Showing papers in "Physical Review D in 1994"

Review of particle properties.

Abstract: This biennial Review summarizes much of Particle Physics. Using data from previous editions, plus 2205 new measurements from 667 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. This edition features expanded coverage of CP violation in B mesons and of neutrino oscillations. For the first time we cover searches for evidence of extra dimensions (both in the particle listings and in a new review). Another new review is on Grand Unified Theories. A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov.

Some properties of Noether charge and a proposal for dynamical black hole entropy

Abstract: We consider a general, classical theory of gravity with arbitrary matter fields in n dimensions, arising from a diffeomorphism-invariant Lagrangian L. We first show that L alwasy can be written in a ``manifestly covariant'' form. We then show that the symplectic potential current (n-1)-form FTHETA and the symplectic current (n-1)-form \ensuremath{\omega} for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current (n-1)-form J and corresponding Noether charge (n-2)-form Q. We derive a general ``decomposition formula'' for Q. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy ${\mathit{S}}_{\mathrm{dyn}}$ of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of L, FTHETA, and Q. However, the issue of whether this dynamical entropy in general obeys a ``second law'' of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.

Computing quark and gluon distribution functions for very large nuclei.

Abstract: We argue that the distribution functions for quarks and gluons are computable at small $x$ for sufficiently large nuclei, perhaps larger than can be physically realized. For such nuclei, we argue that weak coupling methods may be used. We show that the computation of the distribution functions can be recast as a many-body problem with a modified propagator, a coupling constant which depends on the multiplicity of particles per unit rapidity per unit area, and for non-Abelian gauge theories, some extra media-dependent vertices. We explicitly compute the distribution function for gluons to lowest order, and argue how they may be computed in higher order.

Gluon distribution functions for very large nuclei at small transverse momentum.

Abstract: We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two-dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in ${\ensuremath{\alpha}}_{s}$. The gluon distribution function is proportional to $\frac{1}{x}$, and the effect of the finite density of partons is to modify the dependence on the transverse momentum for small transverse momenta.

General relativity as an effective field theory: The leading quantum corrections

Abstract: I describe the treatment of gravity as a quantum effective field theory. This allows a natural separation of the (known) low energy quantum effects from the (unknown) high energy contributions. Within this framework, gravity is a well-behaved quantum field theory at ordinary energies. In studying the class of quantum corrections at low energy, the dominant effects at large distance can be isolated, as these are due to the propagation of the massless particles ( including gravitons) of the theory and are manifested in the nonlocal and/or nonanalytic contributions to vertex functions and propagators. These leading quantum corrections are parameter-free and represent necessary consequences of quantum gravity. The methodology is illustrated by a calculation of the leading quantum corrections to the gravitational interaction of two heavy masses.

Gravitational waves from merging compact binaries: How accurately can one extract the binary's parameters from the inspiral waveform?

