Low Energy Constants from High Energy Theorems

New constraints on resonance saturation in chiral perturbation theory are investigated. These constraints arise because each consistent saturation scheme must map to a representation of the full QCD chiral symmetry group. The low-energy constants of chiral perturbation theory are then related by a set of mixing angles. It is shown that vector meson dominance is a consequence of the fact that nature has chosen the lowest-dimensional nontrivial chiral representation. It is further shown that chiral symmetry places an upper bound on the mass of the lightest scalar in the hadron spectrum.Comment: 11 pages TeX and mtexsis.te

High Energy Theorems at Large-N

Sum rules for products of two, three and four QCD currents are derived using chiral symmetry at infinite momentum in the large-N limit. These exact relations among meson decay constants, axialvector couplings and masses determine the asymptotic behavior of an infinite number of QCD correlators. The familiar spectral function sum rules for products of two QCD currents are among the relations derived. With this precise knowledge of asymptotic behavior, an infinite number of large-N QCD correlators can be constructed using dispersion relations. A detailed derivation is given of the exact large-N pion vector form factor and forward pion-pion scattering amplitudes.Comment: 34 pages TeX and mtexsis.tex, 10 figures (uses epsf

Chiral Dynamics of Low-Energy Kaon-Baryon Interactions with Explicit Resonance

The processes involving low energy $\bar{K}N$ and $Y\pi$ interactions (where $Y= \Sigma$ or $\Lambda$) are studied in the framework of heavy baryon chiral perturbation theory with the $\Lambda$(1405) resonance appearing as an independent field. The leading and next-to-leading terms in the chiral expansion are taken into account. We show that an approach which explicitly includes the $\Lambda$(1405) resonance as an elementary quantum field gives reasonable descriptions of both the threshold branching ratios and the energy dependence of total cross sections.Comment: 16 pages, 6 figure

Three particles in a finite volume: The breakdown of spherical symmetry

Lattice simulations of light nuclei necessarily take place in finite volumes, thus affecting their infrared properties. These effects can be addressed in a model-independent manner using Effective Field Theories. We study the model case of three identical bosons (mass m) with resonant two-body interactions in a cubic box with periodic boundary conditions, which can also be generalized to the three-nucleon system in a straightforward manner. Our results allow for the removal of finite volume effects from lattice results as well as the determination of infinite volume scattering parameters from the volume dependence of the spectrum. We study the volume dependence of several states below the break-up threshold, spanning one order of magnitude in the binding energy in the infinite volume, for box side lengths L between the two-body scattering length a and L = 0.25a. For example, a state with a three-body energy of -3/(ma^2) in the infinite volume has been shifted to -10/(ma^2) at L = a. Special emphasis is put on the consequences of the breakdown of spherical symmetry and several ways to perturbatively treat the ensuing partial wave admixtures. We find their contributions to be on the sub-percent level compared to the strong volume dependence of the S-wave component. For shallow bound states, we find a transition to boson-diboson scattering behavior when decreasing the size of the finite volume.Comment: 21 pages, 4 figures, 2 table

Functional renormalisation group for few-nucleon systems: SU(4) symmetry and its breaking

We apply the functional renormalisation group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalisation group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalisation flow equations decouple, and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for fermions with spin degrees only. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and quintet channels

A Theoretical Investigation of the Drag of Generalized Aircraft Configurations in Supersonic Flow

It seems possible that, in supersonic flight, unconventional arrangements of wings and bodies may offer advantages in the form of drag reduction. It is the purpose of this report to consider the methods for determining the pressure drag for such unconventional configurations, and to consider a few of the possibilities for drag reduction in highly idealized aircraft. The idealized aircraft are defined by distributions of lift and volume in three-dimensional space, and Hayes' method of drag evaluation, which is well adapted to such problems, is the fundamental tool employed. Other methods of drag evaluation are considered also wherever they appear to offer amplifications. The basic singularities such as sources, dipoles, lifting elements and volume elements are discussed, and some of the useful inter-relations between these elements are presented. Hayes' method of drag evaluation is derived in detail starting with the general momentum theorem. In going from planar systems to spatial systems certain new problems arise. For example, interference between lift and thickness distributions generally appears, and such effects are used to explain the difference between the non-zero wave drag of Sears-Haack bodies and the zero wave drag of Ferrari's ring wing plus central body. Another new feature of the spatial systems is that optimum configurations generally are not unique, there being an infinite family of lift or thickness distributions producing the same minimum drag. However it is shown that all members of an optimum family produce the same flow field in a certain region external to the singularity distribution. Other results of the study indicate that certain spatial distributions may produce materially less wave drag and vortex drag than comparable planar systems. It is not at all certain that such advantages can be realized in practical aircraft designs, but further investigation seems to be warranted

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_\pi$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_\pi$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work adde

Constraining Quark-Hadron Duality at Large-Nc

Quark-meson duality for two-point functions of vector and axial-vector QCD currents is investigated in the large-Nc approximation. We find that the joint constraints of duality and chiral symmetry imply degeneracy of excited vector and axial-vector mesons in the large-Nc limit. We compare model-independent constraints with expectations based on the Veneziano-Lovelace-Shapiro string model. Several models of duality are constructed, and phenomenological implications are discussed.Comment: 16 pages TeX, uses mtexsis.te