Showing papers in "Physical Review D in 1999"

Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity

Abstract: We recently proposed a solution to the hierarchy problem not relying on low-energy supersymmetry or technicolor. Instead, the problem is nullified by bringing quantum gravity down to the TeV scale. This is accomplished by the presence of $ng~2$ new dimensions of submillimeter size, with the SM fields localized on a 3-brane in the higher dimensional space. In this paper we systematically study the experimental viability of this scenario. Constraints arise both from strong quantum gravitational effects at the TeV scale, and more importantly from the production of massless higher dimensional gravitons with TeV suppressed couplings. Theories with $ng2$ are safe due mainly to the infrared softness of higher dimensional gravity. For $n=2,$ the six dimensional Planck scale must be pushed above $\ensuremath{\sim}30\mathrm{TeV}$ to avoid cooling SN 1987A and distortions of the diffuse photon background. Nevertheless, the particular implementation of our framework within type I string theory can evade all constraints, for any $ng~2,$ with string scale ${m}_{s}\ensuremath{\sim}1\mathrm{TeV}.$ We also explore novel phenomena resulting from the existence of new states propagating in the higher dimensional space. The Peccei-Quinn solution to the strong $\mathrm{CP}$ problem is revived with a weak scale axion in the bulk. Gauge fields in the bulk can mediate repulsive forces $\ensuremath{\sim}{10}^{6}--{10}^{8}$ times stronger than gravity at submillimeter distances, as well as help stabilize the proton. Higher-dimensional gravitons produced on our brane and captured on a different ``fat'' brane can provide a natural dark matter candidate.

Charged AdS black holes and catastrophic holography

Abstract: We compute the properties of a class of charged black holes in anti--de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals--Maxwell liquid-gas system. In that case, the phases are controlled by the universal ``cusp'' and ``swallowtail'' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

Coupled Quintessence

Abstract: A new component of the cosmic medium, a light scalar field or ''quintessence '', has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant Such a field is expected to be coupled explicitely to ordinary matter, unless some unknown symmetry prevents it I investigate the cosmological consequences of such a coupled quintessence (CQ) model, assuming an exponential potential and a linear coupling This model is conformally equivalent to Brans-Dicke Lagrangians with power-law potential I evaluate the density perturbations on the cosmic microwave background and on the galaxy distribution at the present and derive bounds on the coupling constant from the comparison with observational data A novel feature of CQ is that during the matter dominated era the scalar field has a finite and almost constant energy density This epoch, denoted as $\phi $MDE, is responsible of several differences with respect to uncoupled quintessence: the multipole spectrum of the microwave background is tilted at large angles, the acoustic peaks are shifted, their amplitude is changed, and the present 8Mpc$/h$ density variance is diminished The present data constrain the dimensionless coupling constant to $|\beta |\leq 01$

Cosmological tracking solutions

Abstract: A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly rolling scalar field. Since the energy density of the scalar field generally decreases more slowly than the matter energy density, it appears that the ratio of the two densities must be set to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notion of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And can tracker solutions help to explain why quintessence is becoming important today rather than during the early universe?

Small-x F 2 structure function of a nucleus including multiple Pomeron exchanges

Abstract: We derive an equation determining the small-x evolution of the F{sub 2} structure function of a large nucleus which includes all multiple Pomeron exchanges in the leading logarithmic approximation using Mueller{close_quote}s dipole model. We show that in the double leading logarithmic limit this evolution equation reduces to the Gribov-Levin-Ryskin equation. {copyright} {ital 1999} {ital The American Physical Society}

