pi pi scattering in a nonlocal Nambu -- Jona-Lasinio model

Details pi pi scattering in a nonlocal Nambu -- Jona-Lasinio model pi pi scattering in a nonlocal Nambu -- Jona-Lasinio model

2006-03-17

arxiv.org/abs/hep-ph/0603130v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, 2 figures

Scientific paper

We consider a nonlocal version of the Nambu and Jona-Lasinio model. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favour of the values of the pion mass, the pion decay constant f_pi, and the current quark mass. The pi pi scattering amplitude is obtained by calculating the quark box and the sigma-pole diagrams, where sigma is the scalar isoscalar meson. It is shown that this amplitude satisfies the well-known Weinberg relation. We obtain the s, p, d wave scattering lengths in all isotopic channels and the s wave slope parameters. The results are in satisfactory agreement with both phenomenological data and the basic requirements of low-energy theorems, thus supporting to the form factor used.

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