Abstract: The most promising source of gravitational waves for the planned kilometer-size laser-interferometer detectors LIGO and VIRGO are merging compact binaries, i.e., neutron-star--neutron-star (NS-NS), neutron-star--black-hole (NS-BH), and black-hole--black-hole (BH-BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the inspiral gravitational wave signals by the three-detector LIGO-VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The large number of cycles in the observable waveform increases our sensitivity to those parameters that affect the inspiral rate, and thereby the evolution of the waveform's phase. These parameters are thus measured much more accurately than parameters which affect the waveform's polarization or amplitude. To lowest order in a post-Newtonian expansion, the evolution of the waveform's phase depends only on the combination scrM\ensuremath{\equiv}(${\mathit{M}}_{1}$${\mathit{M}}_{2}$${)}^{3/5}$(${\mathit{M}}_{1}$+${\mathit{M}}_{2}$${)}^{\mathrm{\ensuremath{-}}1/5}$ of the masses ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ of the two bodies, which is known as the ``chirp mass.'' To post-1-Newtonian order, the waveform's phase also depends sensitively on the binary's reduced mass \ensuremath{\mu}\ensuremath{\equiv}${\mathit{M}}_{1}$${\mathit{M}}_{2}$/(${\mathit{M}}_{1}$+${\mathit{M}}_{2}$) allowing, in principle, a measurement of both ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ with high accuracy.We show that the principal obstruction to measuring ${\mathit{M}}_{1}$ and ${\mathit{M}}_{2}$ is the post-1.5-Newtonian effect of the bodies' spins on the waveform's phase, which can mimic the effects that allow \ensuremath{\mu} to be determined. The chirp mass is measurable with an accuracy \ensuremath{\Delta}scrM/scrM\ensuremath{\approxeq}0.1%--1%. Although this is a remarkably small error bar, it is \ensuremath{\sim}10 times larger than previous estimates of \ensuremath{\Delta}scrM/scrM which neglected post-Newtonian effects. The reduced mass is measurable to \ensuremath{\sim}10%--15% for NS-NS and NS-BH binaries, and \ensuremath{\sim}50% for BH-BH binaries (assuming 10${\mathit{M}}_{\mathrm{\ensuremath{\bigodot}}}$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of \ensuremath{\mu} and the spin angular momenta that is measured to within \ensuremath{\sim}1%. Moreover, if both spins were somehow known to be small (\ensuremath{\lesssim}0.01${\mathit{M}}_{1}^{2}$ and \ensuremath{\lesssim}0.01${\mathit{M}}_{2}^{2}$, respectively), then \ensuremath{\mu} could be determined to within \ensuremath{\sim}1%. Finally, building on earlier work of Markovi\ifmmode \acute{c}\else \'{c}\fi{}, we derive an approximate, analytic expression for the accuracy \ensuremath{\Delta}D of mesurements of the distance D to the binary, for an arbitrary network of detectors. This expression is accurate to linear order in 1/\ensuremath{\rho}, where \ensuremath{\rho} is the signal-to-noise ratio. We also show that, contrary to previous expectations, contributions to \ensuremath{\Delta}D/D that are nonlinear in 1/\ensuremath{\rho} are significant, and we develop an approximation scheme for including the dominant of these nonlinear effects. Using a Monte Carlo simulation we estimate that distance measurement accuracies will be \ensuremath{\le}15% for \ensuremath{\sim}8% of the detected signals, and \ensuremath{\le}30% for \ensuremath{\sim}60% of the signals, for the LIGO-VIRGO three-detector network.

False vacuum inflation with Einstein gravity

Abstract: We present a detailed investigation of chaotic inflation models which feature two scalar fields such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the magnitude of the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to the case termed ``hybrid inflation'' by Linde, where the false vacuum energy density dominates so that the phase transition signals the end of inflation. We focus mostly on the case of a second order transition, but treat also the first order case and discuss bubble production in that context for the first time. False-vacuum-dominated inflation is dramatically different from the usual true vacuum case, both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation originating during inflation can be indistinguishable from 1, or it can be up to ten percent or so higher. The energy scale at the end of inflation can be many orders of magnitude less than the value ${10}^{16}$ GeV, which is ususal in the true vacuum case. Reheating occurs promptly at the end of inflation. Cosmic strings or other topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they contribute significantly to large scale structure formation and the cosmic microwave background anisotropy.Turning to particle physics, false vacuum inflaton occurs with the inflaton field far below the Planck scale and is therefore somewhat easier to implement in the context of supergravity than true vacuum chaotic inflation. The smallness of the inflaton mass compared with the inflationary Hubble parameter still presents a difficulty for generic supergravity theories. Remarkably, however, the difficulty can be avoided in a natural way for a class of supergravity models that follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic superstring-derived theory of inflation. One possibility, which we show to be viable at least in the context of global supersymmetry, is that the Peccei-Quinn symmetry is responsible for the false vacuum.