High-energy tests of Lorentz invariance

Abstract: We develop a perturbative framework with which to discuss departures from exact Lorentz invariance and explore their potentially observable ramifications. Tiny noninvariant terms introduced into the standard model Lagrangian are assumed to be renormalizable (dimension \ensuremath{\leqslant}4), invariant under $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(2)\ensuremath{\bigotimes}U(1)$ gauge transformations, and rotationally and translationally invariant in a preferred frame. There are a total of 46 independent CPT-even perturbations of this kind, all of which preserve anomaly cancellation. They define the energy-momentum eigenstates and their maximal attainable velocities in the high-energy limit. The effects of these perturbations increase rapidly with energy in the preferred frame, more rapidly than those of CPT-odd perturbations. Our analysis of Lorentz-violating kinematics reveals several striking new phenomena that are relevant both to cosmic-ray physics (e.g., by undoing the Greisen, Zatsepin, and Kuz'min cutoff) and neutrino physics (e.g., by generating novel types of neutrino oscillations). These may lead to new and sensitive high-energy tests of special relativity.

Effective one-body approach to general relativistic two-body dynamics

Abstract: We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing binary system of compact objects. The transition from the adiabatic inspiral, driven by gravitational radiation damping, to an unstable plunge, induced by strong spacetime curvature, is predicted to occur for orbits more tightly bound than the innermost stable circular orbit in a Schwarzschild metric of mass M 5m11m2 . The binding energy, angular momentum and orbital frequency of the innermost stable circular orbit for the time-symmetric two-body problem are determined as a function of the mass ratio. @S0556-2821~99!04806-7#

Nonstandard optics from quantum space-time

Abstract: We study light propagation in the picture of semiclassical space-time that emerges in canonical quantum gravity in the loop representation. In such a picture, where space-time exhibits a polymerlike structure at microscales, it is natural to expect departures from the perfect nondispersiveness of an ordinary vacuum. We evaluate these departures, computing the modifications to Maxwell's equations due to quantum gravity and showing that under certain circumstances nonvanishing corrections appear that depend on the helicity of propagating waves. These effects could lead to observable cosmological predictions of the discrete nature of quantum space-time. In particular, recent observations of nondispersiveness in the spectra of gamma-ray bursts at various energies could be used to constrain the type of semiclassical state that describes the universe.

Holography, thermodynamics, and fluctuations of charged AdS black holes

Abstract: The physical properties of Reissner-Nordstrom black holes in (n11)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes ~in the canonical ensemble! and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighborhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with A3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations. @S0556-2821~99!06820-4#

Update on vector boson pair production at hadron colliders

Abstract: We present numerical results (including full one-loop QCD corrections) for the processes $p\overline{p}$ and $p\stackrel{\ensuremath{\rightarrow}}{p}{W}^{+}{W}^{\ensuremath{-}},$ ${W}^{\ifmmode\pm\else\textpm\fi{}}Z/{\ensuremath{\gamma}}^{*}$ and $Z/{\ensuremath{\gamma}}^{*}Z/{\ensuremath{\gamma}}^{*}$ followed by the decay of the massive vector bosons into leptons. In addition to their intrinsic importance as tests of the standard model, these processes are also backgrounds to conjectured non-standard model processes. Because of the small cross sections at the Fermilab Tevatron, full experimental control of these backgrounds will be hard to achieve. This accentuates the need for up-to-date theoretical information. A comparison is made with earlier work and cross section results are presented for $p\overline{p}$ collisions at $\sqrt{s}=2$ TeV and $\mathrm{pp}$ collisions at $\sqrt{s}=14$ TeV. Practical examples of the use of our calculations are presented.

Surface terms as counterterms in the AdS-CFT correspondence

Abstract: We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti--de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions $dl~7.$ As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.

Glueball spectrum from an anisotropic lattice study

Abstract: The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations.

Wilson loops and minimal surfaces

Abstract: The AdS-CFT correspondence suggests that the Wilson loop of the large N gauge theory with $\mathcal{N}=4$ supersymmetry in four dimensions is described by a minimal surface in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}.$ We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultraviolet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ gives a solution of the equation. We also discuss the zigzag symmetry of the loop operator. In the $\mathcal{N}=4$ gauge theory, we expect the zigzag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.

