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

Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light

We present a Green's dyadic formulation to calculate the Casimir energy for a dielectric-diamagnetic cylinder with the speed of light differing on the inside and outside. Although the result is in general divergent, special cases are meaningful. It is pointed out how the self-stress on a purely dielectric cylinder vanishes through second order in the deviation of the permittivity from its vacuum value, in agreement with the result calculated from the sum of van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0

Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results

We study the pion mass dependence of the rho(770) and f_0(600) masses and widths from one and two-loop unitarized Chiral Perturbation Theory. We show the consistency of one-loop calculations with lattice results for the M_rho, f_pi and the isospin 2 scattering length a_20.Then, we develop and apply the modified Inverse Amplitude Method formalism for two-loop ChPT. In contrast to the f_0(600), the rho(770) is rather sensitive to the two-loop ChPT parameters --our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M_rho, f_pi, by the qqbar leading 1/N_c behavior of the rho and by existing estimates of low energy constants. These fits yield relatively stable predictions up to m_pi\simeq 300-350 MeV for the rho coupling and width as well as for all the f_0(600) parameters. We confirm, to two-loops, the weak m_pi dependence of the rho coupling and the KSRF relation, and the existence of two virtual f_0(600) poles for sufficiently high m_pi. At two loops one of these poles becomes a bound state when m_pi is somewhat larger than 300 MeV.Comment: 15 pages, to appear in Phys. Rev.

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

Surface Divergences and Boundary Energies in the Casimir Effect

Although Casimir, or quantum vacuum, forces between distinct bodies, or self-stresses of individual bodies, have been calculated by a variety of different methods since 1948, they have always been plagued by divergences. Some of these divergences are associated with the volume, and so may be more or less unambiguously removed, while other divergences are associated with the surface. The interpretation of these has been quite controversial. Particularly mysterious is the contradiction between finite total self-energies and surface divergences in the local energy density. In this paper we clarify the role of surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0

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

On the nature of light scalar mesons from their large NcN_c behavior

We show how to obtain information about the states of an effective field theory in terms of the underlying fundamental theory. In particular we analyze the spectroscopic nature of meson resonances from the meson-meson scattering amplitudes of the QCD low energy effective theory, combined with the expansion in the large number of colors. The vectors follow a qqbar behavior, whereas the sigma, kappa and f_0(980) scalars disappear for large N_c, in support of a qqqbarqbar-like nature. The a_0 shows a similar pattern, but the uncertainties are large enough to accommodate both interpretations.Comment: 4 pages. Slightly shortened version to appear in Phys. Rev. Lett. Two typos correcte

Non-structural carbohydrate pools in a tropical forest

The pool size of mobile, i.e. non-structural carbohydrates (NSC) in trees reflects the balance between net photosynthetic carbon uptake (source) and irreversible investments in structures or loss of carbon (sink). The seasonal variation of NSC concentration should reflect the sink/source relationship, provided all tissues from root to crown tops are considered. Using the Smithsonian canopy crane in Panama we studied NSC concentrations in a semi-deciduous tropical forest over 22months. In the 9 most intensively studied species (out of the 17 investigated), we found higher NSC concentrations (starch, glucose, fructose, sucrose) across all species and organs in the dry season than in the wet season (NSC 7.2% vs 5.8% of dry matter in leaves, 8.8/6.0 in branches, 9.7/8.5 in stems, 8.3/6.4 in coarse and 3.9/2.2 in fine roots). Since this increase was due to starch only, we attribute this to drought-constrained growth (photosynthesis less affected by drought than sink activity). Species-specific phenological rhythms (leafing or fruiting) did not overturn these seasonal trends. Most of the stem volume (diameter at breast height around 40cm) stores NSC. We present the first whole forest estimate of NSC pool size, assuming a 200tha−1 forest biomass: 8% of this i.e. ca. 16tha−1 is NSC, with ca. 13tha−1 in stems and branches, ca. 0.5 and 2.8tha−1 in leaves and roots. Starch alone (ca. 10.5tha−1) accounts for far more C than would be needed to replace the total leaf canopy without additional photosynthesis. NSC never passed through a period of significant depletion. Leaf flushing did not draw heavily upon NSC pools. Overall, the data imply a high carbon supply status of this forest and that growth during the dry season is not carbon limited. Rather, water shortage seems to limit carbon investment (new tissue formation) directly, leaving little leeway for a direct CO2 fertilization effect

Investigation of a0-f0 mixing

We investigate the isospin-violating mixing of the light scalar mesons a0(980) and f0(980) within the unitarized chiral approach. Isospin-violating effects are considered to leading order in the quark mass differences and electromagnetism. In this approach both mesons are generated through meson-meson dynamics. Our results provide a description of the mixing phenomenon within a framework consistent with chiral symmetry and unitarity, where these resonances are not predominantly q q-bar states. Amongst the possible experimental signals, we discuss observable consequences for the reaction J/Psi -> phi pi0 eta in detail. In particular we demonstrate that the effect of a0-f0 mixing is by far the most important isospin-breaking effect in the resonance region and can indeed be extracted from experiment.Comment: 15 pages, 9 figures; discussion extended, title changed, version published in Phys. Rev.