Gauge singlet scalars as cold dark matter

Abstract: We consider a very simple extension of the standard model in which one or more gauge singlet scalars S-i couples to the standard model via an interaction of the form lambda(S)S(i)(dagger)S(i)H(dagger)H, where H is the standard model Higgs doublet. The thermal relic density of S scalars is calculated as a function of the coupling lambda(S) and the S scalar mass ms. The regions of the (m(S),lambda(S)) parameter space which can be probed by present and future experiments designed to detect scattering of S dark matter particles from Ge nuclei, and to observe upward-moving muons and contained events in neutrino detectors due to high-energy neutrinos from annihilations of S dark matter particles in the Sun and the Earth, are discussed. Present experimental bounds place only very weak constraints on the possibility of thermal relic S scalar dark matter. The next generation of cryogenic Ge detectors and of large area (10(4) m(2)) neutrino detectors will be able to investigate most of the parameter space corresponding to thermal relic S scalar dark matter up to m(S) approximate to 50 GeV, while a 1 km(2) detector would in general be able to detect thermal relic S scalar dark matter up to m(S) approximate to 100 GeV and would be able to detect up to m(S) approximate to 500 GeV or more if the Higgs boson is lighter than 100 GeV.

On black hole entropy

Abstract: Two techniques for computing black hole entropy in generally covariant gravity theories including arbitrary higher derivative interactions are studied. The techniques are Wald's Noether charge approach introduced recently, and a field redefinition method developed in this paper. Wald's results are extended by establishing that his local geometric expression for the black hole entropy gives the same result when evaluated on an arbitrary cross section of a Killing horizon (rather than just the bifurcation surface). Further, we show that his expression for the entropy is not affected by ambiguities which arise in the Noether construction. Using the Noether charge expression, the entropy is evaluated explicitly for black holes in a wide class of generally covariant theories. For a Lagrangian of the functional form L\ifmmode \tilde{}\else \~{}\fi{}=L\ifmmode \tilde{}\else \~{}\fi{}(${\mathrm{\ensuremath{\psi}}}_{\mathit{m}}$, ${\mathrm{\ensuremath{ abla}}}_{\mathit{a}}$${\mathrm{\ensuremath{\psi}}}_{\mathit{m}}$,${\mathit{g}}_{\mathit{a}\mathit{b}}$,${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$, ${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$), it is found that the entropy is given by S=-2\ensuremath{\pi}\ensuremath{\oint}(${\mathit{Y}}^{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$-${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{Z}}^{\mathit{e}:\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$) \ensuremath{\epsilon}${\mathrm{^}}_{\mathit{a}\mathit{b}}$\ensuremath{\epsilon}${\mathrm{^}}_{\mathit{c}\mathit{d}}$\ensuremath{\epsilon}\ifmmode\bar\else\textasciimacron\fi{}, where the integral is over an arbitrary cross section of the Killing horizon, \ensuremath{\epsilon}${\mathrm{^}}_{\mathit{a}\mathit{b}}$ is the binormal to the cross section, ${\mathit{Y}}^{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$=\ensuremath{\partial}L\ifmmode \tilde{}\else \~{}\fi{}/\ensuremath{\partial}${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$, and ${\mathit{Z}}^{\mathit{e}:\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$=\ensuremath{\partial}L\ifmmode \tilde{}\else \~{}\fi{}/\ensuremath{\partial}${\mathrm{\ensuremath{ abla}}}_{\mathit{e}}$${\mathit{R}}_{\mathit{a}\mathit{b}\mathit{c}\mathit{d}}$.Further, it is shown that the Killing horizon and surface gravity of a stationary black hole metric are invariant under field redefinitions of the metric of the form g${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{a}\mathit{b}}$\ensuremath{\equiv}${\mathit{g}}_{\mathit{a}\mathit{b}}$+${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$, where ${\mathrm{\ensuremath{\Delta}}}_{\mathit{a}\mathit{b}}$ is a stationary tensor field that vanishes at infinity and is regular on the horizon (including the bifurcation surface). Using this result, a technique is developed for evaluating the black hole entropy in a given theory in terms of that of another theory related by field redefinitions. Remarkably, it is established that certain perturbative, first order, results obtained with this method are in fact exact. A particular result established in this fashion is that a scalar matter term of the form ${\mathrm{\ensuremath{ abla}}}^{2\mathit{p}}$\ensuremath{\varphi}${\mathrm{\ensuremath{ abla}}}^{2\mathit{q}}$\ensuremath{\varphi} in the Lagrangian makes no contribution to the black hole entropy. The possible significance of these results for the problem of finding the statistical origin of black hole entropy is discussed.

Green's function in the color field of a large nucleus.

