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Sigma(770) Resonance and the Breaking of Scale and Chiral Symmetry in Effective QCD

M. Svec
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Abstract

CERN measurements of pi(-)p->pi(-)pi(+)n 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 sigma(770). The assumption of analyticity of production amplitudes in dipion mass allows to determine S-wave helicity amplitudes S_0 and S_1. The amplitude S_1 is related to pi(-)pi(+)->pi(-)pi(+) scattering. There are four "down" solutions (1, 1bar), (2, 1bar), (1, 2bar) and (2, 2bar) selected by unitarity in pipi scattering. Ellis-Lanik relation between the mass m_sigma and partial width Gamma(sigma->pi(-)pi(+)) derived from an effective QCD theory with broken scale and chiral symmetry selects solutions (1, 1bar) and (1, 2bar) and imparts the sigma(770) resonance with a dilaton-gluonium interpretation. Weinberg's mended symmetry selects solutions (1, 1bar) and (2, 1bar). The combin ed solution (1, 1bar) has m_sigma=769 +/- 13 MeV and Gamma_sigma=154 +/- 22 MeV. The observed sigma-rho^0 degeneracy leads to two new relations between gluon condensate and pion decay constant and SU(2) chiral condensate. Both relations are well satisfied. Ellis-Lanik relation relates the existence of sigma(770) to breaking of scale symmetry in QCD. Interaction of chirally invariant and narrow sigma(770) with a chirally noninvariant QCD vacuum in pi(-)pi(+)->pi(-)pi(+) scattering is proposed as a possible mechanism for the metamorphosis of sigma(770) into a broad resonant S-wave structure in pi(-)pi(+)->pi(-)pi(+) related to spontaneous breaking of chiral symmetry in QCD.

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M. Svec. 2002-10-18. Sigma(770) Resonance and the Breaking of Scale and Chiral Symmetry in Effective QCD. https://arxiv.org/abs/hep-ph/0209323

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