Aspects of Nucleon Chiral Perturbation Theory

I review recent progress made in the calculation of nucleon properties in the framework of heavy baryon CHPT. Topics include: Compton scattering, $\pi N$ scattering, the anatomy of a low-energy constant and the induced pseudoscalar form factor.Comment: plain TeX (macro included), 12pp, lecture delivered at the workshop on "Chiral Dynamics: Theory and Experiments", MIT, July 25-29, 199

One-loop vertex integrals in heavy-particle effective theories

We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.Comment: 10 pages, Latex, to appear in J. Phys.

One loop corrections to quantum hadrodynamics with vector mesons

The renormalized elastic $\pi\pi$ scattering amplitude to one loop is calculated in the chiral limit in the $\sigma$ model and in a Quantum Hadrodynamic model (QHD-III) with vector mesons. It is argued that QHD-III reduces to the linear $\sigma$ model in the limit that the vector meson masses become large. The pion decay constant is also calculated to 1-loop in the $\sigma$ model, and at tree level in QHD-III; it is shown that the coefficient of the tree level term in the scattering amplitude equals $F_\pi^{-2}$. The 1-loop correction of $F_\pi$ in QHD-III violates strong isospin current conservation. Thus,it is concluded that QHD-III can, at best, only describe the strongly interacting nuclear sector.Comment: 6 page

The standard model at low energies

The hadronic sector of the standard model at low energies is described by a non--decoupling effective field theory, chiral perturbation theory. An introduction is given to the construction of effective chiral Lagrangians, both in the purely mesonic sector and with inclusion of baryons. The connection between the relativistic formulation and the heavy baryon approach to chiral perturbation theory with baryons is reviewed.Comment: Lectures given at the 6th Indian-Summer School on Intermediate Energy Physics, Prague, Aug. 1993, Latex, 26 pages (with a4.sty), UWThPh-1993-3

Identification of tipping years and shifts in mesozooplankton community structure using multivariate analyses: a long-term study in southern North Sea

Abstract Many previous studies on the changes in zooplankton communities considered only subsets of the total community. In this study, we investigated the temporal dynamics of the mesozooplankton community structure, considering all taxa (holo- and meroplankton) sampled over the last five decades at Helgoland Roads. We identified two tipping years. The first one occurred in 1983, which is consistent with previous studies conducted on copepods. The second shift, even more pronounced, took place in the mid-2000s. During the first shift, most taxa significantly increased in abundance and kept high densities until the end of the 1990s. Then, we observed in the mid-2000s a sharp decrease in community diversity and abundances of almost all taxa. One of the aims of the study was to test the robustness depending on the choice of taxa. To test this, we selected different subsets of the total zooplankton community, both randomly as well as based on functionality. We observed very similar trends over time for all groups, showing the complete community experienced the same changes. However, the timing of the tipping years depended on the organisms considered. These results highlight that the observed changes in the planktonic community are surprisingly robust and visible in most planktonic organisms.</jats:p

The vector form factor of the pion from unitarity and analyticity: a model-independent approach

We study a model-independent parameterization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to sqrt(s) ~ 1.2 GeV and allows a model-independent determination of the mass of the rho(770) resonance, M(rho) = (775.1 +- 0.5) MeV. We analyse the experimental data on tau(-) -> pion(-) pion(0) neutrino(tau), in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two-pion contribution to the anomalous magnetic moment of the muon, a_muon, and to the fine structure constant, alpha(M(Z)^2), is also performed.Comment: 1+15 pages, 2 figure

QCD chiral Lagrangian on the lattice, strong coupling expansion and Ward identities with Wilson fermions

We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the consequences of the chiral symmetry breaking induced by the Wilson term, we study the lattice chiral Lagrangian at the leading order of the strong coupling and large $N$ expansion. We show that the effects of the Wilson term can be conveniently taken into account, in the lattice effective theory, by a suitable renormalization procedure. In particular, we show that, at the leading order of the strong coupling and large N expansion, the chiral symmetry is exactly recovered on the lattice provided that the bare quark mass and the lattice operators are properly renormalized.Comment: 45 pages, no figures. Latex fil

Isospin violation and the proton's neutral weak magnetic form factor

The effects of isospin violation on the neutral weak magnetic form factor of the proton are studied using two-flavour chiral perturbation theory. The first nonzero contributions appear at O(p^4) in the small-momentum expansion, and the O(p^5) corrections are also calculated. The leading contributions from an explicit Delta(1232) isomultiplet are included as well. At such a high order in the chiral expansion, one might have expected a large number of unknown parameters to contribute. However, it is found that no unknown parameters can appear within loop diagrams, and a single tree-level counterterm at O(p^4) is sufficient to absorb all divergences. The momentum dependence of the neutral weak magnetic form factor is not affected by this counterterm.Comment: 26 pages including 9 figure

K_S\rightarrow \gamma\gamma , K_L\rightarrow\pi^0\gamma\gamma$ and Unitarity

Agreement between the experimental value $\Gamma (K_S\rightarrow \gamma\gamma)$ and the number predicted via a one-loop chiral perturbation theory calculation has been cited as a success for the latter. On the other hand the one-loop prediction for the closely related process $K_L\rightarrow \pi^0\gamma\gamma$ has been found to be a factor three below the experimental value. Using the inputs of unitarity and dispersion relations, we demonstrate the importance of higher order loop effects to both of these processes.Comment: 20 pages (4 figures available on request), UMHEP-39