Particle production and complex path analysis

Abstract: This paper discusses particle production in Schwarzschild-like spacetimes and in a uniform electric field. Both problems are approached using the method of complex path analysis which is used to describe tunnelling processes in semiclassical quantum mechanics. Particle production in Schwarzschild-like spacetimes with a horizon is obtained here by a new and simple semiclassical method based on the method of complex paths. Hawking radiation is obtained in the $(t,r)$ coordinate system of the standard Schwarzschild metric without requiring the Kruskal extension. The coordinate singularity present at the horizon manifests itself as a singularity in the expression for the semiclassical propagator for a scalar field. We give a prescription whereby this singularity is regularized with Hawking's result being recovered. The equation satisfied by a scalar field is also reduced to solving a one-dimensional effective Schr\"odinger equation with a potential $(\ensuremath{-}{1/x}^{2})$ near the horizon. Constructing the action for a fictitious nonrelativistic particle moving in this potential and applying the above mentioned prescription, one again recovers Hawking radiation. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely time-dependent gauge. In a purely space-dependent gauge, however, the tunnelling interpretation has to be resorted to in order to recover the previous result. We attempt, in this paper, to provide a tunnelling description using the formal method of complex paths for both the time and space dependent gauges. The usefulness of such a common description becomes evident when ``mixed'' gauges, which are functions of both space and time variables, are analyzed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of elementary functions unlike the standard modes which are transcendental parabolic cylinder functions. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime.

On Kaluza-Klein states from large extra dimensions

Abstract: We consider the novel Kaluza-Klein (KK) scenario where gravity propagates in the $(4+n)$-dimensional bulk of spacetime, while gauge and matter fields are confined to the $(3+1)$-dimensional world volume of a brane configuration. For simplicity we assume compactification of the extra n dimensions on a torus with a common scale $R,$ and identify the massive KK states in the four-dimensional spacetime. For a given KK level $\stackrel{\ensuremath{\rightarrow}}{n}$ there is one spin-2 state, $(n\ensuremath{-}1)$ spin-1 states, and $n(n\ensuremath{-}1)/2$ spin-0 states, all mass degenerate. We construct the effective interactions between these KK states and ordinary matter fields (fermions, gauge bosons, and scalars). We find that the spin-1 states decouple and that the spin-0 states only couple through the dilaton mode. We then derive the interacting Lagrangian for the KK states and standard model fields, and present the complete Feynman rules. We discuss some low-energy phenomenology for these new interactions for the case when $1/R$ is small compared to the electroweak scale, and the ultraviolet cutoff of the effective KK theory is on the order of 1 TeV.

Rotation and the AdS / CFT correspondence

Abstract: In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be corotating faster than light far from the black hole. However in asymptotically anti--de Sitter space such equilibrium is possible for certain ranges of the parameters. We examine the relationship between conformal field theory in rotating Einstein universes of dimensions two to four and Kerr--anti--de Sitter black holes in dimensions three to five. The five-dimensional solution is new. We find similar divergences in the partition function of the conformal field theory and the action of the black hole at the critical angular velocity at which the Einstein universe rotates at the speed of light. This should be an interesting limit in which to study large N Yang-Mills theory.

Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point

Abstract: The event-by-event fluctuations of suitably chosen observables in heavy ion collisions at CERN SPS, BNL RHIC, and CERN LHC can tell us about the thermodynamic properties of the hadronic system at freeze-out. By studying these fluctuations as a function of varying control parameters, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second-order critical end point of the first-order transition between quark-gluon plasma and hadron matter. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We first consider how the event-by-event fluctuations of such observables are affected by Bose-Einstein correlations, by resonances which decay after freeze-out, and by fluctuations in the transverse flow velocity. We compare our thermodynamic predictions for such noncritical event-by-event fluctuations with NA49 data, finding broad agreement. We then focus on effects due to thermal contact between the observed pions and a heat bath with a given (possibly singular) specific heat, due to the direct coupling between themore » critical fluctuations of the sigma field and the observed pions. We also discuss the effect of the pions produced in the decay of sigma particles just above threshold after freeze-out on the inclusive pion spectrum and on multiplicity fluctuations. We estimate the size of these nonmonotonic effects, which appear near the critical point, including restrictions imposed by finite size and finite time, and conclude that they should be easily observable. (c) 1999 The American Physical Society.« less

