| Research Abstract |
In the framework of this project, the following research was performed during Apr.1995 to March 1998 :
1) The relativistic Faddeev equation was solved in the Nambu-Jona-Lasinio model, and an effective 4-Fermi quark interaction lagrangian, which can simultaneously reproduce the masses of the pion, the nucleon and the delta, was derived. Using the solution of the Faddeev equation, the electromagnetic properties of the nucleon were investigated. An important feature of these calculations is that the Lorentz boost effect on the nucleon wave function is properly taken into account. In these calculations, which include only the scalar diquark channel, quantities like the axial vector coupling constant or the charge radii of the nucleon are properly reproduced, but the description of the magnetic moments requires further the inclusion of the acial vector diquark channel.
2) Mesonic degrees of freedom were included in the Faddeev framework. By taking into account the effect of composite pion exc
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hange between quarks in first order perturbation theory, the contribution to the mass of the nucleon was assessed. Since this contribution turned out to be large, the perturbation theory was improved so as to include a part of the ladder-type correlations due to pion exchange. As a result, it was found that the pion exchange between quarks leads to a down-shift of the nucleon mass by about 200 Mev.
3) In order to apply the Faddeev method to the structure function of the nucleon, the quantization of the Nambu-Jona-Lasinio model on the light cone was formulated. The quark-antiquark light cone wave function, and from this the structure function of the pion, were calculated, However, due to the regularization procedure, the equivalence to the usual equal time theory does not hold exactly, and this point requires further theoretical considerations.
4) The theoretical framework for calculating the equation of state of nuclear matter in the mean field approximation, with the structure of a single nucleon described by the Faddeev equation as explained above, was formulated. The numerical calculation of the equation of state is now in progress. Using these results, we plan to calculate the structure function of a nucleon in nuclear matter (EMC effect). Less
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