Abstract: We compute the Green's function for scalars, fermions, and vectors in the color field associated with the infinite momentum frame wave function of a large nucleus. Expectation values of this wave function can be computed by integrating over random orientations of the valence quark charge density. This relates the Green's functions to correlation functions of a two-dimensional, ultraviolet finite, field theory. We show how one can compute the sea quark distribution functions and explicitly compute them in the kinematic range of transverse momenta, ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}^{2}$${\mathrm{\ensuremath{\mu}}}^{2}$\ensuremath{\ll}${\mathit{k}}_{\mathit{t}}^{2}$\ensuremath{\ll}${\mathrm{\ensuremath{\mu}}}^{2}$, where ${\mathrm{\ensuremath{\mu}}}^{2}$ is the average color charge squared per unit area. When ${\mathit{m}}_{\mathrm{quark}}^{2}$\ensuremath{\ll}${\mathrm{\ensuremath{\mu}}}^{2}$\ensuremath{\sim}${\mathit{A}}^{1/3}$, the sea quark contribution to the infinite momentum frame wave function saturates at a value that is the same as that for massless sea quarks.

Exact results on the space of vacua of four-dimensional SUSY gauge theories

Abstract: We consider four-dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states---a moduli space of vacua Classically, the singular points on the moduli space are associated with extra massless particles Quantum mechanically these singularities can be smoothed out Alternatively, new massless states appear there These may be the elementary massless particles or new massless bound states

Top quark mass in supersymmetric SO(10) unification.

Abstract: The successful prediction of the weak mixing angle suggests that the effective theory beneath the grand unification scale is the minimal super- symmetric standard model (MSSM) with just two Higgs doublets. If we further assume that the unified gauge group contains SO(10), that the two light Higgs doublets lie mostly in a single irreducible SO(10) representa- tion, and that the t, b andmasses originate in renormalizable Yukawa interactions of the form 16 3 O16 3 , then also the top quark mass can be predicted in terms of the MSSM parameters. To compute mt we present a precise analytic approximation to the solution of the 2-loop renormal- ization group equations, and study supersymmetric and GUT threshold corrections and the input value of the b quark mass. The large ratio of top to bottom quark masses derives from a large ratio, tan�, of Higgs vacuum expectation values. We point out that when tanis large, so are certain corrections to the b quark mass prediction, unless a particular hierarchy exists in the parameters of the model. With such a hierarchy, which may result from approximate symmetries, the top mass prediction depends only weakly on the spectrum. Our results may be applied to any supersymmetric SO(10) model as long ast ≃ �b ≃ �τ at the GUT scale and there are no intermediate mass scales in the desert.

Equilibrium state of a self-interacting scalar field in the de Sitter background

Abstract: The behavior of a weakly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). The existence of the de Sitter-invariant equilibrium quantum state of the scalar field in the presence of the interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculating an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in the equilibrium state, correlation time, and spatial physical correlation radius are presented. The latter does not depend on time, which implies that the characteristic size of domains with positive and negative values of the scalar field remains the same on average in the equilibrium state in spite of the expansion of the t=const hypersurface of the de Sitter space-time.

Gravitational radiation from first-order phase transitions.

Abstract: We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically collide many bubbles expanding at a velocity v and calculate the resulting spectrum of gravitational radiation in the linearized gravity approximation. Our results are expressed as simple functions of the mean bubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubble walls. A first-order phase transition is also likely to excite a Kolmogoroff spectrum of turbulence. We estimate the gravity waves produced by such a spectrum of turbulence and find that the characteristic amplitude of the gravity waves produced is comparable to that from bubble collisions. Finally, we apply these results to the electroweak transition. Using the one-loop effective potential for the minimal electroweak model, the characteristic amplitude of the gravity waves produced is h≃1.5×10^-27 at a characteristic frequency of 4.1 × 10^-3 Hz corresponding to Ω∼10^-22 in gravity waves, far too small for detection. Gravity waves from more strongly first-order phase transitions, including the electroweak transition in nonminimal models, have better prospects for detection, though probably not by LIGO.

