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

Mar, 2006
13 pages
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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