The Universe as a domain wall

Abstract: It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of N=1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a {open_quotes}non-zero mode{close_quotes} of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten{close_quote}s {open_quotes}deformed{close_quotes} Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the four-dimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane world volume. {copyright} {ital 1999} {ital The American Physical Society}

Bulk versus boundary dynamics in anti–de Sitter spacetime

Abstract: We investigate the details of the bulk-boundary correspondence in Lorentzian signature anti--de Sitter space. Operators in the boundary theory couple to sources identified with the boundary values of non-normalizable bulk modes. Such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate. Normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition. They fluctuate and describe the Hilbert space of physical states. We provide an explicit, complete set of both types of modes for free scalar fields in global and Poincar\'e coordinates. For ${\mathrm{AdS}}_{3},$ the normalizable and non-normalizable modes originate in the possible representations of the isometry group $\mathrm{SL}(2,R{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SL}(2,R{)}_{R}$ for a field of given mass. We discuss the group properties of mode solutions in both global and Poincar\'e coordinates and their relation to different expansions of operators on the cylinder and on the plane. Finally, we discuss the extent to which the boundary theory is a useful description of the bulk spacetime.

Saturation in diffractive deep inelastic scattering

Abstract: We successfully describe the DESY HERA data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $\mathrm{ep}$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of ${Q}^{2}$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.

Scaling solutions in general nonminimal coupling theories

Abstract: A class of generalized nonminimal coupling theories is investigated, in search of scaling attractors able to provide an accelerated expansion at the present time. Solutions are found in the strong coupling regime and when the coupling function and the potential verify a simple relation. In such cases, which include power law and exponential functions, the dynamics is independent of the exact form of the coupling and the potential. The constraint from the time variability of G, however, limits the fraction of energy in the scalar field to less than 4% of the total energy density, and excludes accelerated solutions at the present.

Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

Abstract: We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation that was used to ``experimentally'' verify the theoretical calculations derived in the paper, and which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. This information consists of graphs of the noise power spectra, overlap reduction functions, and optimal filter functions; also included are tables of the signal-to-noise ratios and sensitivity levels for cross-correlation measurements between different detector pairs. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.

Extreme Kerr throat geometry: A vacuum analog of AdS 2 × S 2

Abstract: We study the near-horizon limit of a four-dimensional extreme rotating black hole. The limiting metric is a completely nonsingular vacuum solution, with an enhanced symmetry group $\mathrm{SL}(2,R)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1).$ We show that many of the properties of this solution are similar to the ${\mathrm{AdS}}_{2}{\ifmmode\times\else\texttimes\fi{}\mathrm{S}}^{2}$ geometry arising in the near-horizon limit of extreme charged black holes. In particular, the boundary at infinity is a timelike surface. This suggests the possibility of a dual quantum mechanical description. A five-dimensional generalization is also discussed.

Holographic Probes of Anti-de Sitter Spacetimes

Abstract: We describe probes of anti{endash}de Sitter spacetimes in terms of conformal field theories on the AdS boundary. Our basic tool is a formula that relates bulk and boundary states{emdash}classical bulk field configurations are dual to expectation values of operators on the boundary. At the quantum level we relate the operator expansions of bulk and boundary fields. Using our methods, we discuss the CFT description of local bulk probes including normalizable wave packets, fundamental and D-strings, and D-instantons. Radial motions of probes in the bulk spacetime are related to motions in scale on the boundary, demonstrating a scale-radius duality. We discuss the implications of these results for the holographic description of black hole horizons in the boundary field theory. {copyright} {ital 1999} {ital The American Physical Society}