Black hole entropy in canonical quantum gravity and superstring theory

Abstract: In this paper the entropy of an eternal Schwarzschild black hole is studied in the limit of an infinite black hole mass. The problem is addressed from the point of view of both canonical quantum gravity and superstring theory. The entropy per unit area of a free scalar field propagating in a fixed black hole background is shown to be quadratically divergent near the horizon. It is shown that such quantum corrections to the entropy per unit area are equivalent to the quantum corrections to the gravitational coupling. Unlike field theory, superstring theory provides a set of identifiable configurations which give rise to the classical contribution to the entropy per unit area. These configurations can be understood as open superstrings with both ends attached to the horizon. The entropy per unit area is shown to be finite to all orders in superstring perturbation theory. The importance of these conclusions to the resolution of the problem of black hole information loss is reiterated.

General laws of black hole dynamics

Abstract: A general definition of a black hole is given, and general ``laws of black-hole dynamics'' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four nondegenerate types, described as future or past, and outer or inner. If the boundary of an inextendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. The future outer trapping horizon provides the definition of a black hole. Outer marginal surfaces have spherical or planar topology. Trapping horizons are null only in the instantaneously stationary case, and otherwise outer trapping horizons are spatial and inner trapping horizons are Lorentzian. Future outer trapping horizons have nondecreasing area form, constant only in the null case: the ``second law.'' A definition of the trapping gravity of an outer trapping horizon is given, generalizing surface gravity. The total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant: the ``zeroth law.'' The variation of the area form along an outer trapping horizon is determined by the trapping gravity and an energy flux: the ``first law.''

Two loop renormalization group equations for soft supersymmetry breaking couplings

Abstract: We compute the two-loop renormalization group equations for all soft supersymmetry-breaking couplings in a general softly broken N=1 supersymmetric model. We also specialize these results to the minimal supersymmetric standard model.

Formalizing the slow-roll approximation in inflation.

Abstract: The meaning of the inflationary slow-roll approximation is formalised. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the evolution of the potential energy density. The vital role of the inflationary attractor solution is emphasised, and some of its properties described. We propose a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual $e$-foldings of physical expansion, and derive relevant formulae. We introduce an infinite hierarchy of slow-roll parameters, and show that only a finite number of them are required to produce results to a given order. The extension of the slow-roll approximation into an analytic slow-roll {\em expansion}, converging on the exact solution, is provided. Its role in calculations of inflationary dynamics is discussed. We explore rational-approximants as a method of extending the range of convergence of the slow-roll expansion up to, and beyond, the end of inflation.

Study of constrained minimal supersymmetry.

Abstract: Taking seriously the phenomenological indications for supersymmetry we have made a detailed study of unified minimal SUSY, including many effects at the few percent level in a consistent fashion. We report here a general analysis of what can be studied without choosing a particular gauge group at the unification scale. Firstly, we find that the encouraging SUSY unification results of recent years do survive the challenge of a more complete and accurate analysis. Taking into account effects at the 5-10% level leads to several improvements of previous results and allows us to sharpen our predictions for SUSY in the light of unification. We perform a thorough study of the parameter space and look for patterns to indicate SUSY predictions, so that they do not depend on arbitrary choices of some parameters or untested assumptions. Our results can be viewed as a fully constrained minimal SUSY standard model. The resulting model forms a well-defined basis for comparing the physics potential of different facilities. Very little of the acceptable parameter space has been excluded by CERN LEP or Fermilab so far, but a significant fraction can be covered when these accelerators are upgraded. A number of initial applications to the understanding of the values of ${m}_{h}$ and ${m}_{t}$the SUSY spectrum, detectability of SUSY at LEP II or Fermilab, $B(b\ensuremath{\rightarrow}s\ensuremath{\gamma})$, $\ensuremath{\Gamma}(Z\ensuremath{\rightarrow}b\overline{b})$, dark matter, etc., are included in a separate section that might be of more interest to some readers than the technical aspects of model building. We formulate an approach to extracting SUSY parameters from data when superpartners are detected. For small $tan\ensuremath{\beta}$ or large ${m}_{t}$ both ${m}_{\frac{1}{2}}$ and ${m}_{0}$ are entirely bounded from above at \AA{} 1 TeV without having to use a fine-tuning constraint.

Cosmological implications of dynamical supersymmetry breaking.

