Aspects of UAÂ (1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced 't Hooft interaction, which breaks the unwanted UA (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the UL (3) × UR (3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the “two-loop” approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.