Low energy scattering with a nontrivial pion

Abstract

An earlier calculation in a generalized linear sigma model showed that the well-known current algebra formula for low energy pion pion scattering held even though the massless Nambu Goldstone pion contained a small admixture of a two-quark two-antiquark field. Here we turn on the pion mass and note that the current algebra formula no longer holds exactly. We discuss this small deviation and also study the effects of an SU(3) symmetric quark mass type term on the masses and mixings of the eight SU(3) multiplets in the model. We calculate the s wave scattering lengths, including the beyond current algebra theorem corrections due to the scalar mesons, and observe that the model can fit the data well. In the process, we uncover the way in which linear sigma models give controlled corrections (due to the presence of scalar mesons) to the current algebra scattering formula. Such a feature is commonly thought to exist only in the non-linear sigma model approach.

15 pages, 8 figures

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• Chiral Nonet Mixing in ${\eta }^{\prime }\to \eta \pi \pi$ Decay
• Semi-leptonic $D_s^{+}$(1968) decays as a scalar meson probe
• Are three flavors special?
• Probing the substructure of $f_0(1370)$
• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Remark on pion scattering lengths
• Generalized linear sigma model with two glueballs
• Mixing among lowest-lying scalar mesons and scalar glueball
• Chiral Nonet Mixing in $\pi K$ Scattering
• Probing scalar mesons in semi-leptonic decays of $D_s^{+}$, $D^{+}$ and $D^0$
• Electromagnetic trace anomaly in a generalized linear sigma model
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
• Exploration of a physical picture for the QCD scalar channel
• Decay widths of resonances and pion scattering lengths in a globally invariant linear sigma model with vector mesons
• Two-body decay widths of lowest lying and next-to-lowest lying scalar and pseudoscalar mesons in generalized linear sigma model
• Structure of Scalar Mesons f(0)(600), a(0)(980), f(0)(1370) and a(0)(1450)