Scalar meson masses and mixing angle in a U(3)XU(3) Linear Sigma Model

Abstract

Meson properties are considered within a U(3)\times U(3) Linear Sigma Model(LSM). The importance of the U_A(1)-breaking term and the OZI rule violating term in the generation of meson masses and mixing angles is stressed. The LSM parameters are fitted to the pseudoscalar meson spectrum thus giving predictions for scalar meson properties. The model predicts a scalar meson nonet whose members are: {σ(\approx 400), f_0(980), κ(\approx 900) and a_0(980)} resonances. Scalar meson mixing angle (in the {|ns>, |s>} basis) is predicted to be ϕ_S\approx -14^\circ. Therefore the f_0(980) is predominantly strange while the σ(\approx 400) is mostly non-strange. The model also gives a pseudoscalar mixing angle ϕ_P\approx 35^\circ which corresponds to θ_P \approx -19^\circ in the singlet-octet basis. Comparison with chiral perturbation theory shows that L_8 is saturated by scalar mesons exchange. However, LSM predicts that L_5 is not saturated by scalar mesons exchange as assumed in the literature.

arXiv comment24 pages, 3 figures. Scalar mesons exchange contributions to CHPT LEC included. New mixing angle and mass relations added. Scalar meson mixing angle and sigma mass corrected. 1/N counting rules for OZI violating terms reconsidered. New references added

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