Scaling in few-body nuclear physics

The nuclear matter calculations with realistic nucleon-nucleon potentials present a general scaling between the nucleon-nucleus binding energy, the corresponding saturation density, and the triton binding energy. The Thomas-Efimov three-body effect implies in correlations among low-energy few-body and many-body observables. It is also well known that, by varying the short-range repulsion, keeping the two-nucleon information (deuteron and scattering) fixed, the four-nucleon and three-nucleon binding energies lie on a very narrow band known as a Tjon line. By looking for a universal scaling function connecting the proper scales of the few-body system with those of the many-body system, we suggest that the general nucleus-nucleon scaling mechanism is a manifestation of a universal few-body effect.

Pion structure in the instanton liquid model

The covariant quark model of the pion based on the effective nonlocal quark-hadron Lagrangian involving nonlocality induced by instanton fluctuations of the QCD vacuum is reviewed. Explicit gauge invariant formalism allows us to construct the conserved vector and axial currents and to demonstrate their consistency with the Ward-Takahashi identities and low-energy theorems. The spontaneous breaking of chiral symmetry results in the dynamic quark mass and the vertex of the quark-pion interaction, both momentum-dependent. The parameters of the instanton vacuum, the average size of the instantons, and the effective quark mass are expressed in terms of the vacuum expectation values of the lowest dimension quark-gluon operators and low-energy pion observables. The transition pion form factor for the processes gamma*gamma --> pi (0) and gamma*gamma* --> pi (0) is analyzed in detail. The kinematic dependence of the transition form factor at high momentum transfers allows one to determine the relationship between the light-cone amplitude of the quark distribution in the pion and the quark-pion vertex function. Its dynamic dependence implies that the transition form factor gamma*gamma --> pi (0) at high momentum transfers is acutely sensitive to the size of the nonlocality of nonperturbative fluctuations in the QCD vacuum. In the leading twist, the distribution amplitude and the distribution function of the valence quarks in the pion are calculated at a low normalization point of the order of the inverse average instanton size rho (-1)(c). The QCD results are evolved to higher momentum transfers and are in reasonable agreement with available experimental data on the pion structure.

Positronium-positronium interaction: resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin s(T) = 0) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively, and a binding of 0.43 eV of Ps(2). The scattering length for s(T) = 0 is 3.95 Angstrom and for s(T) = 2 is 0.83 Angstrom. The small s(T) = 2 scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Affine Toda model coupled to matter and the string tension in 2D QCD

The sl(2) affine Toda model coupled to matter is shown to describe various features, such as the spectrum and string tension, of the low-energy effective Lagrangian of two-dimensional QCD (one flavor and N colors). The corresponding string tension is computed when the dynamical quarks are in the fundamental representation of SU(N) and in the adjoint representation of SU(2).

3-3-1 models at electroweak scale

We show that in 3-3-1 models there exist a natural relation among the SU(3)(L) coupling constant g, the electroweak mixing angle theta(W), the mass of the W, and one of the vacuum expectation values, which implies that those models can be realized at low energy scales and, in particular, even at the electroweak scale. So that, being that symmetries realized in Nature, new physics may be really just around the corner. (c) 2006 Elsevier B.V. All rights reserved.

The few scales of nuclei and nuclear matter

The well-known correlations of low-energy three and four-nucleon observables with a typical three-nucleon scale (e.g., the Tjon line) is extended to light nuclei and nuclear matter. Evidence for the scaling between light nuclei binding energies and the triton one are pointed out. We argue that the saturation energy and density of nuclear matter are correlated to the triton binding energy. The available systematic nuclear matter calculations indicate a possible band structure representing these correlations. (c) 2006 Elsevier B.V. All rights reserved.

Three helium atoms and the scaling limit

We show that a scaling limit approach, previously applied in three-body low-energy nuclear physics, is realized for the first excited state of He-4 trimer. The present result suggests that such approach has a wider application.

Direct instantons, topological charge screening, and QCD glueball sum rules

Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on a realistic instanton size distribution and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0(-+) glueball signal) are traced to their neglect. on the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological short-distance physics strongly affects the sum rule results and reveals a rather diverse pattern of glueball properties. New predictions for the spin-0 glueball masses and decay constants and an estimate of the scalar glueball width are given, and several implications for glueball structure and experimental glueball searches are discussed.

Topological charge screening and pseudoscalar glueballs

Topological charge screening in the QCD vacuum is found to provide crucial nonperturbative contributions to the short-distance expansion of the pseudoscalar (0-+) glueball correlator. The screening contributions enter the Wilson coefficients and are an indispensable complement to the direct instanton contributions. They restore consistency with the anomalous axial Ward identity and remedy several flaws in the 0-+ glueball sum rules caused by direct instantons in the absence of screening (lack of resonance signals, violation of the positivity bound and of the underlying low-energy theorem). The impact of the finite width of the instanton size distribution and the (gauge-invariant) renormalization of the instanton contributions are also discussed. New predictions for the 0-+ glueball mass and decay constant are presented.

LARGE ATOMIC and NUCLEAR THREE-BODY SYSTEMS: SCATTERING and BINDING

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universal aspects of light halo nuclei

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Towards a hybrid compactification with a scalar-tensor global cosmic string

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

alpha alpha scattering in halo effective field theory

We study the two-alpha-particle (alpha alpha) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power Counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy aa phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the (8)Be ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles. (c) 2008 Elsevier B.V. All rights reserved.

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

Can quantum mechanics fool the cosmic censor?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)