A Brief Introduction to Chiral Perturbation Theory

A brief introduction to the subject of chiral perturbation theory ($\chi$pt) is presented, including a discussion of effective field theory and applications of $\chi$pt in the arena of purely mesonic interactions as well as in the $\pi N$ sector.Comment: 15 pages, talk given at TAPS detector workshop, Rez, Czech Republic, Sept. 1999, to be published in Czech. J. Phy

Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate

Auxiliary fields and hadron dynamics

The relations existing between the auxiliary field (einbein field) formalism and the spinless Salpeter equation are studied in the case of two particles with the same mass, interacting via a confining potential. The problem of non-orthogonality for radial excited states in the auxiliary field formalism is discussed and found to be non-crucial. It is shown that the classical equations of motion of the rotating string model, derived from the QCD lagrangian, reduce exactly to the classical equations of motion of the phenomenological semirelativistic flux tube model, provided all auxiliary fields are eliminated correctly from the rotating string hamiltonian

Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation

The chiral expansion of nucleon properties such as mass, magnetic moment, and magnetic polarizability are investigated in the framework of chiral perturbation theory, with and without the heavy-baryon expansion. The analysis makes use of a pion-mass dispersion relation, which is shown to hold in both frameworks. The dispersion relation allows an ultraviolet cutoff to be implemented without compromising the symmetries. After renormalization, the leading-order heavy-baryon loops demonstrate a stronger dependence on the cutoff scale, which results in weakened convergence of the expansion. This conclusion is tested against the recent results of lattice quantum chromodynamics simulations for nucleon mass and isovector magnetic moment. In the case of the polarizability, the situation is even more dramatic as the heavy-baryon expansion is unable to reproduce large soft contributions to this quantity. Clearly, the heavy-baryon expansion is not suitable for every quantity.Comment: Accepted for publication in EPJ C. Made changes based on referee comments: clarifying sentences to conclusion 1. of Section IV, beginning of Section V, and new footnote in Section VI, page 8. Added more detailed explanation in paragraph 4 of Section III. Added citations of Phys.Rev. D60, 034014, and Phys.Lett. B716, 33

Axial vector form factor of nucleons in a light-cone diquark model

The nucleon axial vector form factor is investigated in a light-cone quark spectator diquark model, in which Melosh rotations are applied to both the quark and vector diquark. It is found that this model gives a very good description of available experimental data and the results have very little dependence on the parameters of the model. The relation between the nucleon axial constant and the anomalous magnetic moment of nucleons is also discussed.Comment: 8 pages, Revtex4, 1 figure, version to be published in Phys. Rev.

Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100 MeV, using state-of-the-art deuteron wave functions and NN-potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green's functions in order to ensure gauge invariance and the correct Thomson limit. With this Green's-function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use Chiral Effective Field Theory with explicit \Delta(1232) degrees of freedom within the Small Scale Expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic $\gamma d$ data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find \alpha_E^s= (11.3+-0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and \beta_M^s = (3.2-+0.7(stat)+-0.6(Baldin)) x 10^{-4} fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are essentially the same.Comment: 47 pages LaTeX2e with 20 figures in 59 .eps files, using graphicx. Minor modifications; extended discussion of theoretical uncertainties of polarisabilities extraction. Version accepted for publication in EPJ

Chiral Symmetry Restoration at Finite Temperature and Chemical Potential in the Improved Ladder Approximation

The chiral symmetry of QCD is studied at finite temperature and chemical potential using the Schwinger-Dyson equation in the improved ladder approximation. We calculate three order parameters; the vacuum expectation value of the quark bilinear operator, the pion decay constant and the quark mass gap. We have a second order phase transition at the temperature $T_c=169$ MeV along the zero chemical potential line, and a first order phase transition at the chemical potential $\mu_c=598$ MeV along the zero temperature line. We also calculate the critical exponents of the three order parameters.Comment: 16 pages + 10 uuencoded eps figures, LaTe