupled and exhibit a normalizable zero mode, the vector fluctuations, present in the gauge sector of the theory, are naturally coupled to the graviphoton fields associated with the vector perturbations of the warped geometry. Using the invariance under infinitesimal diffeomorphisms, it is found that the zero modes of the graviphoton fields are never localized. On the contrary, the fluctuations of the Abelian gauge field itself admit a normalizable zero mode.

A low energy iteration scheme to study nonlinear gravity in the brane world is developed. As a result, we obtain the brane world effective action at low energies. The relation between the geometrical approach and the approach using the AdS/CFT correspondence is also clarified. In particular, we find generalized dark radiation as homogeneous solutions in our iteration scheme. Moreover, the precise correspondence between the bulk geometry and the brane effective action is established, which gives a holographic view of the brane world.

The lingering problem with high central densities in dark halos has arisen in the context of (L)CDM cosmologies with $n=1\mathrm{}$ scale-invariant initial power spectra. Although $n=1\mathrm{}$ is often justified by appealing to the inflation scenario, the choice is not generally justified. Specifically, inflation models with mild but important deviations from scale invariance $(n\sim 0.9)$ are not uncommon, and those with significant “running” of the spectral index are quite plausible. Even a mild deviation from scale invariance can be important because halo collapse times and densities depend on the relative amount of small-scale power. Here, we choose several popular, often well-motivated, models of inflation and work out the ramifications for galaxy central densities. For each model, we calculate its COBE-normalized primordial power spectrum and deduce the implied halo densities using a semianalytic method calibrated against N-body simulations. We compare our predictions to a sample of $\sim 50$ dark matter-dominated galaxies using a nonparametric measure of the density, ${\Delta }_{\mathrm{V}/2\mathrm{}},$ defined as the mean mass density, relative to the critical density, within the radius at which the rotation curve falls to half of its maximum value. While standard $n=1\mathrm{}$ LCDM halos are overdense by a factor of $\sim 6,$ several of our example inflation+CDM models predict halo densities well within, and even below, the range preferred by observations. We also show how the presence of massive ${(m}_{\nu }\sim 0.5\hspace{0.5em}\mathrm{eV})$ neutrinos can help to alleviate the central density problem, even with a scale-invariant spectrum. We conclude that galaxy central densities may not be as problematic for the CDM paradigm as is sometimes assumed: rather than telling us something about the nature of dark matter, galaxy rotation curves may be telling us something about inflation and/or neutrinos. An important test of this idea will be an eventual consensus on the value of ${\sigma }_8,$ the rms overdensity on the scale ${8h}^{-1}\mathrm{Mpc}.$ Our successful models tend to have values of ${\sigma }_8\approx 0.75,$ which is well within the range of recent determinations. Finally, models with $n>\mathrm{}1\mathrm{}$ (or ${\sigma }_8\gtrsim 1)$ are highly disfavored.

We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star’s surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.

In models of large extra dimensions, the fundamental Planck scale can be as low as TeV. Thus, in hadronic collisions interesting objects such as black holes, string balls, or p-branes can be produced. In scenarios of a fat brane or universal extra dimensions, the standard model particles are allowed to propagate in the extra spatial dimensions, which leads to the enhancement of the production cross sections of black holes and p-branes. Especially, the ratio of the p-brane cross section to the black hole cross section increases substantially, in comparison with the original confined scenario. The ratio can be as large as $105$ (for the case $n=7,m=5=p=r=k).\mathrm{}$

In models of large extra dimensions, the string and Planck scales become accessible at future colliders. When the energy scale is above the string scale or Planck scale a number of interesting phenomena occur, namely, production of stringy states, p-branes, string balls, black hole, etc. In this work, we systematically study the production cross sections of black holes, string balls, and p-branes at hadronic supercolliders. We also discuss their signatures. At the energy scale between the string scale $M_s$ and $M_s{/g}_s^2,$ where $g_s$ is the string coupling, the production is dominated by string balls, while beyond $M_s{/g}_s^2$ it is dominated by black holes. The production of a p-brane is only comparable to black holes when the p-brane wraps entirely on small extra dimensions. Rough estimates on the sensitivity reaches on the fundamental Planck scale $M_D$ are also obtained, based on the number of raw events.

The spectrum of glueballs in $2+1$ dimensions is calculated within an extended class of Isgur-Paton flux tube models and compared to lattice calculations of the low-lying $\mathrm{SU}(N>~2)$ glueball mass spectrum. Our modifications of the model include a string curvature term and a new way of dealing with the short-distance cutoff. We find that the generic model is remarkably successful at reproducing the positive charge conjugation, $C=+,$ sector of the spectrum. The only large (and robust) discrepancy involves the $0^{-+}$ state, raising the interesting possibility that the lattice spin identification is mistaken and that this state is in fact $4^{-+}.$ Additionally, the Isgur-Paton model does not incorporate any mechanism for splitting $C=-$ from $C=+$ (in contrast with the case in $3+1$ dimensions), while the “observed” spectrum does show a substantial splitting. We explore several modifications of the model in an attempt to incorporate this physics in a natural way. At the qualitative level we find that this constrains our choice to the picture in which the $C=\pm$ splitting is driven by mixing with new states built on closed loops of adjoint flux. However, a detailed numerical comparison suggests that a model incorporating an additional direct mixing between loops of opposite orientation is likely to work better, and that, in any case, a nonzero curvature term will be required. We also point out that a characteristic of any string model of glueballs is that the $\mathrm{SU}\left(\overrightarrow{N}\infty \right)$ mass spectrum will consist of multiple towers of states that are scaled up copies of each other. To test this will require a lattice mass spectrum that extends to somewhat larger masses than currently available.

We investigate quark flavor signals in three different supersymmetric models, minimal supergravity, the SU(5) SUSY GUT with right handed neutrinos, and the minimal supersymmetric standard model with U(2) flavor symmetry, in order to study the physics potential of the present and future B factories. We evaluate $\mathrm{CP}$ asymmetries in various B decay modes, $\Delta m_{B_s},$ $\Delta m_{B_d},$ and ${\varepsilon }_K.$ The allowed regions of the $\mathrm{CP}$ asymmetry in $\overrightarrow{B}J/\psi K_S$ and $\Delta m_{B_s}/\Delta m_{B_d}$ are different for the three models so that precise determinations of these observables in near future experiments are useful to distinguish the three models. We also investigate possible deviations from the standard model predictions of $\mathrm{CP}$ asymmetries in other B decay modes. In particular, a large deviation is possible for the U(2) model. The consistency check of the unitarity triangle including $\overrightarrow{B}\pi \pi ,\rho \pi {,D}^{\left(*\right)}{K}^{\left(*\right)}{,D}^{\left(*\right)}\pi {,D}^{*}\rho ,$ and so on, at future high luminosity $e^{+}{e}^{-}$ B factories and hadronic B experiments is therefore important to distinguish flavor structures of different supersymmetric models.

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through operator product expansion have been performed on ${16}^3\times 32$ lattices for Wilson fermions at $\beta =5.6\mathrm{}$ using configurations from the SESAM Collaboration and at $\beta =5.5\mathrm{}$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac sea are small. The close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. A naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. An extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect I argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with the exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional $O\left(N\right)\mathrm{}$ nonlinear sigma model. In these models the leading term in the weak coupling expansion of the nonperturbative effect can be obtained with a good accuracy from the first terms of perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, I suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.