Low energy scattering with a nontrivial pion

Details Low energy scattering with a nontrivial pion Low energy scattering with a nontrivial pion

2007-08-24

arxiv.org/abs/0708.3402v1

Phys.Rev.D76:114001,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, 8 figures

Scientific paper

10.1103/PhysRevD.76.114001

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.

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