Strong Interactions at Low Energy

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field theory used to analyze the low energy structure is briefly sketched. As an illustration, I discuss the implications of the recent data on the decay $K\to \pi\pi e\nu$ for the magnitude of the quark condensate.Comment: Lectures given at the school of physics "Understanding the structure of hadrons", Prague, July 2001, 20 p

More nonperturbative corrections to the fine and hyperfine splitting in the heavy quarkonium

The leading nonperturbative effects to the fine and hyperfine splitting were calculated some time ago. Recently, they have been used in order to obtain realistic numerical results for the lower levels in bottomonium systems. We point out that a contribution of the same order $O(\Lambda_{QCD}^4/m^3 \alpha_s^2)$ has been overlooked. We calculate it in this paper.Comment: 9 pages, LaTeX, More self-contained and lengthier version without changing physical outputs. To be published in Phys. Rev.

Comparative Education at Universities World Wide

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Roy equation analysis of pi pi scattering

We analyze the Roy equations for the lowest partial waves of elastic pi pi scattering and demonstrate that the two S-wave scattering lengths a_0^0 and a_0^2 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S- and P-waves is given and it is shown that the threshold parameters of the D- and F-waves are also fixed very sharply in terms of a_0^0 and a^2_0. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a_0^0,a_0^2) plane. We show that the data on the reactions e+e- -> pi pi and tau -> pi pi nu reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K -> pi pi e nu in restricting the allowed range of a_0^0, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.Comment: Latex, 84 pages, 17 figure

U(3) chiral perturbation theory with infrared regularization

We include the eta-prime in chiral perturbation theory without employing 1/N_c counting rules. The method is illustrated by calculating the masses and decay constants of the Goldstone boson octet (pions, kaons, eta) and the singlet eta-prime up to one-loop order. The effective Lagrangian describing the interactions of the eta-prime with the Goldstone boson octet is presented up to fourth chiral order and the loop integrals are evaluated using infrared regularization, which preserves Lorentz and chiral symmetry.Comment: 29 page

Topology in QCD with 4 flavours of dynamical fermions

We study the topological properties of full QCD with four flavours of dynamical staggered fermions. In particular the topological susceptibility is measured and the problem of the determination of its first derivative is discussed.Comment: LATTICE99(Topology and Confinement). 3 pages, contains espcrc2.sty fil

Chiral Perturbation Theory for the Quenched Approximation of QCD

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.Comment: 14 page

The eta' in baryon chiral perturbation theory

We include in a systematic way the eta' in baryon chiral perturbation theory. The most general relativistic effective Lagrangian describing the interaction of the lowest lying baryon octet with the Goldstone boson octet and the eta' is presented up to linear order in the derivative expansion and its heavy baryon limit is obtained. As explicit examples, we calculate the baryon masses and the pi N sigma-term up to one-loop order in the heavy baryon formulation. A systematic expansion in the meson masses is possible, and appearing divergences are renormalized.Comment: 16 pages, 2 figure

Analytic Confinement and Regge Trajectories

A simple relativistic quantum field model with the Yukawa-type interaction is considered to demonstrate that the analytic confinement of the constituent ("quarks") and carrier ("gluons") particles explains qualitatively the basic dynamical properties of the spectrum of mesons considered as two-particle stable bound states of quarks and gluons: the quarks and gluons are confined, the glueballs represent bound states of massless gluons, the masses of mesons are larger than the sum of the constituent quark masses and the Regge trajectories of mesonic orbital excitations are almost linear.Comment: RevTeX, 16 pages, 3 figures and 2 table

On the extraction of the quark mass ratio (m_d - m_u)/m_s from Gamma(eta' -> pi^0 pi^+ pi^-)/Gamma(eta' -> eta pi^+ pi^-)

The claim that the light quark mass ratio (m_d - m_u)/m_s can be extracted from the decay width ratio Gamma(eta' -> pi^0 pi^+ pi^-)/Gamma(eta' -> eta pi^+ pi^-) is critically investigated within a U(3) chiral unitary framework. The influence of the recent VES data on the eta' -> eta pi^+ pi^- decay is also discussed.Comment: 9 pages, 1 figure, 6 table