Abstract
We explore the interplay between the few-body aspects of few-pion states and the many-body aspects of their quark structure. We show for a schematic quasispin model similar to the Nambu–Jona-Lasinio model how one can derive rather accurately the pion–pion scattering length from the excitation spectrum in a box.
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Bernard V., Blin A.H., Hiller B., Meissner U-G., Ruivo M.C.: Strong and radiative meson decays in a generalized Nambu–Jona-Lasinio model. Phys. Lett. B 305, 163 (1993) also hep-ph/9302245
Kalinovski, Yu. L., Volkov, M. K.: Two photon decays of scalar mesons in the quark NJL model, hep-ph/08091795
Bernard V., Blin A.H., Hiller B., Ivanov Yu.P., Osipov A.A., Meissner U-G.: Pion observables in the extended NJL model with vector and axial-vector mesons. Annals Phys. 249, 499 (1996) and references therein; also hep-ph/9506309
Lüscher M.: Commun. Math. Phys. 104, 177 (1986)
Lüscher M.: Commun. Math. Phys. 105, 153 (1986)
Lüscher M.: Two-particle states on a torus and their relation to the scattering matrix. Nucl. Phys. B354, 531 (1991)
da Providência J., Ruivo M. C., de Sousa C. A.: Time-dependent Hartree-Fock Formalism and the excitations of the Dirac sea in the Nambu–Jona-Lasinio model. Phys. Rev. D 36, 1882 (1987)
Moszkowski S. A.: Connection between the nuclear shell model and the unified model. Phys. Rev. 110, 403 (1958)
Lerma S., Jesgarz H. S., Hess P. O., Civitarese O., Reboiro M.: Schematic model for QCD. I. Low energy meson states. Phys. Rev. C 67, 055209 (2003)
Oblak, B. T., Rosina, M.: The two-level Nambu–Jona-Lasinio model. Bled Workshops in Physics 7(1), 92 (2006); also available at http://www-f1.ijs.si/BledPub
Oblak, B. T., Rosina, M.: Sigma meson in a two-level Nambu–Jona-Lasinio model. Bled Workshops in Physics 8(1), 66 (2007); also available at http://www-f1.ijs.si/BledPub
Oblak, B. T., Rosina, M.: Imitating continuum in lattice models. Bled Workshops in Physics 9(1), 98 (2008); also available at http://www-f1.ijs.si/BledPub
Fiolhais M., da Providência J., Rosina M., de Sousa C. A.: Soliton formation in σ models. Phys. Rev. C 56, 3311 (1997)
Buballa M.: NJL-model analysis of dense quark matter. Phys. Reports 407, 205 (2005)
Kaminski R., Lesniak L., Loiseau B.: Amplitudes fitted to experimental data and to Roy’s equations. Int. J. Mod. Phys. A 20, 693 (2005) and references therein, also hep-ph/0407338; hep-ph 0510218
Lipkin H.J., Meshkov N., Glick A.J.: Nucl. Phys. 62, 188 (1965)
Meshkov N., Glick A.J., Lipkin H.J.: Nucl. Phys. 62, 199 (1965)
Glick A.J., Lipkin H.J., Meshkov N.: Nucl. Phys. 62, 211 (1965)
Agassi D., Lipkin H.J., Meshkov N.: Nucl. Phys. 86, 321 (1966)
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Dedicated to celebrate the 60th birthday of Willibald Plessas.
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Rosina, M., Oblak, B.T. Pion–Pion Interaction in a Soluble Two-Level Nambu–Jona-Lasinio Model. Few-Body Syst 47, 117–123 (2010). https://doi.org/10.1007/s00601-009-0074-z
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DOI: https://doi.org/10.1007/s00601-009-0074-z