Pion Interactions in Chiral Field Theories

We study in various chiral models the pion charge radius, $\pi_{e3}$ form factor ratio, $\pi^\circ \to \gamma \gamma$ amplitude, charge pion polarizabilities, $\gamma\gamma \to \pi^\circ \pi^\circ$ amplitude at low energies and the $\pi\pi$ s-wave I = 0 scattering length. We find that a quark-level linear sigma-model approach (also being consistent with tree-level vector meson dominance) is quite compatible with all of the above data.Comment: 12 pages, 9 eps figure

Momentum Dependent Vertices σγγ\sigma \gamma \gamma, σργ\sigma \rho \gamma and σρρ\sigma \rho \rho : The NJL Scalar Hidden by Chiral Symmetry

We calculate the momentum dependence of three particle vertices $\sigma \gamma \gamma$, $\sigma \rho \gamma$ and $\sigma \rho \rho$ in the context of a Nambu Jona Lasinio type model. We show how they influence the processes $\gamma \gamma \rightarrow \sigma \rightarrow \pi \pi$, $\rho \rightarrow \gamma \sigma$ and $\gamma \gamma \rightarrow \rho \rho$ and how chiral symmetry shadows the presence of the $\sigma$.Comment: 9 pages (latex), 5 figures available from the authors, preprint Coimbra 940506, IJS-TP-94/10, accepted for publication in Zeit. f. Physik

π+\pi^+ and π0\pi^0 Polarizabilities from {γγ→ππ\gamma\gamma\rightarrow\pi\pi} Data on the Base of S-Matrix Approach

We suggest the most model-independent and simple description of the $\gamma\gamma\rightarrow\pi\pi$ process near threshold in framework of S-matrix approach. The amplitudes contain the pion polarizabilities and rather restricted information about $\pi \pi$ interaction. Application of these formulae for description of MARK-II \cite{M2} and Crystal Ball \cite{CB} data gives: $(\alpha-\beta)^{C}=(6.0\pm 1.2)\cdot 10^{-42} {\rm cm}^{3}$, $(\alpha-\beta)^{N}=(-1.4\pm 2.1)\cdot 10^{-42} cm^3$ (in units system $e^2 = 4 \pi \alpha$) at the experimental values of $\pi \pi$ scattering lengths. Both values are compartible with current algebra predictions.Comment: LaTeX, 14 pages plus 6 figures (not included, available upon request) , ISU-IAP.Th93-03, Irkuts

Master Formulae Approach to Photon Fusion Reactions

We analyze the $\gamma\gamma\to \pi\pi, KK, \eta\eta, \pi\eta$ reactions through $\sqrt{s}=2$ GeV, using the master formula approach to QCD with three flavors. In this approach, the constraints of broken chiral symmetry, unitarity and crossing symmetry are manifest in all channels. The pertinent vacuum correlators are analyzed at tree level using straightforward resonance saturation methods. A one-loop chiral power counting analysis at treshold is also carried out and compared to standard chiral perturbation theory. Our results are in overall agreement with the existing data in all channels. We predict the strange meson polarizabilities and a very small cross section for $\gamma\gamma\to\eta\eta$.Comment: 19 pages LaTeX, 7 figure

The Bottom Mass Prediction in Supersymmetric Grand Unification; Uncertainties and Constraints

Grand unified theories often predict unification of Yukawa couplings (e.g., $h_{b} = h_{\tau}$), and thus certain relations among fermion masses. The latter can distinguish these from models that predict only coupling constant unification. The implications of Yukawa couplings of the heavy-family in the supersymmetric extension of the standard model (when embedded in a GUT) are discussed. In particular, uncertainties associated with $m_{t}$ and $m_{b}$, threshold corrections at the low-scale, and threshold and nonrenormalizable-operator corrections associated with a grand-unified sector at the high-scale are parametrized and estimated. The implication of these and of the correlation between $m_{t}$ and the prediction for $\alpha_{s}$ are discussed. Constraints on the $\tan\beta$ range in such models and an upper bound on the $t$-quark pole mass are given and are shown to be affected by the $\alpha_{s}-m_{t}$ correlation. Constraints on the low-scale thresholds are found to be weakened by uncertainties associated with the high-scale.Comment: 23 pages + 7 figures (figures are available upon request), LaTex + RevTex 3.0, UPR-0556

Topics in Chiral Perturbation Theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.Comment: 30 pp, TeX, Review talk, Third Workshop on High Energy Particle Physics (WHEPP III), Madras, India, January 1994. 7 figures available upon request. CRN--94/0

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

Photon-Photon Scattering, Pion Polarizability and Chiral Symmetry

Recent attempts to detect the pion polarizability via analysis of $\gamma\gamma\rightarrow\pi\pi$ measurements are examined. The connection between calculations based on dispersion relations and on chiral perturbation theory is established by matching the low energy chiral amplitude with that given by a full dispersive treatment. Using the values for the polarizability required by chiral symmetry, predicted and experimental cross sections are shown to be in agreement.Comment: 21 pages(+10 figures available on request), LATEX, UMHEP-38

f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach

We discuss a possible interpretation of the f0(980) meson as a hadronic molecule - a bound state of K and bar K mesons. Using a phenomenological Lagrangian approach we calculate the strong f0(980) to pi pi and electromagnetic f0(980) to gamma gamma decays. The compositeness condition provides a self-consistent method to determine the coupling constant between f0 and its constituents, K and bar K. Form factors governing the decays of the f0(980) are calculated by evaluating the kaon loop integrals. The predicted f0(980) to pi pi and f0(980) to gamma gamma decay widths are in good agreement with available data and results of other theoretical approaches.Comment: 21 pages, 11 figures, revised version accepted for publication in Eur. Phys. J.