Operator product expansion for Wilson loops and surfaces in the large N limit

Abstract: The operator product expansion for {open_quotes}small{close_quotes} Wilson loops in N=4, d=4 SYM theory is studied. The OPE coefficients are calculated in the large {ital N} and g{sub YM}{sup 2}N limit by exploiting the AdS-CFT correspondence. We also consider Wilson surfaces in the (0,2), d=6 superconformal theory. In this case, we find that the UV divergent terms include a term proportional to the rigid string action. {copyright} {ital 1999} {ital The American Physical Society}

UV / IR relations in AdS dynamics

Abstract: We point out that two distinct distance-energy relations have been discussed in the AdS-CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.

Time varying speed of light as a solution to cosmological puzzles

Abstract: We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light $c$ is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the standard big bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function $c(t).$ The large entropy inside the horizon nowadays can also be accounted for in this scenario.

Meson-meson interactions in a nonperturbative chiral approach

Abstract: A nonperturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe the meson-meson interaction up to about 1.2 GeV. The approach uses the $\mathcal{O}{(p}^{2})$ and $\mathcal{O}{(p}^{4})$ chiral Lagrangians. The seven free parameters of the $\mathcal{O}{(p}^{4})$ Lagrangian are fitted to the data. The results are in good agreement with a vast amount of experimental analyses. The amplitudes develop poles in the complex plane corresponding to the ${f}_{0}, {a}_{0}, \ensuremath{\rho}, {K}^{*}, \ensuremath{\varphi}, \ensuremath{\sigma},$ and $\ensuremath{\kappa}$ resonances, the latter two being very broad. The total and partial decay widths of the resonances are also well reproduced. Further extensions and applications of this chiral nonperturbative scheme are also discussed.

Cosmological scaling solutions of nonminimally coupled scalar fields

Abstract: We study the existence and stability of cosmological scaling solutions of a nonminimally coupled scalar field evolving in either an exponential or inverse power law potential. We show that, for inverse power law potentials, there exist scaling solutions the stability of which does not depend on the coupling constant $\ensuremath{\xi}.$ We then study the more involved case of exponential potentials and show that the scalar field will asymptotically behave as a baryotropic fluid when $\ensuremath{\xi}\ensuremath{\ll}1.$ The general case $\ensuremath{\xi}\ensuremath{\ll}/1$ is then discussed and we illustrate these results by some numerical examples.

N/D description of two meson amplitudes and chiral symmetry

Abstract: The most general structure of an elastic partial wave amplitude when the unphysical cuts are neglected is deduced in terms of the N/D method. This result is then matched to lowest order, ${\mathcal{O}}(p^2)$, Chiral Perturbation Theory($\chi$PT) and to the exchange (consistent with chiral symmetry) of resonances in the s-channel. The extension of the method to coupled channels is also given. Making use of the former formalism, the $\pi\pi$ and $K\pi$(I=1/2) P-wave scattering amplitudes are described without free parameters when taking into account relations coming from the 1/$N_c$ expansion and unitarity. Next, the scalar sector is studied and good agreement with experiment up to $\sqrt{s}=1.4$ GeV is found. It is observed that the $a_0(980)$, $\sigma$ and $\kappa(900)$ resonances are meson-meson states originating from the unitarization of the ${\mathcal{O}}(p^2)$ $\chi$PT amplitudes. On the other hand, the $f_0(980)$ is a combination of a strong S-wave meson-meson unitarity effect and of a preexisting singlet resonance with a mass around 1 GeV. We have also studied the size of the contributions of the unphysical cuts to the $\pi\pi$(I=0) and $K\pi$(I=1/2) elastic S-wave amplitudes from $\chi$PT and the exchange of resonances in crossed channels up to $\sqrt{s}\approx 800$ MeV. The loops are calculated as in $\chi$PT at next to leading order. We find a small correction from the unphysical cuts to our calculated partial waves.