Abstract: We provide a taxonomy of dynamical supersymmetry-breaking theories, and discuss the cosmological implications of the various types of models. Models in which supersymmetry breaking is produced by chiral superfields which only have interactions of gravitational strength (e.g., string theory moduli) are inconsistent with standard big bang nucleosynthesis unless the gravitino mass is greater than \AA{}3 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ GeV. This problem cannot be solved by inflation. Models in which supersymmetry is dynamically broken by renormalizable interactions in flat space have no such cosmological problems. Supersymmetry can be broken either in a hidden or the visible sector. However, hidden sector models suffer from several naturalness problems and have difficulties in producing an acceptably large gluino mass.

Quantum groups, gravity, and the generalized uncertainty principle.

Abstract: We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincar\'e algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the $\ensuremath{\kappa}$-deformed Poincar\'e algebra a minimal observable length emerges naturally.

From the Big Bang theory to the theory of a stationary universe

Abstract: We consider chaotic inflation in the theories with the effective potentials which at large $\ensuremath{\varphi}$ behave either as ${\ensuremath{\varphi}}^{n}$ or as ${e}^{\ensuremath{\alpha}\ensuremath{\varphi}}$. In such theories inflationary domains containing a sufficiently large and homogeneous scalar field $\ensuremath{\varphi}$ permanently produce new inflationary domains of a similar type. This process may occur at densities considerably smaller than the Planck density. Self-reproduction of inflationary domains is responsible for the fundamental stationarity which is present in many inflationary models: properties of the parts of the Universe formed in the process of self-reproduction do not depend on the time when this process occurs. We call this property of the inflationary Universe local stationarity. In addition to it, there may exist either a stationary distribution of probability ${P}_{c}$ to find a given field $\ensuremath{\varphi}$ at a given time at a given point, or a stationary distribution of probability ${P}_{p}$ to find a given field $\ensuremath{\varphi}$ at a given time in a given physical volume. If any of these distributions is stationary, we will be speaking of a global stationarity of the inflationary Universe. In all realistic inflationary models which are known to us the probability distribution ${P}_{c}$ is not stationary. On the other hand, investigation of the probability distribution ${P}_{p}$ describing a self-reproducing inflationary universe shows that the center of this distribution moves towards greater and greater $\ensuremath{\varphi}$ with increasing time. It is argued, however, that the probability of inflation (and of the self-reproduction of inflationary domains) becomes strongly suppressed when the energy density of the scalar field approaches the Planck density. As a result, the probability distribution ${P}_{p}$ rapidly approaches a stationary regime, which we have found explicitly for the theories $\frac{\ensuremath{\lambda}}{4}{\ensuremath{\varphi}}^{4}$ and ${e}^{\ensuremath{\alpha}\ensuremath{\varphi}}$. In this regime the relative fraction of the physical volume of the Universe in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time, both at the stage of inflation and after it. Each of the two types of stationarity mentioned above constitutes a significant deviation of inflationary cosmology from the standard big bang paradigm. We compare our approach with other approaches to quantum cosmology, and illustrate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.

Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries.

Abstract: Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO laser-interferometer detector system, and will be an important source also for similar, lower-frequency detectors that might be flown in space (e.g., the proposed LISA mission). During the orbital inspiral, if one or both bodies are rapidly rotating, the general relativistic spin-orbit and spin-spin coupling (i.e., the "dragging of inertial frames" by the bodies' spins) cause the binary's orbital plane to precess. In this paper we analyze the resulting modulation of the inspiral gravitational waveform, using post2-Newtonian equations to describe the precession of the orbital plane, but only the leading-order (Newtonian, quadrupole-moment approximation) equations to describe the orbit, the radiation reaction, the inspiral, and the wave generation. We derive all the formulas one needs to readily compute the spin-modulated gravitational waveform (within the post-Newtonian approximation and the approximation that the precession frequency is much smaller than the orbital frequency). We also develop intuition into what the modulated signals "look like," by a variety of means. We provide approximate, analytical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearly equal masses and the case where one of the bodies has negligible spin. For these cases, for almost all choices of binary parameters, the motion is a simple precession of the orbital angular momentum around the nearly fixed direction of the total angular momentum, with a few tens of precession periods as the waves sweep through the LIGO/VIRGO observational band. However, when the spin and orbital angular momenta are approximately anti-aligned, there is a transitional-precession epoch during which their near cancellation causes the binary to "lose its gyroscopic bearings" and tumble in space, with a corresponding peculiar sweep of the waveform modulation. We also explore numerically the precessional behaviors that occur for general masses and spins; these typically appear quite similar to our special-case, simple-precession, and transitional-precession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.

