Σ(770) Resonance and the Breaking of Scale and Chiral Symmetry in Effective Qcd

CERN measurements of πp → ππn on polarized target at 17.2 GeV/c enable experimental determination of partial wave production amplitudes below 1080 MeV. The measured S-wave transversity amplitudes provide evidence for a narrow scalar resonance σ(770). The assumption of analyticity of production amplitudes in dipion mass allows to determine S-wave helicity amplitudes S0 and S1. The helicity flip amplitude S1 is related to π π → ππ scattering. There are four ”down” solutions (1, 1), (2, 1), (1, 2) and (2, 2) selected by the unitarity in ππ → ππ scattering. Ellis-Lanik relation between the mass mσ and partial width Γ(σ → ππ) derived from an effective QCD theory with broken scale and chiral symmetry selects solutions (1, 1) and (1, 2) and imparts the σ(770) resonance with a dilaton gluonium interpretation. Weinberg’s mended symmetry selects solutions (1, 1) and (2, 1). The combined solution (1, 1) has mσ = 769 ± 13 MeV and Γσ = 154 ± 22 MeV. The observed σ − ρ degeneracy leads to new relations between gluon condensate and pion decay constant and SU(2) chiral condensate. The two relations are well satisfied. Ellis-Lanik relation relates the existence of σ(770) to breaking of scale symmetry in QCD. Interaction of chirally invariant and narrow σ(770) with chirally noninvariant QCD vacuum in ππ → ππ scattering is proposed as a possible mechanism for the metamorphosis of σ(770) into a broad resonant S-wave structure in ππ → ππ related to spontaneous breaking of chiral symmetry in QCD. We comment on possible connections of σ(770) to cosmological contstant and QCD/String duality in AdS/CFT brane