Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

About the stability of the dodecatoplet

A new investigation is done of the possibility of binding the "dodecatoplet", a system of six top quarks and six top antiquarks, using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.Comment: 5 pages, two figures merged, refs. added, typos correcte

Can b→sγb\to s\gamma Close the Supersymmetric Higgs Production Window?

We show that the present limit from CLEO on the inclusive decay $b\to s\gamma$ provides strong constraints on the parameters of the charged Higgs sector in two-Higgs-Doublet-Models. Only a slight improvement in the experimental bound will exclude the region in the Supersymmetric Higgs parameter space which is inaccessible to collider searches.Comment: 8 pages plus 3 figures (available by request), latex, ANL-HEP-PR-92-110. Substantial revision to text, results unchange

On the precision of the theoretical predictions for pi pi scattering

In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are very sensitive to the poorly known high energy behaviour of the scattering amplitude. They claim that the asymptotic representation we used is incorrect and propose an alternative one. We repeat their calculations on the basis of the standard, subtracted fixed-t dispersion relations, using their asymptotics. The outcome fully confirms our earlier findings. Moreover, we show that the Regge parametrization proposed by these authors for the region above 1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the behaviour observed at low energies.Comment: Added more material, mostly in Sects. 7, 8 and 9, in support of the same conclusions. Latex, 28 pages, 3 figure

Simultaneous Softening of sigma and rho Mesons associated with Chiral Restoration

Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restoration (f*_{pi}/f_{pi} ~ 1) is also discussed.Comment: 5 pages, 4-eps figures, version accepted by Phys. Rev. C (R) with minor modification

Monotonicity of quantum ground state energies: Bosonic atoms and stars

The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the Newton systems are "bosonic stars". In either case there exists some third order polynomial in N such that the ratio of the ground state energy to the respective polynomial grows monotonically in N. Some applications of these new monotonicity results are discussed

Probing Heavy Higgs Boson Models with a TeV Linear Collider

The last years have seen a great development in our understanding of particle physics at the weak scale. Precision electroweak observables have played a key role in this process and their values are consistent, within the Standard Model interpretation, with a light Higgs boson with mass lower than about 200 GeV. If new physics were responsible for the mechanism of electroweak symmetry breaking, there would, quite generally, be modifications to this prediction induced by the non-standard contributions to the precision electroweak observables. In this article, we analyze the experimental signatures of a heavy Higgs boson at linear colliders. We show that a linear collider, with center of mass energy \sqrt{s} <= 1 TeV, would be very useful to probe the basic ingredients of well motivated heavy Higgs boson models: a relatively heavy SM-like Higgs, together with either extra scalar or fermionic degrees of freedom, or with the mixing of the third generation quarks with non-standard heavy quark modes.Comment: 21 page

RQM description of the charge form factor of the pion and its asymptotic behavior

The pion charge and scalar form factors, $F_1(Q^2)$ and $F_0(Q^2)$, are first calculated in different forms of relativistic quantum mechanics. This is done using the solution of a mass operator that contains both confinement and one-gluon-exchange interactions. Results of calculations, based on a one-body current, are compared to experiment for the first one. As it could be expected, those point-form, and instant and front-form ones in a parallel momentum configuration fail to reproduce experiment. The other results corresponding to a perpendicular momentum configuration (instant form in the Breit frame and front form with $q^+=0$) do much better. The comparison of charge and scalar form factors shows that the spin-1/2 nature of the constituents plays an important role. Taking into account that only the last set of results represents a reasonable basis for improving the description of the charge form factor, this one is then discussed with regard to the asymptotic QCD-power-law behavior $Q^{-2}$. The contribution of two-body currents in achieving the right power law is considered while the scalar form factor, $F_0(Q^2)$, is shown to have the right power-law behavior in any case. The low-$Q^2$ behavior of the charge form factor and the pion-decay constant are also discussed.}Comment: 30 pages, 10 figure

Tests for a Strong Electroweak Sector at Future e^+e^- High Energy Colliders

The study of the scattering at high energy of the gauge bosons W and Z, in particular longitudinally polarized W and Z, can clarify the mechanism of spontaneous symmetry breaking in the Standard Model of the electroweak interactions. Different models of strong electroweak sector, based on the effective lagrangian approach are briefly reviewed. They include models with no resonance, with scalar resonance, additional vector and axial-vector resonances. The effective Lagrangians are derived from the chiral symmetry of the symmetry breaking sector. Limits on these models from existing measurements, mainly LEP and Tevatron, are considered. We study also direct and indirect effects of the new interactions at high energy future e^+e^- linear colliders, through WW scattering and the direct production of these new vector gauge bosons.Comment: 74 pages, 19 figures and 4 tables included, Latex, uses epsf, to appear in La Rivista del Nuovo Cimento, some minor change

Realistic Equations of State for the Primeval Universe

Early universe equations of state including realistic interactions between constituents are built up. Under certain reasonable assumptions, these equations are able to generate an inflationary regime prior to the nucleosynthesis period. The resulting accelerated expansion is intense enough to solve the flatness and horizon problems. In the cases of curvature parameter \kappa equal to 0 or +1, the model is able to avoid the initial singularity and offers a natural explanation for why the universe is in expansion.Comment: 32 pages, 5 figures. Citations added in this version. Accepted EPJ