Physical equivalence between nonlinear gravity theories and a general-relativistic self-gravitating scalar field.

Abstract: We argue that in a nonlinear gravity theory (the Lagrangian being an arbitrary function of the curvature scalar R), which according to well-known results is dynamically equivalent to a self-gravitating scalar field in general relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as the Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical, in the sense that Minkowski space is unstable due to the existence of negative-energy solutions close to it. To this aim we first clarify the global net of relationships between the nonlinear gravity theories, scalar-tensor theories, and general relativity, showing that in a sense these are ``canonically conjugated'' to each other. We stress that the isomorphisms are in most cases local; in the regions where these are defined, we explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and vice versa. We study energetics for asymptotically flat solutions for those Lagrangians which admit conformal rescaling to the Einstein frame in the vicinity of flat space. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space, and this is determined by the lowest-order terms R+${\mathit{aR}}^{2}$ in the Lagrangian. The proof of this positive-energy theorem relies on the existence of the Einstein frame, since in the (Helmholtz-)Jordan frame the dominant energy condition does not hold and the field variables are unrelated to the total energy of the system. This is why we regard the Jordan frame as unphysical, while the Einstein frame is physical and reveals the physical contents of the theory. The latter should hence be viewed as physically equivalent to a self-interacting general-relativistic scalar field.

Late time cosmological phase transition and galactic halo as Bose liquid

Abstract: We consider the ultra light pseudo Nambu-Goldstone boson appearing in the late time cosmological phase transition theories as a dark matter candidate. Since it is almost massless, its nature is more wave like than particle like. Hence we apply quantum mechanics to study how they form the galactic halos. Three predictions are made; (1)the mass profile $\rho\sim r^{-1.6}$, (2)there are ripple-like fine structures in rotation curve, (3) the rotation velocity times ripple's wave length is largely galaxy independent. We compare the rotation curves predicted by our theory with the data observed.

Diffractive leptoproduction of vector mesons in QCD

Abstract: We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone [ital q[bar q]] wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the [ital Q][sup 2] and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as [ital Q][sup [minus]6]. The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.

Inflation and primordial black holes as dark matter

Abstract: We discuss the hypothesis that a large (or even a major) fraction of dark matter in the Universe consists of primordial black holes (PBH's). PBH's may arise from adiabatic quantum fluctuations appearing during inflation. We demonstrate that the inflation potential V(cphi) leading to the formation of a great number of PBH's should have a feature of the ``plateau''-type in some range ${\mathit{cphi}}_{1}$cphi${\mathit{cphi}}_{2}$ of the inflation field cphi. The mass spectrum of PBH's for such a potential is calculated.

Yukawa coupling unification with supersymmetric threshold corrections.

Abstract: Radiative corrections to the down-type fermion masses at the supersymmetric threshold are enhanced by the ratio of vacuum expectation values, tan[beta]. This can have a strong impact on the unification of Yukawa couplings in supersymmetric grand unified theories. We present an example of such a model with a horizontal gauge symmetry that naturally explains the fermion mass hierarchy and the small mixing angles of the Kobayashi-Maskawa matrix. The unification of the lepton and the down-quark Yukawa couplings is achieved without introducing large Higgs multiplets.

SIBYLL: An event generator for simulation of high energy cosmic ray cascades.

Abstract: We describe the physical basis and some applications of an efficient event generator designed for Monte Carlo simulations of atmospheric cascades at ultrahigh energies. The event generator (sibyll) incorporates many features of the Lund programs, but emphasizes the fragmentation region and the production of minijets. A consistent treatment of hadron-hadron and hadron-nucleus interactions is emphasized. Examples of applications are the calculation of coincident muons observed in deep underground detectors and the simulation of the longitudinal development of air shower components in the atmosphere.