Large Nc means Nc=3

We show that the nonperturbative solution of the SU(2) linear sigma model field theory requires color number Nc=3. Also, we show that the three-point and four-point functions bootstrap (or nonperturbatively ``shrink'') in the chiral limit to the tree amplitudes. Independently, we show that a chiral phase transition for Nf=2 requires Tc=180 MeV, consistent with the computer lattice value (173 +/- 8 MeV).Comment: 9 pages, LaTeX. Invited talk given at the Large Nc Workshop, ASU, January 200

Consistently computing the K -> pi long distance weak transition

First we extract the long-distance (LD) weak matrix element from certain data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale and then test the latter SQL scale against the decuplet weak decay amplitude ratio. Finally, we study LD decay. All of these experimental and theoretical values are in good agreement. We deduce an average value from eleven experimental determinations compared to the theoretical SQL values average.Comment: 19 pages, 9 figures minor change to the Conclusions and abstract sectio

Circumventing the axial anomalies and the strong CP problem

Many meson processes are related to the U_A(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.Comment: 13 pages, some typos corrected, published in Prof. D. Tadic's memorial issue of Fizika B, expanded version of hep-ph/051212

Constituent and current quark masses at low chiral energies

Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the Quark-Level Linear $\sigma$ Model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses which reproduce the experimental pion and kaon masses very accurately, by simple additivity. Moreover, the masses of the light scalar mesons $\sigma(600)$ and $\kappa(800)$ can be obtained straightforwardly from the constituent quark masses. In contrast, the usual nonstrange and strange current quark masses employed by Chiral Perturbation Theory do not allow a simple quantitative explanation of the pion and kaon masses.Comment: 5 pages, EPL style, accepted for publication in Europhys. Let