On the low energy end of the QCD spectrum

Abstract

The experimental results on the Ke4 and K3π decays, those on pionic atoms and recent work on the lattice confirm the predictions obtained on the basis of χPT. As a result, the energy gap of QCD is now understood very well and there is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of ms, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the OkuboIizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. In view of the remarkable progress being made with the numerical simulation of light quarks, I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on ms can reliably be determined, to next-to-next-toleading order of the chiral expansion.The range of validity of χPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KK threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances. The application to the ππ partial wave amplitude with I = ℓ = 0 shows that there is a resonance in this channel, at Mσ − i 2 Γσ ≃ 441 − i 272 MeV: the lowest resonance of QCD carries the quantum numbers of the vacuum.Talks given at QCD08,

Hidden Local Field Theory and Dileptons in Relativistic Heavy Ion Collisions

“…where the ellipsis stands for higher derivative and quark mass terms. At energies much less than the vector-meson excitation m V ∼ 800 MeV, when treated in a systematic expansion, this represents QCD [6]. The validity of this theory is however highly limited to low energy, so if one wants to study the vector mesons whose masses are much higher than that of the pion, chiral perturbation theory with pions alone loses its power.…”