Ipno/th 94-26 Chiral Symmetry Aspects of the Scalars

Electromagnetic decays of the scalar mesons are shown to be constrained by chiral symmetry as a consequence of the fact that, in the chiral limit, the two and threepoint functions< SS−PP > and< V V S > satisfy super-convergent dispersion relations. The QCD asymptotic behavior of the latter is canonical and it can be saturated by a finite number of resonances. The corresponding chiral lagrangian for vector and scalar resonances is constructed. Matching to the correct asymptotic structure generates non-minimal terms which have so far been ignored. It is found that the width a0(980) → 2γ can be naturally reproduced suggesting that the a0(980) is not an exotic particle. 1Introduction: The chiral symmetry limit of QCD, which is expected to be a reasonably good approximation in the light quark sector, may be at the origin of some of the surprising ( at first sight) properties that the scalar mesons seem to have. We will concentrate here on the question of the two photon width of the a0(980) (since this is a gammagamma meeting) and it will be shown that the fact that this width is anomalously small (as compared, for instance, with the expectation from the naive quark model) has a natural explanation in this limit, and is by no means incompatible with a standard nonet status for the a0. Our starting point is to assume exact chiral symmetry (i.e. we set mu = md = ms = 0 in the lagrangian) and , furthermore, we will work in the leading Nc approximation. In these limits, QCD still cannot be solved in closed form, but analytic approximation methods, at least, are available. The one that we will use is similar to the boundary-layer technique used, for instance, in hydrodynamics and consists in matching three asymptotic expansions for a given correlation function: a) For large momenta, the operator product expansion (OPE) generates an expansion in inverse powers of the momenta b)for small or moderate momenta the correlation function is dominated by the contributions from the light resonances and c)at very low momenta the expansion is generated by chiral perturbation theory (χpt ). The method is effective only for those n-point functions which transform in a non trivial way under the chiral group and thereby satisfy super-convergent dispersion relations. Only in that case is it possible to match the QCD asymptotic behavior with a finite Talk given at the workshop ”Two-photon physics from DAΦNE to LEP200 and beyond”, Paris 2-4 Feb. 1994 Unité de Recherche des Universités Paris 11 et Paris 6 associée au CNRS