The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 \sigma$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.Comment: Plain TeX. 29 figures. Version to be published in PRD, with improved P and F wave

Three-Body Dynamics and Self-Powering of an Electrodynamic Tether in a Plasmasphere

The dynamics of an electrodynamic tether in a three-body gravitational environment are investigated. In the classical two-body scenario the extraction of power is at the expense of orbital kinetic energy. As a result of power extraction, an electrodynamic tether satellite system loses altitude and deorbits. This concept has been proposed and well investigated in the past, for example for orbital debris mitigation and spent stages reentry. On the other hand, in the three-body scenario an electrodynamic tether can be placed in an equilibrium position fixed with respect to the two primary bodies without deorbiting, and at the same time generate power for onboard use. The appearance of new equilibrium positions in the perturbed three-body problem allow this to happen as the electrical power is extracted at the expenses of the plasma corotating with the primary body. Fundamental differences between the classical twobody dynamics and the new phenomena appearing in the circular restricted three-body problem perturbed by the electrodynamic force of the electrodynamic tether are shown in the paper. An interesting application of an electrodynamic tether placed in the Jupiter plasma torus is then considered, in which the electrodynamic tether generates useful electrical power of about 1 kW with a 20-km-long electrodynamic tether from the environmental plasma without losing orbital energy

The pion-pion scattering amplitude

We obtain reliable $\pi\pi$ scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy ($s^{1/2}\leq1.42 {\rm GeV}$) phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin~0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behaviour as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing $\pi\pi$ scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as $s - t - u$ crossing sum rules and other consistency conditions. The improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating $K$ decays. In this respect, we find $[a_0^{(0)}-a_0^{(2)}]^2=(0.077\pm0.008) M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=52.9\pm1.6^{\rm o}$.Comment: Version to be published in Phys. Rev. D. Plain TeX file. (minor changes). 16 figures (some multiple

Chiral condensate thermal evolution at finite baryon chemical potential within Chiral Perturbation Theory

We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson-meson interactions are described within Chiral Perturbation Theory and the pion-nucleon interaction by means of Heavy Baryon Chiral Perturbation Theory, both at one loop, and nucleon-nucleon interactions can be safely neglected within our hadronic gas domain of validity. Together with the virial expansion, this provides a systematic expansion at low temperatures and chemical potentials, which includes the physical quark masses. This can serve as a guideline for further studies on the lattice. We also obtain estimates of the critical line of temperature and chemical potential where the chiral condensate melts, which systematically lie somewhat higher than recent lattice calculations but are consistent with several hadronic models. We have also estimated uncertainties due to chiral parameters, heavier hadrons and higher orders through unitarized Chiral Perturbation Theory.Comment: 15 pages, 15 figures, 3 tables, ReVTeX. Version to appear in Phys. Rev. D. References added. More conservative estimate of applicability domain, with new figure. More detailed explanation of final results with two more figures. Results unchange

Chiral Perturbation Theory, the 1/Nc{1/N_c} expansion and Regge behaviour determine the structure of the lightest scalar meson

The leading $1/N_c$ behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the $\rho$ and the $\sigma$. At one loop order the $\rho$ is a ${\bar q}q$ meson, while the $\sigma$ is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger $N_c$, if such a distinction holds. While the $\sigma$ at $N_c=3$ is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as $N_c$ increases above 6-8, the $\sigma$ has a sub-dominant ${\bar q}q$ fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of $N_c \lesssim 15$, where the unitarisation procedure adopted applies.Comment: 22 pages, 8 figures. Version to be published in Physical Review

Statistical analysis of Ni nanowires breaking processes: a numerical simulation study

A statistical analysis of the breaking behavior of Ni nanowires is presented. Using molecular dynamic simulations, we have determined the time evolution of both the nanowire atomic structure and its minimum cross section (Sm(t)). Accumulating thousands of independent breaking events, Sm histograms are built and used to study the influence of the temperature, the crystalline stretching direction and the initial nanowire size. The proportion of monomers, dimers and more complex structures at the latest stages of the breaking process are calculated, finding important differences among results obtained for different nanowire orientations and sizes. Three main cases have been observed. (A) [111] stretching direction and large nanowire sizes: the wire evolves from more complex structures to monomers and dimers prior its rupture; well ordered structures is presented during the breaking process. (B) Large nanowires stretched along the [100] and [110] directions: the system mainly breaks from complex structures (low probability of finding monomers and dimers), having disordered regions during their breakage; at room temperature, a huge histogram peak around Sm=5 appears, showing the presence of long staggered pentagonal Ni wires with ...-5-1-5-... structure. (C) Initial wire size is small: strong size effects independently on the temperature and stretching direction. Finally, the local structure around monomers and dimmers do not depend on the stretching direction. These configurations differ from those usually chosen in static studies of conductance.Comment: 18 pages, 13 figure

Fast CP Violation

$B$ flavor tagging will be extensively studied at the asymmetric $B$ factories due to its importance in CP asymmetry measurements. The primary tagging modes are the semileptonic decays of the $b$ (lepton tag), or the hadronic $b \to c (\to s)$ decays (kaon tag). We suggest that looking for time dependent CP asymmetries in events where one $B$ is tagged leptonically and the other one is tagged with a kaon could result in an early detection of CP violation. Although in the Standard Model these asymmetries are expected to be small, $\sim 1$, they could be measured with about the same amount of data as in the ``gold-plated'' decay $B_d \to \psi K_S$. In the presence of physics beyond the Standard Model, these asymmetries could be as large as $\sim 5$, and the first CP violation signal in the $B$ system may show up in these events. We give explicit examples of new physics scenarios where this occurs.Comment: 9 pages, revtex, no figures. Discussion of new physics effects on CP violation with two lepton tags expanded. Factors of 2 correcte

Two-meson cloud contribution to the baryon antidecuplet binding

We study the two-meson virtual cloud contribution to the self-energy of the SU(3) antidecuplet, to which the Theta+ pentaquark is assumed to belong. This is motivated by the large branching ratio of the N(1710) decay into two pions and one nucleon. We derive effective Lagrangians that describe the N(1710) decay into N-pi-pi with two pions in s or p wave. We obtain increased binding for all members of the antidecuplet and a contribution to the mass splitting between states with different strangeness which is at least 20 % of the empirical one. We also provide predictions for three-body decays of the pentaquark antidecuplet.Comment: 13 pages, To appear in Phys. Rev.