pi pi scattering in a nonlocal Nambu-Jona-Lasinio model
Mar, 2006Citations per year
Abstract:
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.- pi pi: scattering amplitude
- quark: four-fermion interaction
- Jona-Lasinio-Nambu model: nonlocal
- symmetry: SU(2) x SU(2)
- pi: mass
- pi: decay constant
- quark: mass
- partial wave: scattering length
- PCAC model
- pi: decay
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